# Question 24219: One Convolution Degree Is Not the Whole Exponential Addition Proof [Return to catalogue page 122](https://ocme.evemisslab.com/en/questions/page/122/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261015-advance-20261113-r02-real-exponential-function-foundations/#q-20261015-advance-20261113-r02-real-exponential-function-0069) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0047-24219 · q-20261015-advance-20261113-r02-real-exponential-function-0069 ## Original question and givens Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=19/20, y=-20/21, declared degree=18. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate). - G001 — Use the whole real series E(x)=sum over n≥0 of x^n/n!, with power-series coefficients1/n!. A finite sum is a separate object; whole-series identities require the declared convergence and rearrangement obligations. Use x=19/20, y=-20/21, declared degree=18. Give (x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate). ## Definition and scope Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate. - [mko-real-exponential-function](https://ocme.evemisslab.com/en/mko/mko-real-exponential-function/) ## Step-by-step derivation S001 · impliesBefore source roles = [exp-addition-convolution] After derived = [[x, y, degree, coefficient_terms, convolution_coefficient, sum_argument_coefficient, equal, certificate]] Conditions: none List the source field order without JavaScript.Gradient boundary uses its original mode to choose6,8 or7 fields;no padding or answer-derived mode. Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001 S002 · impliesBefore (19/20)^0 After Exp convolution x power0 = 1 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S001 S003 · impliesBefore (-20/21)^18 After Exp convolution y power18 = 262144000000000000000000/630880792396715529789561 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S002 S004 · calculationBefore Exp convolution numerator0 := mul(1, 262144000000000000000000/630880792396715529789561) After Exp convolution numerator0 = 262144000000000000000000/630880792396715529789561 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003 S005 · impliesBefore source roles = [0] After derived = [1] Conditions: none The empty product0! is1,not0. Step identifiers and dependenciesRule: empty_factorial_is_multiplicative_unit · Uses: G001, S004 S006 · calculationBefore Exp convolution right0 factorial step1 := mul(1, 1) After Exp convolution right0 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S005 S007 · calculationBefore Exp convolution right0 factorial step2 := mul(1, 2) After Exp convolution right0 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S006 S008 · calculationBefore Exp convolution right0 factorial step3 := mul(2, 3) After Exp convolution right0 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S007 S009 · calculationBefore Exp convolution right0 factorial step4 := mul(6, 4) After Exp convolution right0 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S008 S010 · calculationBefore Exp convolution right0 factorial step5 := mul(24, 5) After Exp convolution right0 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S009 S011 · calculationBefore Exp convolution right0 factorial step6 := mul(120, 6) After Exp convolution right0 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S010 S012 · calculationBefore Exp convolution right0 factorial step7 := mul(720, 7) After Exp convolution right0 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S011 S013 · calculationBefore Exp convolution right0 factorial step8 := mul(5040, 8) After Exp convolution right0 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S012 S014 · calculationBefore Exp convolution right0 factorial step9 := mul(40320, 9) After Exp convolution right0 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S013 S015 · calculationBefore Exp convolution right0 factorial step10 := mul(362880, 10) After Exp convolution right0 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S014 S016 · calculationBefore Exp convolution right0 factorial step11 := mul(3628800, 11) After Exp convolution right0 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S015 S017 · calculationBefore Exp convolution right0 factorial step12 := mul(39916800, 12) After Exp convolution right0 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S016 S018 · calculationBefore Exp convolution right0 factorial step13 := mul(479001600, 13) After Exp convolution right0 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S017 S019 · calculationBefore Exp convolution right0 factorial step14 := mul(6227020800, 14) After Exp convolution right0 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S018 S020 · calculationBefore Exp convolution right0 factorial step15 := mul(87178291200, 15) After Exp convolution right0 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S019 S021 · calculationBefore Exp convolution right0 factorial step16 := mul(1307674368000, 16) After Exp convolution right0 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S020 S022 · calculationBefore Exp convolution right0 factorial step17 := mul(20922789888000, 17) After Exp convolution right0 factorial step17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S021 S023 · calculationBefore Exp convolution right0 factorial step18 := mul(355687428096000, 18) After Exp convolution right0 factorial step18 = 6402373705728000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S022 S024 · calculationBefore Exp convolution denominator0 := mul(1, 6402373705728000) After Exp convolution denominator0 = 6402373705728000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S023 S025 · calculationBefore Exp convolution coefficient term0 := div(262144000000000000000000/630880792396715529789561, 6402373705728000) After Exp convolution coefficient term0 = 32000000000000000/493058422447458087543290824655799 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S024 S026 · impliesBefore (19/20)^1 After Exp convolution x power1 = 19/20 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S025 S027 · impliesBefore (-20/21)^17 After Exp convolution y power17 = -13107200000000000000000/30041942495081691894741 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S026 S028 · calculationBefore Exp convolution numerator1 := mul(19/20, -13107200000000000000000/30041942495081691894741) After Exp convolution numerator1 = -12451840000000000000000/30041942495081691894741 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S027 S029 · calculationBefore Exp convolution left1 factorial step1 := mul(1, 1) After Exp convolution left1 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S028 S030 · calculationBefore Exp convolution right1 factorial step1 := mul(1, 1) After Exp convolution right1 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S029 S031 · calculationBefore Exp convolution right1 factorial step2 := mul(1, 2) After Exp convolution right1 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S030 S032 · calculationBefore Exp convolution right1 factorial step3 := mul(2, 3) After Exp convolution right1 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S031 S033 · calculationBefore Exp convolution right1 factorial step4 := mul(6, 4) After Exp convolution right1 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S032 S034 · calculationBefore Exp convolution right1 factorial step5 := mul(24, 5) After Exp convolution right1 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S033 S035 · calculationBefore Exp convolution right1 factorial step6 := mul(120, 6) After Exp convolution right1 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S034 S036 · calculationBefore Exp convolution right1 factorial step7 := mul(720, 7) After Exp convolution right1 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S035 S037 · calculationBefore Exp convolution right1 factorial step8 := mul(5040, 8) After Exp convolution right1 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S036 S038 · calculationBefore Exp convolution right1 factorial step9 := mul(40320, 9) After Exp convolution right1 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S037 S039 · calculationBefore Exp convolution right1 factorial step10 := mul(362880, 10) After Exp convolution right1 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S038 S040 · calculationBefore Exp convolution right1 factorial step11 := mul(3628800, 11) After Exp convolution right1 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S039 S041 · calculationBefore Exp convolution right1 factorial step12 := mul(39916800, 12) After Exp convolution right1 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S040 S042 · calculationBefore Exp convolution right1 factorial step13 := mul(479001600, 13) After Exp convolution right1 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S041 S043 · calculationBefore Exp convolution right1 factorial step14 := mul(6227020800, 14) After Exp convolution right1 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S042 S044 · calculationBefore Exp convolution right1 factorial step15 := mul(87178291200, 15) After Exp convolution right1 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S043 S045 · calculationBefore Exp convolution right1 factorial step16 := mul(1307674368000, 16) After Exp convolution right1 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S044 S046 · calculationBefore Exp convolution right1 factorial step17 := mul(20922789888000, 17) After Exp convolution right1 factorial step17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S045 S047 · calculationBefore Exp convolution denominator1 := mul(1, 355687428096000) After Exp convolution denominator1 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S046 S048 · calculationBefore Exp convolution coefficient term1 := div(-12451840000000000000000/30041942495081691894741, 355687428096000) After Exp convolution coefficient term1 = -3040000000000000/2608774721944222685414237167491 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S047 S049 · impliesBefore (19/20)^2 After Exp convolution x power2 = 361/400 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S048 S050 · impliesBefore (-20/21)^16 After Exp convolution y power16 = 655360000000000000000/1430568690241985328321 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S049 S051 · calculationBefore Exp convolution numerator2 := mul(361/400, 655360000000000000000/1430568690241985328321) After Exp convolution numerator2 = 591462400000000000000/1430568690241985328321 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S050 S052 · calculationBefore Exp convolution left2 factorial step1 := mul(1, 1) After Exp convolution left2 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S051 S053 · calculationBefore Exp convolution left2 factorial step2 := mul(1, 2) After Exp convolution left2 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S052 S054 · calculationBefore Exp convolution right2 factorial step1 := mul(1, 1) After Exp convolution right2 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S053 S055 · calculationBefore Exp convolution right2 factorial step2 := mul(1, 2) After Exp convolution right2 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S054 S056 · calculationBefore Exp convolution right2 factorial step3 := mul(2, 3) After Exp convolution right2 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S055 S057 · calculationBefore Exp convolution right2 factorial step4 := mul(6, 4) After Exp convolution right2 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S056 S058 · calculationBefore Exp convolution right2 factorial step5 := mul(24, 5) After Exp convolution right2 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S057 S059 · calculationBefore Exp convolution right2 factorial step6 := mul(120, 6) After Exp convolution right2 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S058 S060 · calculationBefore Exp convolution right2 factorial step7 := mul(720, 7) After Exp convolution right2 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S059 S061 · calculationBefore Exp convolution right2 factorial step8 := mul(5040, 8) After Exp convolution right2 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S060 S062 · calculationBefore Exp convolution right2 factorial step9 := mul(40320, 9) After Exp convolution right2 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S061 S063 · calculationBefore Exp convolution right2 factorial step10 := mul(362880, 10) After Exp convolution right2 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S062 S064 · calculationBefore Exp convolution right2 factorial step11 := mul(3628800, 11) After Exp convolution right2 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S063 S065 · calculationBefore Exp convolution right2 factorial step12 := mul(39916800, 12) After Exp convolution right2 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S064 S066 · calculationBefore Exp convolution right2 factorial step13 := mul(479001600, 13) After Exp convolution right2 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S065 S067 · calculationBefore Exp convolution right2 factorial step14 := mul(6227020800, 14) After Exp convolution right2 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S066 S068 · calculationBefore Exp convolution right2 factorial step15 := mul(87178291200, 15) After Exp convolution right2 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S067 S069 · calculationBefore Exp convolution right2 factorial step16 := mul(1307674368000, 16) After Exp convolution right2 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S068 S070 · calculationBefore Exp convolution denominator2 := mul(2, 20922789888000) After Exp convolution denominator2 = 41845579776000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S069 S071 · calculationBefore Exp convolution coefficient term2 := div(591462400000000000000/1430568690241985328321, 41845579776000) After Exp convolution coefficient term2 = 72200000000000/7307492218331155981552485063 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S070 S072 · impliesBefore (19/20)^3 After Exp convolution x power3 = 6859/8000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S071 S073 · impliesBefore (-20/21)^15 After Exp convolution y power15 = -32768000000000000000/68122318582951682301 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S072 S074 · calculationBefore Exp convolution numerator3 := mul(6859/8000, -32768000000000000000/68122318582951682301) After Exp convolution numerator3 = -28094464000000000000/68122318582951682301 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S073 S075 · calculationBefore Exp convolution left3 factorial step1 := mul(1, 1) After Exp convolution left3 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S074 S076 · calculationBefore Exp convolution left3 factorial step2 := mul(1, 2) After Exp convolution left3 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S075 S077 · calculationBefore Exp convolution left3 factorial step3 := mul(2, 3) After Exp convolution left3 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S076 S078 · calculationBefore Exp convolution right3 factorial step1 := mul(1, 1) After Exp convolution right3 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S077 S079 · calculationBefore Exp convolution right3 factorial step2 := mul(1, 2) After Exp convolution right3 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S078 S080 · calculationBefore Exp convolution right3 factorial step3 := mul(2, 3) After Exp convolution right3 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S079 S081 · calculationBefore Exp convolution right3 factorial step4 := mul(6, 4) After Exp convolution right3 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S080 S082 · calculationBefore Exp convolution right3 factorial step5 := mul(24, 5) After Exp convolution right3 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S081 S083 · calculationBefore Exp convolution right3 factorial step6 := mul(120, 6) After Exp convolution right3 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S082 S084 · calculationBefore Exp convolution right3 factorial step7 := mul(720, 7) After Exp convolution right3 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S083 S085 · calculationBefore Exp convolution right3 factorial step8 := mul(5040, 8) After Exp convolution right3 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S084 S086 · calculationBefore Exp convolution right3 factorial step9 := mul(40320, 9) After Exp convolution right3 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S085 S087 · calculationBefore Exp convolution right3 factorial step10 := mul(362880, 10) After Exp convolution right3 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S086 S088 · calculationBefore Exp convolution right3 factorial step11 := mul(3628800, 11) After Exp convolution right3 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S087 S089 · calculationBefore Exp convolution right3 factorial step12 := mul(39916800, 12) After Exp convolution right3 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S088 S090 · calculationBefore Exp convolution right3 factorial step13 := mul(479001600, 13) After Exp convolution right3 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S089 S091 · calculationBefore Exp convolution right3 factorial step14 := mul(6227020800, 14) After Exp convolution right3 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S090 S092 · calculationBefore Exp convolution right3 factorial step15 := mul(87178291200, 15) After Exp convolution right3 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S091 S093 · calculationBefore Exp convolution denominator3 := mul(6, 1307674368000) After Exp convolution denominator3 = 7846046208000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S092 S094 · calculationBefore Exp convolution coefficient term3 := div(-28094464000000000000/68122318582951682301, 7846046208000) After Exp convolution coefficient term3 = -54872000000000/1043927459761593711650355009 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S093 S095 · impliesBefore (19/20)^4 After Exp convolution x power4 = 130321/160000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S094 S096 · impliesBefore (-20/21)^14 After Exp convolution y power14 = 1638400000000000000/3243919932521508681 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S095 S097 · calculationBefore Exp convolution numerator4 := mul(130321/160000, 1638400000000000000/3243919932521508681) After Exp convolution numerator4 = 1334487040000000000/3243919932521508681 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S096 S098 · calculationBefore Exp convolution left4 factorial step1 := mul(1, 1) After Exp convolution left4 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S097 S099 · calculationBefore Exp convolution left4 factorial step2 := mul(1, 2) After Exp convolution left4 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S098 S100 · calculationBefore Exp convolution left4 factorial step3 := mul(2, 3) After Exp convolution left4 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S099 S101 · calculationBefore Exp convolution left4 factorial step4 := mul(6, 4) After Exp convolution left4 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S100 S102 · calculationBefore Exp convolution right4 factorial step1 := mul(1, 1) After Exp convolution right4 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S101 S103 · calculationBefore Exp convolution right4 factorial step2 := mul(1, 2) After Exp convolution right4 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S102 S104 · calculationBefore Exp convolution right4 factorial step3 := mul(2, 3) After Exp convolution right4 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S103 S105 · calculationBefore Exp convolution right4 factorial step4 := mul(6, 4) After Exp convolution right4 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S104 S106 · calculationBefore Exp convolution right4 factorial step5 := mul(24, 5) After Exp convolution right4 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S105 S107 · calculationBefore Exp convolution right4 factorial step6 := mul(120, 6) After Exp convolution right4 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S106 S108 · calculationBefore Exp convolution right4 factorial step7 := mul(720, 7) After Exp convolution right4 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S107 S109 · calculationBefore Exp convolution right4 factorial step8 := mul(5040, 8) After Exp convolution right4 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S108 S110 · calculationBefore Exp convolution right4 factorial step9 := mul(40320, 9) After Exp convolution right4 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S109 S111 · calculationBefore Exp convolution right4 factorial step10 := mul(362880, 10) After Exp convolution right4 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S110 S112 · calculationBefore Exp convolution right4 factorial step11 := mul(3628800, 11) After Exp convolution right4 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S111 S113 · calculationBefore Exp convolution right4 factorial step12 := mul(39916800, 12) After Exp convolution right4 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S112 S114 · calculationBefore Exp convolution right4 factorial step13 := mul(479001600, 13) After Exp convolution right4 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S113 S115 · calculationBefore Exp convolution right4 factorial step14 := mul(6227020800, 14) After Exp convolution right4 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S114 S116 · calculationBefore Exp convolution denominator4 := mul(24, 87178291200) After Exp convolution denominator4 = 2092278988800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S115 S117 · calculationBefore Exp convolution coefficient term4 := div(1334487040000000000/3243919932521508681, 2092278988800) After Exp convolution coefficient term4 = 3258025000000/16570277139072916057942143 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S116 S118 · impliesBefore (19/20)^5 After Exp convolution x power5 = 2476099/3200000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S117 S119 · impliesBefore (-20/21)^13 After Exp convolution y power13 = -81920000000000000/154472377739119461 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S118 S120 · calculationBefore Exp convolution numerator5 := mul(2476099/3200000, -81920000000000000/154472377739119461) After Exp convolution numerator5 = -63388134400000000/154472377739119461 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S119 S121 · calculationBefore Exp convolution left5 factorial step1 := mul(1, 1) After Exp convolution left5 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S120 S122 · calculationBefore Exp convolution left5 factorial step2 := mul(1, 2) After Exp convolution left5 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S121 S123 · calculationBefore Exp convolution left5 factorial step3 := mul(2, 3) After Exp convolution left5 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S122 S124 · calculationBefore Exp convolution left5 factorial step4 := mul(6, 4) After Exp convolution left5 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S123 S125 · calculationBefore Exp convolution left5 factorial step5 := mul(24, 5) After Exp convolution left5 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S124 S126 · calculationBefore Exp convolution right5 factorial step1 := mul(1, 1) After Exp convolution right5 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S125 S127 · calculationBefore Exp convolution right5 factorial step2 := mul(1, 2) After Exp convolution right5 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S126 S128 · calculationBefore Exp convolution right5 factorial step3 := mul(2, 3) After Exp convolution right5 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S127 S129 · calculationBefore Exp convolution right5 factorial step4 := mul(6, 4) After Exp convolution right5 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S128 S130 · calculationBefore Exp convolution right5 factorial step5 := mul(24, 5) After Exp convolution right5 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S129 S131 · calculationBefore Exp convolution right5 factorial step6 := mul(120, 6) After Exp convolution right5 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S130 S132 · calculationBefore Exp convolution right5 factorial step7 := mul(720, 7) After Exp convolution right5 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S131 S133 · calculationBefore Exp convolution right5 factorial step8 := mul(5040, 8) After Exp convolution right5 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S132 S134 · calculationBefore Exp convolution right5 factorial step9 := mul(40320, 9) After Exp convolution right5 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S133 S135 · calculationBefore Exp convolution right5 factorial step10 := mul(362880, 10) After Exp convolution right5 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S134 S136 · calculationBefore Exp convolution right5 factorial step11 := mul(3628800, 11) After Exp convolution right5 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S135 S137 · calculationBefore Exp convolution right5 factorial step12 := mul(39916800, 12) After Exp convolution right5 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S136 S138 · calculationBefore Exp convolution right5 factorial step13 := mul(479001600, 13) After Exp convolution right5 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S137 S139 · calculationBefore Exp convolution denominator5 := mul(120, 6227020800) After Exp convolution denominator5 = 747242496000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S138 S140 · calculationBefore Exp convolution coefficient term5 := div(-63388134400000000/154472377739119461, 747242496000) After Exp convolution coefficient term5 = -61902475000/112722973735189905156069 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S139 S141 · impliesBefore (19/20)^6 After Exp convolution x power6 = 47045881/64000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S140 S142 · impliesBefore (-20/21)^12 After Exp convolution y power12 = 4096000000000000/7355827511386641 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S141 S143 · calculationBefore Exp convolution numerator6 := mul(47045881/64000000, 4096000000000000/7355827511386641) After Exp convolution numerator6 = 3010936384000000/7355827511386641 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S142 S144 · calculationBefore Exp convolution left6 factorial step1 := mul(1, 1) After Exp convolution left6 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S143 S145 · calculationBefore Exp convolution left6 factorial step2 := mul(1, 2) After Exp convolution left6 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S144 S146 · calculationBefore Exp convolution left6 factorial step3 := mul(2, 3) After Exp convolution left6 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S145 S147 · calculationBefore Exp convolution left6 factorial step4 := mul(6, 4) After Exp convolution left6 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S146 S148 · calculationBefore Exp convolution left6 factorial step5 := mul(24, 5) After Exp convolution left6 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S147 S149 · calculationBefore Exp convolution left6 factorial step6 := mul(120, 6) After Exp convolution left6 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S148 S150 · calculationBefore Exp convolution right6 factorial step1 := mul(1, 1) After Exp convolution right6 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S149 S151 · calculationBefore Exp convolution right6 factorial step2 := mul(1, 2) After Exp convolution right6 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S150 S152 · calculationBefore Exp convolution right6 factorial step3 := mul(2, 3) After Exp convolution right6 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S151 S153 · calculationBefore Exp convolution right6 factorial step4 := mul(6, 4) After Exp convolution right6 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S152 S154 · calculationBefore Exp convolution right6 factorial step5 := mul(24, 5) After Exp convolution right6 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S153 S155 · calculationBefore Exp convolution right6 factorial step6 := mul(120, 6) After Exp convolution right6 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S154 S156 · calculationBefore Exp convolution right6 factorial step7 := mul(720, 7) After Exp convolution right6 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S155 S157 · calculationBefore Exp convolution right6 factorial step8 := mul(5040, 8) After Exp convolution right6 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S156 S158 · calculationBefore Exp convolution right6 factorial step9 := mul(40320, 9) After Exp convolution right6 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S157 S159 · calculationBefore Exp convolution right6 factorial step10 := mul(362880, 10) After Exp convolution right6 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S158 S160 · calculationBefore Exp convolution right6 factorial step11 := mul(3628800, 11) After Exp convolution right6 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S159 S161 · calculationBefore Exp convolution right6 factorial step12 := mul(39916800, 12) After Exp convolution right6 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S160 S162 · calculationBefore Exp convolution denominator6 := mul(720, 479001600) After Exp convolution denominator6 = 344881152000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S161 S163 · calculationBefore Exp convolution coefficient term6 := div(3010936384000000/7355827511386641, 344881152000) After Exp convolution coefficient term6 = 5880735125/4954855988359995831036 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S162 S164 · impliesBefore (19/20)^7 After Exp convolution x power7 = 893871739/1280000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S163 S165 · impliesBefore (-20/21)^11 After Exp convolution y power11 = -204800000000000/350277500542221 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S164 S166 · calculationBefore Exp convolution numerator7 := mul(893871739/1280000000, -204800000000000/350277500542221) After Exp convolution numerator7 = -143019478240000/350277500542221 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S165 S167 · calculationBefore Exp convolution left7 factorial step1 := mul(1, 1) After Exp convolution left7 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S166 S168 · calculationBefore Exp convolution left7 factorial step2 := mul(1, 2) After Exp convolution left7 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S167 S169 · calculationBefore Exp convolution left7 factorial step3 := mul(2, 3) After Exp convolution left7 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S168 S170 · calculationBefore Exp convolution left7 factorial step4 := mul(6, 4) After Exp convolution left7 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S169 S171 · calculationBefore Exp convolution left7 factorial step5 := mul(24, 5) After Exp convolution left7 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S170 S172 · calculationBefore Exp convolution left7 factorial step6 := mul(120, 6) After Exp convolution left7 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S171 S173 · calculationBefore Exp convolution left7 factorial step7 := mul(720, 7) After Exp convolution left7 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S172 S174 · calculationBefore Exp convolution right7 factorial step1 := mul(1, 1) After Exp convolution right7 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S173 S175 · calculationBefore Exp convolution right7 factorial step2 := mul(1, 2) After Exp convolution right7 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S174 S176 · calculationBefore Exp convolution right7 factorial step3 := mul(2, 3) After Exp convolution right7 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S175 S177 · calculationBefore Exp convolution right7 factorial step4 := mul(6, 4) After Exp convolution right7 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S176 S178 · calculationBefore Exp convolution right7 factorial step5 := mul(24, 5) After Exp convolution right7 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S177 S179 · calculationBefore Exp convolution right7 factorial step6 := mul(120, 6) After Exp convolution right7 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S178 S180 · calculationBefore Exp convolution right7 factorial step7 := mul(720, 7) After Exp convolution right7 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S179 S181 · calculationBefore Exp convolution right7 factorial step8 := mul(5040, 8) After Exp convolution right7 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S180 S182 · calculationBefore Exp convolution right7 factorial step9 := mul(40320, 9) After Exp convolution right7 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S181 S183 · calculationBefore Exp convolution right7 factorial step10 := mul(362880, 10) After Exp convolution right7 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S182 S184 · calculationBefore Exp convolution right7 factorial step11 := mul(3628800, 11) After Exp convolution right7 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S183 S185 · calculationBefore Exp convolution denominator7 := mul(5040, 39916800) After Exp convolution denominator7 = 201180672000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S184 S186 · calculationBefore Exp convolution coefficient term7 := div(-143019478240000/350277500542221, 201180672000) After Exp convolution coefficient term7 = -4469358695/2202158217048887036016 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S185 S187 · impliesBefore (19/20)^8 After Exp convolution x power8 = 16983563041/25600000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S186 S188 · impliesBefore (-20/21)^10 After Exp convolution y power10 = 10240000000000/16679880978201 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S187 S189 · calculationBefore Exp convolution numerator8 := mul(16983563041/25600000000, 10240000000000/16679880978201) After Exp convolution numerator8 = 6793425216400/16679880978201 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S188 S190 · calculationBefore Exp convolution left8 factorial step1 := mul(1, 1) After Exp convolution left8 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S189 S191 · calculationBefore Exp convolution left8 factorial step2 := mul(1, 2) After Exp convolution left8 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S190 S192 · calculationBefore Exp convolution left8 factorial step3 := mul(2, 3) After Exp convolution left8 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S191 S193 · calculationBefore Exp convolution left8 factorial step4 := mul(6, 4) After Exp convolution left8 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S192 S194 · calculationBefore Exp convolution left8 factorial step5 := mul(24, 5) After Exp convolution left8 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S193 S195 · calculationBefore Exp convolution left8 factorial step6 := mul(120, 6) After Exp convolution left8 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S194 S196 · calculationBefore Exp convolution left8 factorial step7 := mul(720, 7) After Exp convolution left8 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S195 S197 · calculationBefore Exp convolution left8 factorial step8 := mul(5040, 8) After Exp convolution left8 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S196 S198 · calculationBefore Exp convolution right8 factorial step1 := mul(1, 1) After Exp convolution right8 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S197 S199 · calculationBefore Exp convolution right8 factorial step2 := mul(1, 2) After Exp convolution right8 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S198 S200 · calculationBefore Exp convolution right8 factorial step3 := mul(2, 3) After Exp convolution right8 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S199 S201 · calculationBefore Exp convolution right8 factorial step4 := mul(6, 4) After Exp convolution right8 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S200 S202 · calculationBefore Exp convolution right8 factorial step5 := mul(24, 5) After Exp convolution right8 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S201 S203 · calculationBefore Exp convolution right8 factorial step6 := mul(120, 6) After Exp convolution right8 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S202 S204 · calculationBefore Exp convolution right8 factorial step7 := mul(720, 7) After Exp convolution right8 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S203 S205 · calculationBefore Exp convolution right8 factorial step8 := mul(5040, 8) After Exp convolution right8 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S204 S206 · calculationBefore Exp convolution right8 factorial step9 := mul(40320, 9) After Exp convolution right8 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S205 S207 · calculationBefore Exp convolution right8 factorial step10 := mul(362880, 10) After Exp convolution right8 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S206 S208 · calculationBefore Exp convolution denominator8 := mul(40320, 3628800) After Exp convolution denominator8 = 146313216000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S207 S209 · calculationBefore Exp convolution coefficient term8 := div(6793425216400/16679880978201, 146313216000) After Exp convolution coefficient term8 = 16983563041/6101217571044535511040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S208 S210 · impliesBefore (19/20)^9 After Exp convolution x power9 = 322687697779/512000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S209 S211 · impliesBefore (-20/21)^9 After Exp convolution y power9 = -512000000000/794280046581 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S210 S212 · calculationBefore Exp convolution numerator9 := mul(322687697779/512000000000, -512000000000/794280046581) After Exp convolution numerator9 = -322687697779/794280046581 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S211 S213 · calculationBefore Exp convolution left9 factorial step1 := mul(1, 1) After Exp convolution left9 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S212 S214 · calculationBefore Exp convolution left9 factorial step2 := mul(1, 2) After Exp convolution left9 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S213 S215 · calculationBefore Exp convolution left9 factorial step3 := mul(2, 3) After Exp convolution left9 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S214 S216 · calculationBefore Exp convolution left9 factorial step4 := mul(6, 4) After Exp convolution left9 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S215 S217 · calculationBefore Exp convolution left9 factorial step5 := mul(24, 5) After Exp convolution left9 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S216 S218 · calculationBefore Exp convolution left9 factorial step6 := mul(120, 6) After Exp convolution left9 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S217 S219 · calculationBefore Exp convolution left9 factorial step7 := mul(720, 7) After Exp convolution left9 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S218 S220 · calculationBefore Exp convolution left9 factorial step8 := mul(5040, 8) After Exp convolution left9 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S219 S221 · calculationBefore Exp convolution left9 factorial step9 := mul(40320, 9) After Exp convolution left9 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S220 S222 · calculationBefore Exp convolution right9 factorial step1 := mul(1, 1) After Exp convolution right9 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S221 S223 · calculationBefore Exp convolution right9 factorial step2 := mul(1, 2) After Exp convolution right9 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S222 S224 · calculationBefore Exp convolution right9 factorial step3 := mul(2, 3) After Exp convolution right9 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S223 S225 · calculationBefore Exp convolution right9 factorial step4 := mul(6, 4) After Exp convolution right9 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S224 S226 · calculationBefore Exp convolution right9 factorial step5 := mul(24, 5) After Exp convolution right9 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S225 S227 · calculationBefore Exp convolution right9 factorial step6 := mul(120, 6) After Exp convolution right9 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S226 S228 · calculationBefore Exp convolution right9 factorial step7 := mul(720, 7) After Exp convolution right9 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S227 S229 · calculationBefore Exp convolution right9 factorial step8 := mul(5040, 8) After Exp convolution right9 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S228 S230 · calculationBefore Exp convolution right9 factorial step9 := mul(40320, 9) After Exp convolution right9 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S229 S231 · calculationBefore Exp convolution denominator9 := mul(362880, 362880) After Exp convolution denominator9 = 131681894400 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S230 S232 · calculationBefore Exp convolution coefficient term9 := div(-322687697779/794280046581, 131681894400) After Exp convolution coefficient term9 = -322687697779/104592301217906323046400 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S231 S233 · impliesBefore (19/20)^10 After Exp convolution x power10 = 6131066257801/10240000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S232 S234 · impliesBefore (-20/21)^8 After Exp convolution y power8 = 25600000000/37822859361 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S233 S235 · calculationBefore Exp convolution numerator10 := mul(6131066257801/10240000000000, 25600000000/37822859361) After Exp convolution numerator10 = 6131066257801/15129143744400 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S234 S236 · calculationBefore Exp convolution left10 factorial step1 := mul(1, 1) After Exp convolution left10 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S235 S237 · calculationBefore Exp convolution left10 factorial step2 := mul(1, 2) After Exp convolution left10 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S236 S238 · calculationBefore Exp convolution left10 factorial step3 := mul(2, 3) After Exp convolution left10 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S237 S239 · calculationBefore Exp convolution left10 factorial step4 := mul(6, 4) After Exp convolution left10 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S238 S240 · calculationBefore Exp convolution left10 factorial step5 := mul(24, 5) After Exp convolution left10 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S239 S241 · calculationBefore Exp convolution left10 factorial step6 := mul(120, 6) After Exp convolution left10 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S240 S242 · calculationBefore Exp convolution left10 factorial step7 := mul(720, 7) After Exp convolution left10 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S241 S243 · calculationBefore Exp convolution left10 factorial step8 := mul(5040, 8) After Exp convolution left10 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S242 S244 · calculationBefore Exp convolution left10 factorial step9 := mul(40320, 9) After Exp convolution left10 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S243 S245 · calculationBefore Exp convolution left10 factorial step10 := mul(362880, 10) After Exp convolution left10 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S244 S246 · calculationBefore Exp convolution right10 factorial step1 := mul(1, 1) After Exp convolution right10 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S245 S247 · calculationBefore Exp convolution right10 factorial step2 := mul(1, 2) After Exp convolution right10 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S246 S248 · calculationBefore Exp convolution right10 factorial step3 := mul(2, 3) After Exp convolution right10 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S247 S249 · calculationBefore Exp convolution right10 factorial step4 := mul(6, 4) After Exp convolution right10 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S248 S250 · calculationBefore Exp convolution right10 factorial step5 := mul(24, 5) After Exp convolution right10 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S249 S251 · calculationBefore Exp convolution right10 factorial step6 := mul(120, 6) After Exp convolution right10 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S250 S252 · calculationBefore Exp convolution right10 factorial step7 := mul(720, 7) After Exp convolution right10 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S251 S253 · calculationBefore Exp convolution right10 factorial step8 := mul(5040, 8) After Exp convolution right10 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S252 S254 · calculationBefore Exp convolution denominator10 := mul(3628800, 40320) After Exp convolution denominator10 = 146313216000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S253 S255 · calculationBefore Exp convolution coefficient term10 := div(6131066257801/15129143744400, 146313216000) After Exp convolution coefficient term10 = 6131066257801/2213593676569445990400000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S254 S256 · impliesBefore (19/20)^11 After Exp convolution x power11 = 116490258898219/204800000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S255 S257 · impliesBefore (-20/21)^7 After Exp convolution y power7 = -1280000000/1801088541 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S256 S258 · calculationBefore Exp convolution numerator11 := mul(116490258898219/204800000000000, -1280000000/1801088541) After Exp convolution numerator11 = -116490258898219/288174166560000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S257 S259 · calculationBefore Exp convolution left11 factorial step1 := mul(1, 1) After Exp convolution left11 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S258 S260 · calculationBefore Exp convolution left11 factorial step2 := mul(1, 2) After Exp convolution left11 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S259 S261 · calculationBefore Exp convolution left11 factorial step3 := mul(2, 3) After Exp convolution left11 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S260 S262 · calculationBefore Exp convolution left11 factorial step4 := mul(6, 4) After Exp convolution left11 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S261 S263 · calculationBefore Exp convolution left11 factorial step5 := mul(24, 5) After Exp convolution left11 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S262 S264 · calculationBefore Exp convolution left11 factorial step6 := mul(120, 6) After Exp convolution left11 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S263 S265 · calculationBefore Exp convolution left11 factorial step7 := mul(720, 7) After Exp convolution left11 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S264 S266 · calculationBefore Exp convolution left11 factorial step8 := mul(5040, 8) After Exp convolution left11 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S265 S267 · calculationBefore Exp convolution left11 factorial step9 := mul(40320, 9) After Exp convolution left11 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S266 S268 · calculationBefore Exp convolution left11 factorial step10 := mul(362880, 10) After Exp convolution left11 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S267 S269 · calculationBefore Exp convolution left11 factorial step11 := mul(3628800, 11) After Exp convolution left11 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S268 S270 · calculationBefore Exp convolution right11 factorial step1 := mul(1, 1) After Exp convolution right11 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S269 S271 · calculationBefore Exp convolution right11 factorial step2 := mul(1, 2) After Exp convolution right11 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S270 S272 · calculationBefore Exp convolution right11 factorial step3 := mul(2, 3) After Exp convolution right11 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S271 S273 · calculationBefore Exp convolution right11 factorial step4 := mul(6, 4) After Exp convolution right11 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S272 S274 · calculationBefore Exp convolution right11 factorial step5 := mul(24, 5) After Exp convolution right11 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S273 S275 · calculationBefore Exp convolution right11 factorial step6 := mul(120, 6) After Exp convolution right11 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S274 S276 · calculationBefore Exp convolution right11 factorial step7 := mul(720, 7) After Exp convolution right11 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S275 S277 · calculationBefore Exp convolution denominator11 := mul(39916800, 5040) After Exp convolution denominator11 = 201180672000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S276 S278 · calculationBefore Exp convolution coefficient term11 := div(-116490258898219/288174166560000, 201180672000) After Exp convolution coefficient term11 = -116490258898219/57975072481580728320000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S277 S279 · impliesBefore (19/20)^12 After Exp convolution x power12 = 2213314919066161/4096000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S278 S280 · impliesBefore (-20/21)^6 After Exp convolution y power6 = 64000000/85766121 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S279 S281 · calculationBefore Exp convolution numerator12 := mul(2213314919066161/4096000000000000, 64000000/85766121) After Exp convolution numerator12 = 2213314919066161/5489031744000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S280 S282 · calculationBefore Exp convolution left12 factorial step1 := mul(1, 1) After Exp convolution left12 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S281 S283 · calculationBefore Exp convolution left12 factorial step2 := mul(1, 2) After Exp convolution left12 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S282 S284 · calculationBefore Exp convolution left12 factorial step3 := mul(2, 3) After Exp convolution left12 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S283 S285 · calculationBefore Exp convolution left12 factorial step4 := mul(6, 4) After Exp convolution left12 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S284 S286 · calculationBefore Exp convolution left12 factorial step5 := mul(24, 5) After Exp convolution left12 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S285 S287 · calculationBefore Exp convolution left12 factorial step6 := mul(120, 6) After Exp convolution left12 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S286 S288 · calculationBefore Exp convolution left12 factorial step7 := mul(720, 7) After Exp convolution left12 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S287 S289 · calculationBefore Exp convolution left12 factorial step8 := mul(5040, 8) After Exp convolution left12 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S288 S290 · calculationBefore Exp convolution left12 factorial step9 := mul(40320, 9) After Exp convolution left12 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S289 S291 · calculationBefore Exp convolution left12 factorial step10 := mul(362880, 10) After Exp convolution left12 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S290 S292 · calculationBefore Exp convolution left12 factorial step11 := mul(3628800, 11) After Exp convolution left12 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S291 S293 · calculationBefore Exp convolution left12 factorial step12 := mul(39916800, 12) After Exp convolution left12 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S292 S294 · calculationBefore Exp convolution right12 factorial step1 := mul(1, 1) After Exp convolution right12 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S293 S295 · calculationBefore Exp convolution right12 factorial step2 := mul(1, 2) After Exp convolution right12 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S294 S296 · calculationBefore Exp convolution right12 factorial step3 := mul(2, 3) After Exp convolution right12 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S295 S297 · calculationBefore Exp convolution right12 factorial step4 := mul(6, 4) After Exp convolution right12 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S296 S298 · calculationBefore Exp convolution right12 factorial step5 := mul(24, 5) After Exp convolution right12 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S297 S299 · calculationBefore Exp convolution right12 factorial step6 := mul(120, 6) After Exp convolution right12 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S298 S300 · calculationBefore Exp convolution denominator12 := mul(479001600, 720) After Exp convolution denominator12 = 344881152000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S299 S301 · calculationBefore Exp convolution coefficient term12 := div(2213314919066161/5489031744000000, 344881152000) After Exp convolution coefficient term12 = 2213314919066161/1893063591235289088000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S300 S302 · impliesBefore (19/20)^13 After Exp convolution x power13 = 42052983462257059/81920000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S301 S303 · impliesBefore (-20/21)^5 After Exp convolution y power5 = -3200000/4084101 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S302 S304 · calculationBefore Exp convolution numerator13 := mul(42052983462257059/81920000000000000, -3200000/4084101) After Exp convolution numerator13 = -42052983462257059/104552985600000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S303 S305 · calculationBefore Exp convolution left13 factorial step1 := mul(1, 1) After Exp convolution left13 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S304 S306 · calculationBefore Exp convolution left13 factorial step2 := mul(1, 2) After Exp convolution left13 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S305 S307 · calculationBefore Exp convolution left13 factorial step3 := mul(2, 3) After Exp convolution left13 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S306 S308 · calculationBefore Exp convolution left13 factorial step4 := mul(6, 4) After Exp convolution left13 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S307 S309 · calculationBefore Exp convolution left13 factorial step5 := mul(24, 5) After Exp convolution left13 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S308 S310 · calculationBefore Exp convolution left13 factorial step6 := mul(120, 6) After Exp convolution left13 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S309 S311 · calculationBefore Exp convolution left13 factorial step7 := mul(720, 7) After Exp convolution left13 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S310 S312 · calculationBefore Exp convolution left13 factorial step8 := mul(5040, 8) After Exp convolution left13 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S311 S313 · calculationBefore Exp convolution left13 factorial step9 := mul(40320, 9) After Exp convolution left13 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S312 S314 · calculationBefore Exp convolution left13 factorial step10 := mul(362880, 10) After Exp convolution left13 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S313 S315 · calculationBefore Exp convolution left13 factorial step11 := mul(3628800, 11) After Exp convolution left13 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S314 S316 · calculationBefore Exp convolution left13 factorial step12 := mul(39916800, 12) After Exp convolution left13 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S315 S317 · calculationBefore Exp convolution left13 factorial step13 := mul(479001600, 13) After Exp convolution left13 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S316 S318 · calculationBefore Exp convolution right13 factorial step1 := mul(1, 1) After Exp convolution right13 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S317 S319 · calculationBefore Exp convolution right13 factorial step2 := mul(1, 2) After Exp convolution right13 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S318 S320 · calculationBefore Exp convolution right13 factorial step3 := mul(2, 3) After Exp convolution right13 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S319 S321 · calculationBefore Exp convolution right13 factorial step4 := mul(6, 4) After Exp convolution right13 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S320 S322 · calculationBefore Exp convolution right13 factorial step5 := mul(24, 5) After Exp convolution right13 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S321 S323 · calculationBefore Exp convolution denominator13 := mul(6227020800, 120) After Exp convolution denominator13 = 747242496000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S322 S324 · calculationBefore Exp convolution coefficient term13 := div(-42052983462257059/104552985600000000, 747242496000) After Exp convolution coefficient term13 = -42052983462257059/78126433923996057600000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S323 S325 · impliesBefore (19/20)^14 After Exp convolution x power14 = 799006685782884121/1638400000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S324 S326 · impliesBefore (-20/21)^4 After Exp convolution y power4 = 160000/194481 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S325 S327 · calculationBefore Exp convolution numerator14 := mul(799006685782884121/1638400000000000000, 160000/194481) After Exp convolution numerator14 = 799006685782884121/1991485440000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S326 S328 · calculationBefore Exp convolution left14 factorial step1 := mul(1, 1) After Exp convolution left14 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S327 S329 · calculationBefore Exp convolution left14 factorial step2 := mul(1, 2) After Exp convolution left14 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S328 S330 · calculationBefore Exp convolution left14 factorial step3 := mul(2, 3) After Exp convolution left14 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S329 S331 · calculationBefore Exp convolution left14 factorial step4 := mul(6, 4) After Exp convolution left14 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S330 S332 · calculationBefore Exp convolution left14 factorial step5 := mul(24, 5) After Exp convolution left14 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S331 S333 · calculationBefore Exp convolution left14 factorial step6 := mul(120, 6) After Exp convolution left14 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S332 S334 · calculationBefore Exp convolution left14 factorial step7 := mul(720, 7) After Exp convolution left14 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S333 S335 · calculationBefore Exp convolution left14 factorial step8 := mul(5040, 8) After Exp convolution left14 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S334 S336 · calculationBefore Exp convolution left14 factorial step9 := mul(40320, 9) After Exp convolution left14 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S335 S337 · calculationBefore Exp convolution left14 factorial step10 := mul(362880, 10) After Exp convolution left14 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S336 S338 · calculationBefore Exp convolution left14 factorial step11 := mul(3628800, 11) After Exp convolution left14 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S337 S339 · calculationBefore Exp convolution left14 factorial step12 := mul(39916800, 12) After Exp convolution left14 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S338 S340 · calculationBefore Exp convolution left14 factorial step13 := mul(479001600, 13) After Exp convolution left14 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S339 S341 · calculationBefore Exp convolution left14 factorial step14 := mul(6227020800, 14) After Exp convolution left14 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S340 S342 · calculationBefore Exp convolution right14 factorial step1 := mul(1, 1) After Exp convolution right14 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S341 S343 · calculationBefore Exp convolution right14 factorial step2 := mul(1, 2) After Exp convolution right14 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S342 S344 · calculationBefore Exp convolution right14 factorial step3 := mul(2, 3) After Exp convolution right14 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S343 S345 · calculationBefore Exp convolution right14 factorial step4 := mul(6, 4) After Exp convolution right14 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S344 S346 · calculationBefore Exp convolution denominator14 := mul(87178291200, 24) After Exp convolution denominator14 = 2092278988800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S345 S347 · calculationBefore Exp convolution coefficient term14 := div(799006685782884121/1991485440000000000, 2092278988800) After Exp convolution coefficient term14 = 799006685782884121/4166743142613123072000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S346 S348 · impliesBefore (19/20)^15 After Exp convolution x power15 = 15181127029874798299/32768000000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S347 S349 · impliesBefore (-20/21)^3 After Exp convolution y power3 = -8000/9261 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S348 S350 · calculationBefore Exp convolution numerator15 := mul(15181127029874798299/32768000000000000000, -8000/9261) After Exp convolution numerator15 = -15181127029874798299/37933056000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S349 S351 · calculationBefore Exp convolution left15 factorial step1 := mul(1, 1) After Exp convolution left15 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S350 S352 · calculationBefore Exp convolution left15 factorial step2 := mul(1, 2) After Exp convolution left15 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S351 S353 · calculationBefore Exp convolution left15 factorial step3 := mul(2, 3) After Exp convolution left15 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S352 S354 · calculationBefore Exp convolution left15 factorial step4 := mul(6, 4) After Exp convolution left15 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S353 S355 · calculationBefore Exp convolution left15 factorial step5 := mul(24, 5) After Exp convolution left15 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S354 S356 · calculationBefore Exp convolution left15 factorial step6 := mul(120, 6) After Exp convolution left15 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S355 S357 · calculationBefore Exp convolution left15 factorial step7 := mul(720, 7) After Exp convolution left15 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S356 S358 · calculationBefore Exp convolution left15 factorial step8 := mul(5040, 8) After Exp convolution left15 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S357 S359 · calculationBefore Exp convolution left15 factorial step9 := mul(40320, 9) After Exp convolution left15 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S358 S360 · calculationBefore Exp convolution left15 factorial step10 := mul(362880, 10) After Exp convolution left15 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S359 S361 · calculationBefore Exp convolution left15 factorial step11 := mul(3628800, 11) After Exp convolution left15 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S360 S362 · calculationBefore Exp convolution left15 factorial step12 := mul(39916800, 12) After Exp convolution left15 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S361 S363 · calculationBefore Exp convolution left15 factorial step13 := mul(479001600, 13) After Exp convolution left15 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S362 S364 · calculationBefore Exp convolution left15 factorial step14 := mul(6227020800, 14) After Exp convolution left15 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S363 S365 · calculationBefore Exp convolution left15 factorial step15 := mul(87178291200, 15) After Exp convolution left15 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S364 S366 · calculationBefore Exp convolution right15 factorial step1 := mul(1, 1) After Exp convolution right15 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S365 S367 · calculationBefore Exp convolution right15 factorial step2 := mul(1, 2) After Exp convolution right15 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S366 S368 · calculationBefore Exp convolution right15 factorial step3 := mul(2, 3) After Exp convolution right15 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S367 S369 · calculationBefore Exp convolution denominator15 := mul(1307674368000, 6) After Exp convolution denominator15 = 7846046208000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S368 S370 · calculationBefore Exp convolution coefficient term15 := div(-15181127029874798299/37933056000000000000, 7846046208000) After Exp convolution coefficient term15 = -15181127029874798299/297624510186651648000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S369 S371 · impliesBefore (19/20)^16 After Exp convolution x power16 = 288441413567621167681/655360000000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S370 S372 · impliesBefore (-20/21)^2 After Exp convolution y power2 = 400/441 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S371 S373 · calculationBefore Exp convolution numerator16 := mul(288441413567621167681/655360000000000000000, 400/441) After Exp convolution numerator16 = 288441413567621167681/722534400000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S372 S374 · calculationBefore Exp convolution left16 factorial step1 := mul(1, 1) After Exp convolution left16 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S373 S375 · calculationBefore Exp convolution left16 factorial step2 := mul(1, 2) After Exp convolution left16 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S374 S376 · calculationBefore Exp convolution left16 factorial step3 := mul(2, 3) After Exp convolution left16 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S375 S377 · calculationBefore Exp convolution left16 factorial step4 := mul(6, 4) After Exp convolution left16 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S376 S378 · calculationBefore Exp convolution left16 factorial step5 := mul(24, 5) After Exp convolution left16 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S377 S379 · calculationBefore Exp convolution left16 factorial step6 := mul(120, 6) After Exp convolution left16 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S378 S380 · calculationBefore Exp convolution left16 factorial step7 := mul(720, 7) After Exp convolution left16 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S379 S381 · calculationBefore Exp convolution left16 factorial step8 := mul(5040, 8) After Exp convolution left16 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S380 S382 · calculationBefore Exp convolution left16 factorial step9 := mul(40320, 9) After Exp convolution left16 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S381 S383 · calculationBefore Exp convolution left16 factorial step10 := mul(362880, 10) After Exp convolution left16 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S382 S384 · calculationBefore Exp convolution left16 factorial step11 := mul(3628800, 11) After Exp convolution left16 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S383 S385 · calculationBefore Exp convolution left16 factorial step12 := mul(39916800, 12) After Exp convolution left16 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S384 S386 · calculationBefore Exp convolution left16 factorial step13 := mul(479001600, 13) After Exp convolution left16 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S385 S387 · calculationBefore Exp convolution left16 factorial step14 := mul(6227020800, 14) After Exp convolution left16 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S386 S388 · calculationBefore Exp convolution left16 factorial step15 := mul(87178291200, 15) After Exp convolution left16 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S387 S389 · calculationBefore Exp convolution left16 factorial step16 := mul(1307674368000, 16) After Exp convolution left16 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S388 S390 · calculationBefore Exp convolution right16 factorial step1 := mul(1, 1) After Exp convolution right16 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S389 S391 · calculationBefore Exp convolution right16 factorial step2 := mul(1, 2) After Exp convolution right16 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S390 S392 · calculationBefore Exp convolution denominator16 := mul(20922789888000, 2) After Exp convolution denominator16 = 41845579776000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S391 S393 · calculationBefore Exp convolution coefficient term16 := div(288441413567621167681/722534400000000000000, 41845579776000) After Exp convolution coefficient term16 = 288441413567621167681/30234870876104294400000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S392 S394 · impliesBefore (19/20)^17 After Exp convolution x power17 = 5480386857784802185939/13107200000000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S393 S395 · impliesBefore (-20/21)^1 After Exp convolution y power1 = -20/21 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S394 S396 · calculationBefore Exp convolution numerator17 := mul(5480386857784802185939/13107200000000000000000, -20/21) After Exp convolution numerator17 = -5480386857784802185939/13762560000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S395 S397 · calculationBefore Exp convolution left17 factorial step1 := mul(1, 1) After Exp convolution left17 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S396 S398 · calculationBefore Exp convolution left17 factorial step2 := mul(1, 2) After Exp convolution left17 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S397 S399 · calculationBefore Exp convolution left17 factorial step3 := mul(2, 3) After Exp convolution left17 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S398 S400 · calculationBefore Exp convolution left17 factorial step4 := mul(6, 4) After Exp convolution left17 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S399 S401 · calculationBefore Exp convolution left17 factorial step5 := mul(24, 5) After Exp convolution left17 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S400 S402 · calculationBefore Exp convolution left17 factorial step6 := mul(120, 6) After Exp convolution left17 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S401 S403 · calculationBefore Exp convolution left17 factorial step7 := mul(720, 7) After Exp convolution left17 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S402 S404 · calculationBefore Exp convolution left17 factorial step8 := mul(5040, 8) After Exp convolution left17 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S403 S405 · calculationBefore Exp convolution left17 factorial step9 := mul(40320, 9) After Exp convolution left17 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S404 S406 · calculationBefore Exp convolution left17 factorial step10 := mul(362880, 10) After Exp convolution left17 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S405 S407 · calculationBefore Exp convolution left17 factorial step11 := mul(3628800, 11) After Exp convolution left17 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S406 S408 · calculationBefore Exp convolution left17 factorial step12 := mul(39916800, 12) After Exp convolution left17 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S407 S409 · calculationBefore Exp convolution left17 factorial step13 := mul(479001600, 13) After Exp convolution left17 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S408 S410 · calculationBefore Exp convolution left17 factorial step14 := mul(6227020800, 14) After Exp convolution left17 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S409 S411 · calculationBefore Exp convolution left17 factorial step15 := mul(87178291200, 15) After Exp convolution left17 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S410 S412 · calculationBefore Exp convolution left17 factorial step16 := mul(1307674368000, 16) After Exp convolution left17 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S411 S413 · calculationBefore Exp convolution left17 factorial step17 := mul(20922789888000, 17) After Exp convolution left17 factorial step17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S412 S414 · calculationBefore Exp convolution right17 factorial step1 := mul(1, 1) After Exp convolution right17 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S413 S415 · calculationBefore Exp convolution denominator17 := mul(355687428096000, 1) After Exp convolution denominator17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S414 S416 · calculationBefore Exp convolution coefficient term17 := div(-5480386857784802185939/13762560000000000000000, 355687428096000) After Exp convolution coefficient term17 = -5480386857784802185939/4895169570416885760000000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S415 S417 · impliesBefore (19/20)^18 After Exp convolution x power18 = 104127350297911241532841/262144000000000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S416 S418 · impliesBefore (-20/21)^0 After Exp convolution y power0 = 1 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S417 S419 · calculationBefore Exp convolution numerator18 := mul(104127350297911241532841/262144000000000000000000, 1) After Exp convolution numerator18 = 104127350297911241532841/262144000000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S418 S420 · calculationBefore Exp convolution left18 factorial step1 := mul(1, 1) After Exp convolution left18 factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S419 S421 · calculationBefore Exp convolution left18 factorial step2 := mul(1, 2) After Exp convolution left18 factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S420 S422 · calculationBefore Exp convolution left18 factorial step3 := mul(2, 3) After Exp convolution left18 factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S421 S423 · calculationBefore Exp convolution left18 factorial step4 := mul(6, 4) After Exp convolution left18 factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S422 S424 · calculationBefore Exp convolution left18 factorial step5 := mul(24, 5) After Exp convolution left18 factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S423 S425 · calculationBefore Exp convolution left18 factorial step6 := mul(120, 6) After Exp convolution left18 factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S424 S426 · calculationBefore Exp convolution left18 factorial step7 := mul(720, 7) After Exp convolution left18 factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S425 S427 · calculationBefore Exp convolution left18 factorial step8 := mul(5040, 8) After Exp convolution left18 factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S426 S428 · calculationBefore Exp convolution left18 factorial step9 := mul(40320, 9) After Exp convolution left18 factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S427 S429 · calculationBefore Exp convolution left18 factorial step10 := mul(362880, 10) After Exp convolution left18 factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S428 S430 · calculationBefore Exp convolution left18 factorial step11 := mul(3628800, 11) After Exp convolution left18 factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S429 S431 · calculationBefore Exp convolution left18 factorial step12 := mul(39916800, 12) After Exp convolution left18 factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S430 S432 · calculationBefore Exp convolution left18 factorial step13 := mul(479001600, 13) After Exp convolution left18 factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S431 S433 · calculationBefore Exp convolution left18 factorial step14 := mul(6227020800, 14) After Exp convolution left18 factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S432 S434 · calculationBefore Exp convolution left18 factorial step15 := mul(87178291200, 15) After Exp convolution left18 factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S433 S435 · calculationBefore Exp convolution left18 factorial step16 := mul(1307674368000, 16) After Exp convolution left18 factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S434 S436 · calculationBefore Exp convolution left18 factorial step17 := mul(20922789888000, 17) After Exp convolution left18 factorial step17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S435 S437 · calculationBefore Exp convolution left18 factorial step18 := mul(355687428096000, 18) After Exp convolution left18 factorial step18 = 6402373705728000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S436 S438 · impliesBefore source roles = [0] After derived = [1] Conditions: none The empty product0! is1,not0. Step identifiers and dependenciesRule: empty_factorial_is_multiplicative_unit · Uses: G001, S437 S439 · calculationBefore Exp convolution denominator18 := mul(6402373705728000, 1) After Exp convolution denominator18 = 6402373705728000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S438 S440 · calculationBefore Exp convolution coefficient term18 := div(104127350297911241532841/262144000000000000000000, 6402373705728000) After Exp convolution coefficient term18 = 104127350297911241532841/1678343852714360832000000000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S439 S441 · calculationBefore Exp complete declared-degree convolution := sum(32000000000000000/493058422447458087543290824655799, -3040000000000000/2608774721944222685414237167491, 72200000000000/7307492218331155981552485063, -54872000000000/1043927459761593711650355009, 3258025000000/16570277139072916057942143, -61902475000/112722973735189905156069, 5880735125/4954855988359995831036, -4469358695/2202158217048887036016, 16983563041/6101217571044535511040, -322687697779/104592301217906323046400, 6131066257801/2213593676569445990400000, -116490258898219/57975072481580728320000000, 2213314919066161/1893063591235289088000000000, -42052983462257059/78126433923996057600000000000, 799006685782884121/4166743142613123072000000000000, -15181127029874798299/297624510186651648000000000000000, 288441413567621167681/30234870876104294400000000000000000, -5480386857784802185939/4895169570416885760000000000000000000, 104127350297911241532841/1678343852714360832000000000000000000000) After Exp complete declared-degree convolution = 1/1058834899714592382164569538056763580874752000000000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S440 S442 · calculationBefore Exp ORIGINAL arguments sum := sum(19/20, -20/21) After Exp ORIGINAL arguments sum = -1/420 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S441 S443 · impliesBefore (-1/420)^18 After Exp sum argument declared power = 1/165381614442044595841154678784000000000000000000 Conditions: none Evaluate the finite nonnegative-integer power exactly; exponent0 uses the polynomial multiplicative identity. Step identifiers and dependenciesRule: integer_power · Uses: G001, S442 S444 · calculationBefore Exp sum argument factorial step1 := mul(1, 1) After Exp sum argument factorial step1 = 1 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S443 S445 · calculationBefore Exp sum argument factorial step2 := mul(1, 2) After Exp sum argument factorial step2 = 2 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S444 S446 · calculationBefore Exp sum argument factorial step3 := mul(2, 3) After Exp sum argument factorial step3 = 6 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S445 S447 · calculationBefore Exp sum argument factorial step4 := mul(6, 4) After Exp sum argument factorial step4 = 24 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S446 S448 · calculationBefore Exp sum argument factorial step5 := mul(24, 5) After Exp sum argument factorial step5 = 120 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S447 S449 · calculationBefore Exp sum argument factorial step6 := mul(120, 6) After Exp sum argument factorial step6 = 720 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S448 S450 · calculationBefore Exp sum argument factorial step7 := mul(720, 7) After Exp sum argument factorial step7 = 5040 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S449 S451 · calculationBefore Exp sum argument factorial step8 := mul(5040, 8) After Exp sum argument factorial step8 = 40320 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S450 S452 · calculationBefore Exp sum argument factorial step9 := mul(40320, 9) After Exp sum argument factorial step9 = 362880 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S451 S453 · calculationBefore Exp sum argument factorial step10 := mul(362880, 10) After Exp sum argument factorial step10 = 3628800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S452 S454 · calculationBefore Exp sum argument factorial step11 := mul(3628800, 11) After Exp sum argument factorial step11 = 39916800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S453 S455 · calculationBefore Exp sum argument factorial step12 := mul(39916800, 12) After Exp sum argument factorial step12 = 479001600 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S454 S456 · calculationBefore Exp sum argument factorial step13 := mul(479001600, 13) After Exp sum argument factorial step13 = 6227020800 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S455 S457 · calculationBefore Exp sum argument factorial step14 := mul(6227020800, 14) After Exp sum argument factorial step14 = 87178291200 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S456 S458 · calculationBefore Exp sum argument factorial step15 := mul(87178291200, 15) After Exp sum argument factorial step15 = 1307674368000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S457 S459 · calculationBefore Exp sum argument factorial step16 := mul(1307674368000, 16) After Exp sum argument factorial step16 = 20922789888000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S458 S460 · calculationBefore Exp sum argument factorial step17 := mul(20922789888000, 17) After Exp sum argument factorial step17 = 355687428096000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S459 S461 · calculationBefore Exp sum argument factorial step18 := mul(355687428096000, 18) After Exp sum argument factorial step18 = 6402373705728000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S460 S462 · calculationBefore Exp sum argument coefficient := div(1/165381614442044595841154678784000000000000000000, 6402373705728000) After Exp sum argument coefficient = 1/1058834899714592382164569538056763580874752000000000000000000000 Conditions: none Substitute original roles and established intermediates exactly;check nonzero denominators and do not round. Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S461 S463 · impliesBefore source roles = [[19/20, -20/21], a_n=1/n! for EVERY n>=0] After derived = [coefficient ratio=1/(n+1), for EVERY fixed real z,term absolute ratio=|z|/(n+1)->0, absolute convergence and real-valued E(z)] Conditions: none For any fixed real z,choose N+1>2|z|;later absolute term ratios are below1/2 and a geometric tail proves absolute convergence.This is not finite-prefix extrapolation or omission of |z|. Step identifiers and dependenciesRule: Exp_WHOLE_factorial_law_ALL_fixed_real_arguments · Uses: G001, S462 S464 · impliesBefore source roles = [[19/20, -20/21, 18], E(x),E(y) absolutely convergent] After derived = [for EVERY n,sum_k x^k*y^(n-k)/(k!*(n-k)!)=(x+y)^n/n!, E(x)E(y)=E(x+y)] Conditions: none Multiply the finite degree-n convolution by n!:choosing k of n factors gives the binomial expansion for arbitrary n.Absolute convergence permits regrouping the double sum into the Cauchy product,establishing the whole addition law,not extrapolating one degree. Step identifiers and dependenciesRule: Exp_ALL_degree_binomial_and_absolute_Cauchy_product · Uses: G001, S463 ## Reverse checks - S464 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S463 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S462 · premise_and_result_audit — Recompute Exp sum argument coefficient with exact rational arithmetic, not rounded decimals. - S461 · premise_and_result_audit — Recompute Exp sum argument factorial step18 with exact rational arithmetic, not rounded decimals. - S460 · premise_and_result_audit — Recompute Exp sum argument factorial step17 with exact rational arithmetic, not rounded decimals. - S459 · premise_and_result_audit — Recompute Exp sum argument factorial step16 with exact rational arithmetic, not rounded decimals. - S458 · premise_and_result_audit — Recompute Exp sum argument factorial step15 with exact rational arithmetic, not rounded decimals. - S457 · premise_and_result_audit — Recompute Exp sum argument factorial step14 with exact rational arithmetic, not rounded decimals. - S456 · premise_and_result_audit — Recompute Exp sum argument factorial step13 with exact rational arithmetic, not rounded decimals. - S455 · premise_and_result_audit — Recompute Exp sum argument factorial step12 with exact rational arithmetic, not rounded decimals. - S454 · premise_and_result_audit — Recompute Exp sum argument factorial step11 with exact rational arithmetic, not rounded decimals. - S453 · premise_and_result_audit — Recompute Exp sum argument factorial step10 with exact rational arithmetic, not rounded decimals. - S452 · premise_and_result_audit — Recompute Exp sum argument factorial step9 with exact rational arithmetic, not rounded decimals. - S451 · premise_and_result_audit — Recompute Exp sum argument factorial step8 with exact rational arithmetic, not rounded decimals. - S450 · premise_and_result_audit — Recompute Exp sum argument factorial step7 with exact rational arithmetic, not rounded decimals. - S449 · premise_and_result_audit — Recompute Exp sum argument factorial step6 with exact rational arithmetic, not rounded decimals. - S448 · premise_and_result_audit — Recompute Exp sum argument factorial step5 with exact rational arithmetic, not rounded decimals. - S447 · premise_and_result_audit — Recompute Exp sum argument factorial step4 with exact rational arithmetic, not rounded decimals. - S446 · premise_and_result_audit — Recompute Exp sum argument factorial step3 with exact rational arithmetic, not rounded decimals. - S445 · premise_and_result_audit — Recompute Exp sum argument factorial step2 with exact rational arithmetic, not rounded decimals. - S444 · premise_and_result_audit — Recompute Exp sum argument factorial step1 with exact rational arithmetic, not rounded decimals. - S443 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S442 · premise_and_result_audit — Recompute Exp ORIGINAL arguments sum with exact rational arithmetic, not rounded decimals. - S441 · premise_and_result_audit — Recompute Exp complete declared-degree convolution with exact rational arithmetic, not rounded decimals. - S440 · premise_and_result_audit — Recompute Exp convolution coefficient term18 with exact rational arithmetic, not rounded decimals. - S439 · premise_and_result_audit — Recompute Exp convolution denominator18 with exact rational arithmetic, not rounded decimals. - S438 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S437 · premise_and_result_audit — Recompute Exp convolution left18 factorial step18 with exact rational arithmetic, not rounded decimals. - S436 · premise_and_result_audit — Recompute Exp convolution left18 factorial step17 with exact rational arithmetic, not rounded decimals. - S435 · premise_and_result_audit — Recompute Exp convolution left18 factorial step16 with exact rational arithmetic, not rounded decimals. - S434 · premise_and_result_audit — Recompute Exp convolution left18 factorial step15 with exact rational arithmetic, not rounded decimals. - S433 · premise_and_result_audit — Recompute Exp convolution left18 factorial step14 with exact rational arithmetic, not rounded decimals. - S432 · premise_and_result_audit — Recompute Exp convolution left18 factorial step13 with exact rational arithmetic, not rounded decimals. - S431 · premise_and_result_audit — Recompute Exp convolution left18 factorial step12 with exact rational arithmetic, not rounded decimals. - S430 · premise_and_result_audit — Recompute Exp convolution left18 factorial step11 with exact rational arithmetic, not rounded decimals. - S429 · premise_and_result_audit — Recompute Exp convolution left18 factorial step10 with exact rational arithmetic, not rounded decimals. - S428 · premise_and_result_audit — Recompute Exp convolution left18 factorial step9 with exact rational arithmetic, not rounded decimals. - S427 · premise_and_result_audit — Recompute Exp convolution left18 factorial step8 with exact rational arithmetic, not rounded decimals. - S426 · premise_and_result_audit — Recompute Exp convolution left18 factorial step7 with exact rational arithmetic, not rounded decimals. - S425 · premise_and_result_audit — Recompute Exp convolution left18 factorial step6 with exact rational arithmetic, not rounded decimals. - S424 · premise_and_result_audit — Recompute Exp convolution left18 factorial step5 with exact rational arithmetic, not rounded decimals. - S423 · premise_and_result_audit — Recompute Exp convolution left18 factorial step4 with exact rational arithmetic, not rounded decimals. - S422 · premise_and_result_audit — Recompute Exp convolution left18 factorial step3 with exact rational arithmetic, not rounded decimals. - S421 · premise_and_result_audit — Recompute Exp convolution left18 factorial step2 with exact rational arithmetic, not rounded decimals. - S420 · premise_and_result_audit — Recompute Exp convolution left18 factorial step1 with exact rational arithmetic, not rounded decimals. - S419 · premise_and_result_audit — Recompute Exp convolution numerator18 with exact rational arithmetic, not rounded decimals. - S418 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S417 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S416 · premise_and_result_audit — Recompute Exp convolution coefficient term17 with exact rational arithmetic, not rounded decimals. - S415 · premise_and_result_audit — Recompute Exp convolution denominator17 with exact rational arithmetic, not rounded decimals. - S414 · premise_and_result_audit — Recompute Exp convolution right17 factorial step1 with exact rational arithmetic, not rounded decimals. - S413 · premise_and_result_audit — Recompute Exp convolution left17 factorial step17 with exact rational arithmetic, not rounded decimals. - S412 · premise_and_result_audit — Recompute Exp convolution left17 factorial step16 with exact rational arithmetic, not rounded decimals. - S411 · premise_and_result_audit — Recompute Exp convolution left17 factorial step15 with exact rational arithmetic, not rounded decimals. - S410 · premise_and_result_audit — Recompute Exp convolution left17 factorial step14 with exact rational arithmetic, not rounded decimals. - S409 · premise_and_result_audit — Recompute Exp convolution left17 factorial step13 with exact rational arithmetic, not rounded decimals. - S408 · premise_and_result_audit — Recompute Exp convolution left17 factorial step12 with exact rational arithmetic, not rounded decimals. - S407 · premise_and_result_audit — Recompute Exp convolution left17 factorial step11 with exact rational arithmetic, not rounded decimals. - S406 · premise_and_result_audit — Recompute Exp convolution left17 factorial step10 with exact rational arithmetic, not rounded decimals. - S405 · premise_and_result_audit — Recompute Exp convolution left17 factorial step9 with exact rational arithmetic, not rounded decimals. - S404 · premise_and_result_audit — Recompute Exp convolution left17 factorial step8 with exact rational arithmetic, not rounded decimals. - S403 · premise_and_result_audit — Recompute Exp convolution left17 factorial step7 with exact rational arithmetic, not rounded decimals. - S402 · premise_and_result_audit — Recompute Exp convolution left17 factorial step6 with exact rational arithmetic, not rounded decimals. - S401 · premise_and_result_audit — Recompute Exp convolution left17 factorial step5 with exact rational arithmetic, not rounded decimals. - S400 · premise_and_result_audit — Recompute Exp convolution left17 factorial step4 with exact rational arithmetic, not rounded decimals. - S399 · premise_and_result_audit — Recompute Exp convolution left17 factorial step3 with exact rational arithmetic, not rounded decimals. - S398 · premise_and_result_audit — Recompute Exp convolution left17 factorial step2 with exact rational arithmetic, not rounded decimals. - S397 · premise_and_result_audit — Recompute Exp convolution left17 factorial step1 with exact rational arithmetic, not rounded decimals. - S396 · premise_and_result_audit — Recompute Exp convolution numerator17 with exact rational arithmetic, not rounded decimals. - S395 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S394 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S393 · premise_and_result_audit — Recompute Exp convolution coefficient term16 with exact rational arithmetic, not rounded decimals. - S392 · premise_and_result_audit — Recompute Exp convolution denominator16 with exact rational arithmetic, not rounded decimals. - S391 · premise_and_result_audit — Recompute Exp convolution right16 factorial step2 with exact rational arithmetic, not rounded decimals. - S390 · premise_and_result_audit — Recompute Exp convolution right16 factorial step1 with exact rational arithmetic, not rounded decimals. - S389 · premise_and_result_audit — Recompute Exp convolution left16 factorial step16 with exact rational arithmetic, not rounded decimals. - S388 · premise_and_result_audit — Recompute Exp convolution left16 factorial step15 with exact rational arithmetic, not rounded decimals. - S387 · premise_and_result_audit — Recompute Exp convolution left16 factorial step14 with exact rational arithmetic, not rounded decimals. - S386 · premise_and_result_audit — Recompute Exp convolution left16 factorial step13 with exact rational arithmetic, not rounded decimals. - S385 · premise_and_result_audit — Recompute Exp convolution left16 factorial step12 with exact rational arithmetic, not rounded decimals. - S384 · premise_and_result_audit — Recompute Exp convolution left16 factorial step11 with exact rational arithmetic, not rounded decimals. - S383 · premise_and_result_audit — Recompute Exp convolution left16 factorial step10 with exact rational arithmetic, not rounded decimals. - S382 · premise_and_result_audit — Recompute Exp convolution left16 factorial step9 with exact rational arithmetic, not rounded decimals. - S381 · premise_and_result_audit — Recompute Exp convolution left16 factorial step8 with exact rational arithmetic, not rounded decimals. - S380 · premise_and_result_audit — Recompute Exp convolution left16 factorial step7 with exact rational arithmetic, not rounded decimals. - S379 · premise_and_result_audit — Recompute Exp convolution left16 factorial step6 with exact rational arithmetic, not rounded decimals. - S378 · premise_and_result_audit — Recompute Exp convolution left16 factorial step5 with exact rational arithmetic, not rounded decimals. - S377 · premise_and_result_audit — Recompute Exp convolution left16 factorial step4 with exact rational arithmetic, not rounded decimals. - S376 · premise_and_result_audit — Recompute Exp convolution left16 factorial step3 with exact rational arithmetic, not rounded decimals. - S375 · premise_and_result_audit — Recompute Exp convolution left16 factorial step2 with exact rational arithmetic, not rounded decimals. - S374 · premise_and_result_audit — Recompute Exp convolution left16 factorial step1 with exact rational arithmetic, not rounded decimals. - S373 · premise_and_result_audit — Recompute Exp convolution numerator16 with exact rational arithmetic, not rounded decimals. - S372 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S371 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S370 · premise_and_result_audit — Recompute Exp convolution coefficient term15 with exact rational arithmetic, not rounded decimals. - S369 · premise_and_result_audit — Recompute Exp convolution denominator15 with exact rational arithmetic, not rounded decimals. - S368 · premise_and_result_audit — Recompute Exp convolution right15 factorial step3 with exact rational arithmetic, not rounded decimals. - S367 · premise_and_result_audit — Recompute Exp convolution right15 factorial step2 with exact rational arithmetic, not rounded decimals. - S366 · premise_and_result_audit — Recompute Exp convolution right15 factorial step1 with exact rational arithmetic, not rounded decimals. - S365 · premise_and_result_audit — Recompute Exp convolution left15 factorial step15 with exact rational arithmetic, not rounded decimals. - S364 · premise_and_result_audit — Recompute Exp convolution left15 factorial step14 with exact rational arithmetic, not rounded decimals. - S363 · premise_and_result_audit — Recompute Exp convolution left15 factorial step13 with exact rational arithmetic, not rounded decimals. - S362 · premise_and_result_audit — Recompute Exp convolution left15 factorial step12 with exact rational arithmetic, not rounded decimals. - S361 · premise_and_result_audit — Recompute Exp convolution left15 factorial step11 with exact rational arithmetic, not rounded decimals. - S360 · premise_and_result_audit — Recompute Exp convolution left15 factorial step10 with exact rational arithmetic, not rounded decimals. - S359 · premise_and_result_audit — Recompute Exp convolution left15 factorial step9 with exact rational arithmetic, not rounded decimals. - S358 · premise_and_result_audit — Recompute Exp convolution left15 factorial step8 with exact rational arithmetic, not rounded decimals. - S357 · premise_and_result_audit — Recompute Exp convolution left15 factorial step7 with exact rational arithmetic, not rounded decimals. - S356 · premise_and_result_audit — Recompute Exp convolution left15 factorial step6 with exact rational arithmetic, not rounded decimals. - S355 · premise_and_result_audit — Recompute Exp convolution left15 factorial step5 with exact rational arithmetic, not rounded decimals. - S354 · premise_and_result_audit — Recompute Exp convolution left15 factorial step4 with exact rational arithmetic, not rounded decimals. - S353 · premise_and_result_audit — Recompute Exp convolution left15 factorial step3 with exact rational arithmetic, not rounded decimals. - S352 · premise_and_result_audit — Recompute Exp convolution left15 factorial step2 with exact rational arithmetic, not rounded decimals. - S351 · premise_and_result_audit — Recompute Exp convolution left15 factorial step1 with exact rational arithmetic, not rounded decimals. - S350 · premise_and_result_audit — Recompute Exp convolution numerator15 with exact rational arithmetic, not rounded decimals. - S349 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S348 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S347 · premise_and_result_audit — Recompute Exp convolution coefficient term14 with exact rational arithmetic, not rounded decimals. - S346 · premise_and_result_audit — Recompute Exp convolution denominator14 with exact rational arithmetic, not rounded decimals. - S345 · premise_and_result_audit — Recompute Exp convolution right14 factorial step4 with exact rational arithmetic, not rounded decimals. - S344 · premise_and_result_audit — Recompute Exp convolution right14 factorial step3 with exact rational arithmetic, not rounded decimals. - S343 · premise_and_result_audit — Recompute Exp convolution right14 factorial step2 with exact rational arithmetic, not rounded decimals. - S342 · premise_and_result_audit — Recompute Exp convolution right14 factorial step1 with exact rational arithmetic, not rounded decimals. - S341 · premise_and_result_audit — Recompute Exp convolution left14 factorial step14 with exact rational arithmetic, not rounded decimals. - S340 · premise_and_result_audit — Recompute Exp convolution left14 factorial step13 with exact rational arithmetic, not rounded decimals. - S339 · premise_and_result_audit — Recompute Exp convolution left14 factorial step12 with exact rational arithmetic, not rounded decimals. - S338 · premise_and_result_audit — Recompute Exp convolution left14 factorial step11 with exact rational arithmetic, not rounded decimals. - S337 · premise_and_result_audit — Recompute Exp convolution left14 factorial step10 with exact rational arithmetic, not rounded decimals. - S336 · premise_and_result_audit — Recompute Exp convolution left14 factorial step9 with exact rational arithmetic, not rounded decimals. - S335 · premise_and_result_audit — Recompute Exp convolution left14 factorial step8 with exact rational arithmetic, not rounded decimals. - S334 · premise_and_result_audit — Recompute Exp convolution left14 factorial step7 with exact rational arithmetic, not rounded decimals. - S333 · premise_and_result_audit — Recompute Exp convolution left14 factorial step6 with exact rational arithmetic, not rounded decimals. - S332 · premise_and_result_audit — Recompute Exp convolution left14 factorial step5 with exact rational arithmetic, not rounded decimals. - S331 · premise_and_result_audit — Recompute Exp convolution left14 factorial step4 with exact rational arithmetic, not rounded decimals. - S330 · premise_and_result_audit — Recompute Exp convolution left14 factorial step3 with exact rational arithmetic, not rounded decimals. - S329 · premise_and_result_audit — Recompute Exp convolution left14 factorial step2 with exact rational arithmetic, not rounded decimals. - S328 · premise_and_result_audit — Recompute Exp convolution left14 factorial step1 with exact rational arithmetic, not rounded decimals. - S327 · premise_and_result_audit — Recompute Exp convolution numerator14 with exact rational arithmetic, not rounded decimals. - S326 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S325 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S324 · premise_and_result_audit — Recompute Exp convolution coefficient term13 with exact rational arithmetic, not rounded decimals. - S323 · premise_and_result_audit — Recompute Exp convolution denominator13 with exact rational arithmetic, not rounded decimals. - S322 · premise_and_result_audit — Recompute Exp convolution right13 factorial step5 with exact rational arithmetic, not rounded decimals. - S321 · premise_and_result_audit — Recompute Exp convolution right13 factorial step4 with exact rational arithmetic, not rounded decimals. - S320 · premise_and_result_audit — Recompute Exp convolution right13 factorial step3 with exact rational arithmetic, not rounded decimals. - S319 · premise_and_result_audit — Recompute Exp convolution right13 factorial step2 with exact rational arithmetic, not rounded decimals. - S318 · premise_and_result_audit — Recompute Exp convolution right13 factorial step1 with exact rational arithmetic, not rounded decimals. - S317 · premise_and_result_audit — Recompute Exp convolution left13 factorial step13 with exact rational arithmetic, not rounded decimals. - S316 · premise_and_result_audit — Recompute Exp convolution left13 factorial step12 with exact rational arithmetic, not rounded decimals. - S315 · premise_and_result_audit — Recompute Exp convolution left13 factorial step11 with exact rational arithmetic, not rounded decimals. - S314 · premise_and_result_audit — Recompute Exp convolution left13 factorial step10 with exact rational arithmetic, not rounded decimals. - S313 · premise_and_result_audit — Recompute Exp convolution left13 factorial step9 with exact rational arithmetic, not rounded decimals. - S312 · premise_and_result_audit — Recompute Exp convolution left13 factorial step8 with exact rational arithmetic, not rounded decimals. - S311 · premise_and_result_audit — Recompute Exp convolution left13 factorial step7 with exact rational arithmetic, not rounded decimals. - S310 · premise_and_result_audit — Recompute Exp convolution left13 factorial step6 with exact rational arithmetic, not rounded decimals. - S309 · premise_and_result_audit — Recompute Exp convolution left13 factorial step5 with exact rational arithmetic, not rounded decimals. - S308 · premise_and_result_audit — Recompute Exp convolution left13 factorial step4 with exact rational arithmetic, not rounded decimals. - S307 · premise_and_result_audit — Recompute Exp convolution left13 factorial step3 with exact rational arithmetic, not rounded decimals. - S306 · premise_and_result_audit — Recompute Exp convolution left13 factorial step2 with exact rational arithmetic, not rounded decimals. - S305 · premise_and_result_audit — Recompute Exp convolution left13 factorial step1 with exact rational arithmetic, not rounded decimals. - S304 · premise_and_result_audit — Recompute Exp convolution numerator13 with exact rational arithmetic, not rounded decimals. - S303 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S302 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S301 · premise_and_result_audit — Recompute Exp convolution coefficient term12 with exact rational arithmetic, not rounded decimals. - S300 · premise_and_result_audit — Recompute Exp convolution denominator12 with exact rational arithmetic, not rounded decimals. - S299 · premise_and_result_audit — Recompute Exp convolution right12 factorial step6 with exact rational arithmetic, not rounded decimals. - S298 · premise_and_result_audit — Recompute Exp convolution right12 factorial step5 with exact rational arithmetic, not rounded decimals. - S297 · premise_and_result_audit — Recompute Exp convolution right12 factorial step4 with exact rational arithmetic, not rounded decimals. - S296 · premise_and_result_audit — Recompute Exp convolution right12 factorial step3 with exact rational arithmetic, not rounded decimals. - S295 · premise_and_result_audit — Recompute Exp convolution right12 factorial step2 with exact rational arithmetic, not rounded decimals. - S294 · premise_and_result_audit — Recompute Exp convolution right12 factorial step1 with exact rational arithmetic, not rounded decimals. - S293 · premise_and_result_audit — Recompute Exp convolution left12 factorial step12 with exact rational arithmetic, not rounded decimals. - S292 · premise_and_result_audit — Recompute Exp convolution left12 factorial step11 with exact rational arithmetic, not rounded decimals. - S291 · premise_and_result_audit — Recompute Exp convolution left12 factorial step10 with exact rational arithmetic, not rounded decimals. - S290 · premise_and_result_audit — Recompute Exp convolution left12 factorial step9 with exact rational arithmetic, not rounded decimals. - S289 · premise_and_result_audit — Recompute Exp convolution left12 factorial step8 with exact rational arithmetic, not rounded decimals. - S288 · premise_and_result_audit — Recompute Exp convolution left12 factorial step7 with exact rational arithmetic, not rounded decimals. - S287 · premise_and_result_audit — Recompute Exp convolution left12 factorial step6 with exact rational arithmetic, not rounded decimals. - S286 · premise_and_result_audit — Recompute Exp convolution left12 factorial step5 with exact rational arithmetic, not rounded decimals. - S285 · premise_and_result_audit — Recompute Exp convolution left12 factorial step4 with exact rational arithmetic, not rounded decimals. - S284 · premise_and_result_audit — Recompute Exp convolution left12 factorial step3 with exact rational arithmetic, not rounded decimals. - S283 · premise_and_result_audit — Recompute Exp convolution left12 factorial step2 with exact rational arithmetic, not rounded decimals. - S282 · premise_and_result_audit — Recompute Exp convolution left12 factorial step1 with exact rational arithmetic, not rounded decimals. - S281 · premise_and_result_audit — Recompute Exp convolution numerator12 with exact rational arithmetic, not rounded decimals. - S280 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S279 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S278 · premise_and_result_audit — Recompute Exp convolution coefficient term11 with exact rational arithmetic, not rounded decimals. - S277 · premise_and_result_audit — Recompute Exp convolution denominator11 with exact rational arithmetic, not rounded decimals. - S276 · premise_and_result_audit — Recompute Exp convolution right11 factorial step7 with exact rational arithmetic, not rounded decimals. - S275 · premise_and_result_audit — Recompute Exp convolution right11 factorial step6 with exact rational arithmetic, not rounded decimals. - S274 · premise_and_result_audit — Recompute Exp convolution right11 factorial step5 with exact rational arithmetic, not rounded decimals. - S273 · premise_and_result_audit — Recompute Exp convolution right11 factorial step4 with exact rational arithmetic, not rounded decimals. - S272 · premise_and_result_audit — Recompute Exp convolution right11 factorial step3 with exact rational arithmetic, not rounded decimals. - S271 · premise_and_result_audit — Recompute Exp convolution right11 factorial step2 with exact rational arithmetic, not rounded decimals. - S270 · premise_and_result_audit — Recompute Exp convolution right11 factorial step1 with exact rational arithmetic, not rounded decimals. - S269 · premise_and_result_audit — Recompute Exp convolution left11 factorial step11 with exact rational arithmetic, not rounded decimals. - S268 · premise_and_result_audit — Recompute Exp convolution left11 factorial step10 with exact rational arithmetic, not rounded decimals. - S267 · premise_and_result_audit — Recompute Exp convolution left11 factorial step9 with exact rational arithmetic, not rounded decimals. - S266 · premise_and_result_audit — Recompute Exp convolution left11 factorial step8 with exact rational arithmetic, not rounded decimals. - S265 · premise_and_result_audit — Recompute Exp convolution left11 factorial step7 with exact rational arithmetic, not rounded decimals. - S264 · premise_and_result_audit — Recompute Exp convolution left11 factorial step6 with exact rational arithmetic, not rounded decimals. - S263 · premise_and_result_audit — Recompute Exp convolution left11 factorial step5 with exact rational arithmetic, not rounded decimals. - S262 · premise_and_result_audit — Recompute Exp convolution left11 factorial step4 with exact rational arithmetic, not rounded decimals. - S261 · premise_and_result_audit — Recompute Exp convolution left11 factorial step3 with exact rational arithmetic, not rounded decimals. - S260 · premise_and_result_audit — Recompute Exp convolution left11 factorial step2 with exact rational arithmetic, not rounded decimals. - S259 · premise_and_result_audit — Recompute Exp convolution left11 factorial step1 with exact rational arithmetic, not rounded decimals. - S258 · premise_and_result_audit — Recompute Exp convolution numerator11 with exact rational arithmetic, not rounded decimals. - S257 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S256 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S255 · premise_and_result_audit — Recompute Exp convolution coefficient term10 with exact rational arithmetic, not rounded decimals. - S254 · premise_and_result_audit — Recompute Exp convolution denominator10 with exact rational arithmetic, not rounded decimals. - S253 · premise_and_result_audit — Recompute Exp convolution right10 factorial step8 with exact rational arithmetic, not rounded decimals. - S252 · premise_and_result_audit — Recompute Exp convolution right10 factorial step7 with exact rational arithmetic, not rounded decimals. - S251 · premise_and_result_audit — Recompute Exp convolution right10 factorial step6 with exact rational arithmetic, not rounded decimals. - S250 · premise_and_result_audit — Recompute Exp convolution right10 factorial step5 with exact rational arithmetic, not rounded decimals. - S249 · premise_and_result_audit — Recompute Exp convolution right10 factorial step4 with exact rational arithmetic, not rounded decimals. - S248 · premise_and_result_audit — Recompute Exp convolution right10 factorial step3 with exact rational arithmetic, not rounded decimals. - S247 · premise_and_result_audit — Recompute Exp convolution right10 factorial step2 with exact rational arithmetic, not rounded decimals. - S246 · premise_and_result_audit — Recompute Exp convolution right10 factorial step1 with exact rational arithmetic, not rounded decimals. - S245 · premise_and_result_audit — Recompute Exp convolution left10 factorial step10 with exact rational arithmetic, not rounded decimals. - S244 · premise_and_result_audit — Recompute Exp convolution left10 factorial step9 with exact rational arithmetic, not rounded decimals. - S243 · premise_and_result_audit — Recompute Exp convolution left10 factorial step8 with exact rational arithmetic, not rounded decimals. - S242 · premise_and_result_audit — Recompute Exp convolution left10 factorial step7 with exact rational arithmetic, not rounded decimals. - S241 · premise_and_result_audit — Recompute Exp convolution left10 factorial step6 with exact rational arithmetic, not rounded decimals. - S240 · premise_and_result_audit — Recompute Exp convolution left10 factorial step5 with exact rational arithmetic, not rounded decimals. - S239 · premise_and_result_audit — Recompute Exp convolution left10 factorial step4 with exact rational arithmetic, not rounded decimals. - S238 · premise_and_result_audit — Recompute Exp convolution left10 factorial step3 with exact rational arithmetic, not rounded decimals. - S237 · premise_and_result_audit — Recompute Exp convolution left10 factorial step2 with exact rational arithmetic, not rounded decimals. - S236 · premise_and_result_audit — Recompute Exp convolution left10 factorial step1 with exact rational arithmetic, not rounded decimals. - S235 · premise_and_result_audit — Recompute Exp convolution numerator10 with exact rational arithmetic, not rounded decimals. - S234 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S233 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S232 · premise_and_result_audit — Recompute Exp convolution coefficient term9 with exact rational arithmetic, not rounded decimals. - S231 · premise_and_result_audit — Recompute Exp convolution denominator9 with exact rational arithmetic, not rounded decimals. - S230 · premise_and_result_audit — Recompute Exp convolution right9 factorial step9 with exact rational arithmetic, not rounded decimals. - S229 · premise_and_result_audit — Recompute Exp convolution right9 factorial step8 with exact rational arithmetic, not rounded decimals. - S228 · premise_and_result_audit — Recompute Exp convolution right9 factorial step7 with exact rational arithmetic, not rounded decimals. - S227 · premise_and_result_audit — Recompute Exp convolution right9 factorial step6 with exact rational arithmetic, not rounded decimals. - S226 · premise_and_result_audit — Recompute Exp convolution right9 factorial step5 with exact rational arithmetic, not rounded decimals. - S225 · premise_and_result_audit — Recompute Exp convolution right9 factorial step4 with exact rational arithmetic, not rounded decimals. - S224 · premise_and_result_audit — Recompute Exp convolution right9 factorial step3 with exact rational arithmetic, not rounded decimals. - S223 · premise_and_result_audit — Recompute Exp convolution right9 factorial step2 with exact rational arithmetic, not rounded decimals. - S222 · premise_and_result_audit — Recompute Exp convolution right9 factorial step1 with exact rational arithmetic, not rounded decimals. - S221 · premise_and_result_audit — Recompute Exp convolution left9 factorial step9 with exact rational arithmetic, not rounded decimals. - S220 · premise_and_result_audit — Recompute Exp convolution left9 factorial step8 with exact rational arithmetic, not rounded decimals. - S219 · premise_and_result_audit — Recompute Exp convolution left9 factorial step7 with exact rational arithmetic, not rounded decimals. - S218 · premise_and_result_audit — Recompute Exp convolution left9 factorial step6 with exact rational arithmetic, not rounded decimals. - S217 · premise_and_result_audit — Recompute Exp convolution left9 factorial step5 with exact rational arithmetic, not rounded decimals. - S216 · premise_and_result_audit — Recompute Exp convolution left9 factorial step4 with exact rational arithmetic, not rounded decimals. - S215 · premise_and_result_audit — Recompute Exp convolution left9 factorial step3 with exact rational arithmetic, not rounded decimals. - S214 · premise_and_result_audit — Recompute Exp convolution left9 factorial step2 with exact rational arithmetic, not rounded decimals. - S213 · premise_and_result_audit — Recompute Exp convolution left9 factorial step1 with exact rational arithmetic, not rounded decimals. - S212 · premise_and_result_audit — Recompute Exp convolution numerator9 with exact rational arithmetic, not rounded decimals. - S211 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S210 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S209 · premise_and_result_audit — Recompute Exp convolution coefficient term8 with exact rational arithmetic, not rounded decimals. - S208 · premise_and_result_audit — Recompute Exp convolution denominator8 with exact rational arithmetic, not rounded decimals. - S207 · premise_and_result_audit — Recompute Exp convolution right8 factorial step10 with exact rational arithmetic, not rounded decimals. - S206 · premise_and_result_audit — Recompute Exp convolution right8 factorial step9 with exact rational arithmetic, not rounded decimals. - S205 · premise_and_result_audit — Recompute Exp convolution right8 factorial step8 with exact rational arithmetic, not rounded decimals. - S204 · premise_and_result_audit — Recompute Exp convolution right8 factorial step7 with exact rational arithmetic, not rounded decimals. - S203 · premise_and_result_audit — Recompute Exp convolution right8 factorial step6 with exact rational arithmetic, not rounded decimals. - S202 · premise_and_result_audit — Recompute Exp convolution right8 factorial step5 with exact rational arithmetic, not rounded decimals. - S201 · premise_and_result_audit — Recompute Exp convolution right8 factorial step4 with exact rational arithmetic, not rounded decimals. - S200 · premise_and_result_audit — Recompute Exp convolution right8 factorial step3 with exact rational arithmetic, not rounded decimals. - S199 · premise_and_result_audit — Recompute Exp convolution right8 factorial step2 with exact rational arithmetic, not rounded decimals. - S198 · premise_and_result_audit — Recompute Exp convolution right8 factorial step1 with exact rational arithmetic, not rounded decimals. - S197 · premise_and_result_audit — Recompute Exp convolution left8 factorial step8 with exact rational arithmetic, not rounded decimals. - S196 · premise_and_result_audit — Recompute Exp convolution left8 factorial step7 with exact rational arithmetic, not rounded decimals. - S195 · premise_and_result_audit — Recompute Exp convolution left8 factorial step6 with exact rational arithmetic, not rounded decimals. - S194 · premise_and_result_audit — Recompute Exp convolution left8 factorial step5 with exact rational arithmetic, not rounded decimals. - S193 · premise_and_result_audit — Recompute Exp convolution left8 factorial step4 with exact rational arithmetic, not rounded decimals. - S192 · premise_and_result_audit — Recompute Exp convolution left8 factorial step3 with exact rational arithmetic, not rounded decimals. - S191 · premise_and_result_audit — Recompute Exp convolution left8 factorial step2 with exact rational arithmetic, not rounded decimals. - S190 · premise_and_result_audit — Recompute Exp convolution left8 factorial step1 with exact rational arithmetic, not rounded decimals. - S189 · premise_and_result_audit — Recompute Exp convolution numerator8 with exact rational arithmetic, not rounded decimals. - S188 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S187 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S186 · premise_and_result_audit — Recompute Exp convolution coefficient term7 with exact rational arithmetic, not rounded decimals. - S185 · premise_and_result_audit — Recompute Exp convolution denominator7 with exact rational arithmetic, not rounded decimals. - S184 · premise_and_result_audit — Recompute Exp convolution right7 factorial step11 with exact rational arithmetic, not rounded decimals. - S183 · premise_and_result_audit — Recompute Exp convolution right7 factorial step10 with exact rational arithmetic, not rounded decimals. - S182 · premise_and_result_audit — Recompute Exp convolution right7 factorial step9 with exact rational arithmetic, not rounded decimals. - S181 · premise_and_result_audit — Recompute Exp convolution right7 factorial step8 with exact rational arithmetic, not rounded decimals. - S180 · premise_and_result_audit — Recompute Exp convolution right7 factorial step7 with exact rational arithmetic, not rounded decimals. - S179 · premise_and_result_audit — Recompute Exp convolution right7 factorial step6 with exact rational arithmetic, not rounded decimals. - S178 · premise_and_result_audit — Recompute Exp convolution right7 factorial step5 with exact rational arithmetic, not rounded decimals. - S177 · premise_and_result_audit — Recompute Exp convolution right7 factorial step4 with exact rational arithmetic, not rounded decimals. - S176 · premise_and_result_audit — Recompute Exp convolution right7 factorial step3 with exact rational arithmetic, not rounded decimals. - S175 · premise_and_result_audit — Recompute Exp convolution right7 factorial step2 with exact rational arithmetic, not rounded decimals. - S174 · premise_and_result_audit — Recompute Exp convolution right7 factorial step1 with exact rational arithmetic, not rounded decimals. - S173 · premise_and_result_audit — Recompute Exp convolution left7 factorial step7 with exact rational arithmetic, not rounded decimals. - S172 · premise_and_result_audit — Recompute Exp convolution left7 factorial step6 with exact rational arithmetic, not rounded decimals. - S171 · premise_and_result_audit — Recompute Exp convolution left7 factorial step5 with exact rational arithmetic, not rounded decimals. - S170 · premise_and_result_audit — Recompute Exp convolution left7 factorial step4 with exact rational arithmetic, not rounded decimals. - S169 · premise_and_result_audit — Recompute Exp convolution left7 factorial step3 with exact rational arithmetic, not rounded decimals. - S168 · premise_and_result_audit — Recompute Exp convolution left7 factorial step2 with exact rational arithmetic, not rounded decimals. - S167 · premise_and_result_audit — Recompute Exp convolution left7 factorial step1 with exact rational arithmetic, not rounded decimals. - S166 · premise_and_result_audit — Recompute Exp convolution numerator7 with exact rational arithmetic, not rounded decimals. - S165 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S164 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S163 · premise_and_result_audit — Recompute Exp convolution coefficient term6 with exact rational arithmetic, not rounded decimals. - S162 · premise_and_result_audit — Recompute Exp convolution denominator6 with exact rational arithmetic, not rounded decimals. - S161 · premise_and_result_audit — Recompute Exp convolution right6 factorial step12 with exact rational arithmetic, not rounded decimals. - S160 · premise_and_result_audit — Recompute Exp convolution right6 factorial step11 with exact rational arithmetic, not rounded decimals. - S159 · premise_and_result_audit — Recompute Exp convolution right6 factorial step10 with exact rational arithmetic, not rounded decimals. - S158 · premise_and_result_audit — Recompute Exp convolution right6 factorial step9 with exact rational arithmetic, not rounded decimals. - S157 · premise_and_result_audit — Recompute Exp convolution right6 factorial step8 with exact rational arithmetic, not rounded decimals. - S156 · premise_and_result_audit — Recompute Exp convolution right6 factorial step7 with exact rational arithmetic, not rounded decimals. - S155 · premise_and_result_audit — Recompute Exp convolution right6 factorial step6 with exact rational arithmetic, not rounded decimals. - S154 · premise_and_result_audit — Recompute Exp convolution right6 factorial step5 with exact rational arithmetic, not rounded decimals. - S153 · premise_and_result_audit — Recompute Exp convolution right6 factorial step4 with exact rational arithmetic, not rounded decimals. - S152 · premise_and_result_audit — Recompute Exp convolution right6 factorial step3 with exact rational arithmetic, not rounded decimals. - S151 · premise_and_result_audit — Recompute Exp convolution right6 factorial step2 with exact rational arithmetic, not rounded decimals. - S150 · premise_and_result_audit — Recompute Exp convolution right6 factorial step1 with exact rational arithmetic, not rounded decimals. - S149 · premise_and_result_audit — Recompute Exp convolution left6 factorial step6 with exact rational arithmetic, not rounded decimals. - S148 · premise_and_result_audit — Recompute Exp convolution left6 factorial step5 with exact rational arithmetic, not rounded decimals. - S147 · premise_and_result_audit — Recompute Exp convolution left6 factorial step4 with exact rational arithmetic, not rounded decimals. - S146 · premise_and_result_audit — Recompute Exp convolution left6 factorial step3 with exact rational arithmetic, not rounded decimals. - S145 · premise_and_result_audit — Recompute Exp convolution left6 factorial step2 with exact rational arithmetic, not rounded decimals. - S144 · premise_and_result_audit — Recompute Exp convolution left6 factorial step1 with exact rational arithmetic, not rounded decimals. - S143 · premise_and_result_audit — Recompute Exp convolution numerator6 with exact rational arithmetic, not rounded decimals. - S142 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S141 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S140 · premise_and_result_audit — Recompute Exp convolution coefficient term5 with exact rational arithmetic, not rounded decimals. - S139 · premise_and_result_audit — Recompute Exp convolution denominator5 with exact rational arithmetic, not rounded decimals. - S138 · premise_and_result_audit — Recompute Exp convolution right5 factorial step13 with exact rational arithmetic, not rounded decimals. - S137 · premise_and_result_audit — Recompute Exp convolution right5 factorial step12 with exact rational arithmetic, not rounded decimals. - S136 · premise_and_result_audit — Recompute Exp convolution right5 factorial step11 with exact rational arithmetic, not rounded decimals. - S135 · premise_and_result_audit — Recompute Exp convolution right5 factorial step10 with exact rational arithmetic, not rounded decimals. - S134 · premise_and_result_audit — Recompute Exp convolution right5 factorial step9 with exact rational arithmetic, not rounded decimals. - S133 · premise_and_result_audit — Recompute Exp convolution right5 factorial step8 with exact rational arithmetic, not rounded decimals. - S132 · premise_and_result_audit — Recompute Exp convolution right5 factorial step7 with exact rational arithmetic, not rounded decimals. - S131 · premise_and_result_audit — Recompute Exp convolution right5 factorial step6 with exact rational arithmetic, not rounded decimals. - S130 · premise_and_result_audit — Recompute Exp convolution right5 factorial step5 with exact rational arithmetic, not rounded decimals. - S129 · premise_and_result_audit — Recompute Exp convolution right5 factorial step4 with exact rational arithmetic, not rounded decimals. - S128 · premise_and_result_audit — Recompute Exp convolution right5 factorial step3 with exact rational arithmetic, not rounded decimals. - S127 · premise_and_result_audit — Recompute Exp convolution right5 factorial step2 with exact rational arithmetic, not rounded decimals. - S126 · premise_and_result_audit — Recompute Exp convolution right5 factorial step1 with exact rational arithmetic, not rounded decimals. - S125 · premise_and_result_audit — Recompute Exp convolution left5 factorial step5 with exact rational arithmetic, not rounded decimals. - S124 · premise_and_result_audit — Recompute Exp convolution left5 factorial step4 with exact rational arithmetic, not rounded decimals. - S123 · premise_and_result_audit — Recompute Exp convolution left5 factorial step3 with exact rational arithmetic, not rounded decimals. - S122 · premise_and_result_audit — Recompute Exp convolution left5 factorial step2 with exact rational arithmetic, not rounded decimals. - S121 · premise_and_result_audit — Recompute Exp convolution left5 factorial step1 with exact rational arithmetic, not rounded decimals. - S120 · premise_and_result_audit — Recompute Exp convolution numerator5 with exact rational arithmetic, not rounded decimals. - S119 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S118 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S117 · premise_and_result_audit — Recompute Exp convolution coefficient term4 with exact rational arithmetic, not rounded decimals. - S116 · premise_and_result_audit — Recompute Exp convolution denominator4 with exact rational arithmetic, not rounded decimals. - S115 · premise_and_result_audit — Recompute Exp convolution right4 factorial step14 with exact rational arithmetic, not rounded decimals. - S114 · premise_and_result_audit — Recompute Exp convolution right4 factorial step13 with exact rational arithmetic, not rounded decimals. - S113 · premise_and_result_audit — Recompute Exp convolution right4 factorial step12 with exact rational arithmetic, not rounded decimals. - S112 · premise_and_result_audit — Recompute Exp convolution right4 factorial step11 with exact rational arithmetic, not rounded decimals. - S111 · premise_and_result_audit — Recompute Exp convolution right4 factorial step10 with exact rational arithmetic, not rounded decimals. - S110 · premise_and_result_audit — Recompute Exp convolution right4 factorial step9 with exact rational arithmetic, not rounded decimals. - S109 · premise_and_result_audit — Recompute Exp convolution right4 factorial step8 with exact rational arithmetic, not rounded decimals. - S108 · premise_and_result_audit — Recompute Exp convolution right4 factorial step7 with exact rational arithmetic, not rounded decimals. - S107 · premise_and_result_audit — Recompute Exp convolution right4 factorial step6 with exact rational arithmetic, not rounded decimals. - S106 · premise_and_result_audit — Recompute Exp convolution right4 factorial step5 with exact rational arithmetic, not rounded decimals. - S105 · premise_and_result_audit — Recompute Exp convolution right4 factorial step4 with exact rational arithmetic, not rounded decimals. - S104 · premise_and_result_audit — Recompute Exp convolution right4 factorial step3 with exact rational arithmetic, not rounded decimals. - S103 · premise_and_result_audit — Recompute Exp convolution right4 factorial step2 with exact rational arithmetic, not rounded decimals. - S102 · premise_and_result_audit — Recompute Exp convolution right4 factorial step1 with exact rational arithmetic, not rounded decimals. - S101 · premise_and_result_audit — Recompute Exp convolution left4 factorial step4 with exact rational arithmetic, not rounded decimals. - S100 · premise_and_result_audit — Recompute Exp convolution left4 factorial step3 with exact rational arithmetic, not rounded decimals. - S099 · premise_and_result_audit — Recompute Exp convolution left4 factorial step2 with exact rational arithmetic, not rounded decimals. - S098 · premise_and_result_audit — Recompute Exp convolution left4 factorial step1 with exact rational arithmetic, not rounded decimals. - S097 · premise_and_result_audit — Recompute Exp convolution numerator4 with exact rational arithmetic, not rounded decimals. - S096 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S095 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S094 · premise_and_result_audit — Recompute Exp convolution coefficient term3 with exact rational arithmetic, not rounded decimals. - S093 · premise_and_result_audit — Recompute Exp convolution denominator3 with exact rational arithmetic, not rounded decimals. - S092 · premise_and_result_audit — Recompute Exp convolution right3 factorial step15 with exact rational arithmetic, not rounded decimals. - S091 · premise_and_result_audit — Recompute Exp convolution right3 factorial step14 with exact rational arithmetic, not rounded decimals. - S090 · premise_and_result_audit — Recompute Exp convolution right3 factorial step13 with exact rational arithmetic, not rounded decimals. - S089 · premise_and_result_audit — Recompute Exp convolution right3 factorial step12 with exact rational arithmetic, not rounded decimals. - S088 · premise_and_result_audit — Recompute Exp convolution right3 factorial step11 with exact rational arithmetic, not rounded decimals. - S087 · premise_and_result_audit — Recompute Exp convolution right3 factorial step10 with exact rational arithmetic, not rounded decimals. - S086 · premise_and_result_audit — Recompute Exp convolution right3 factorial step9 with exact rational arithmetic, not rounded decimals. - S085 · premise_and_result_audit — Recompute Exp convolution right3 factorial step8 with exact rational arithmetic, not rounded decimals. - S084 · premise_and_result_audit — Recompute Exp convolution right3 factorial step7 with exact rational arithmetic, not rounded decimals. - S083 · premise_and_result_audit — Recompute Exp convolution right3 factorial step6 with exact rational arithmetic, not rounded decimals. - S082 · premise_and_result_audit — Recompute Exp convolution right3 factorial step5 with exact rational arithmetic, not rounded decimals. - S081 · premise_and_result_audit — Recompute Exp convolution right3 factorial step4 with exact rational arithmetic, not rounded decimals. - S080 · premise_and_result_audit — Recompute Exp convolution right3 factorial step3 with exact rational arithmetic, not rounded decimals. - S079 · premise_and_result_audit — Recompute Exp convolution right3 factorial step2 with exact rational arithmetic, not rounded decimals. - S078 · premise_and_result_audit — Recompute Exp convolution right3 factorial step1 with exact rational arithmetic, not rounded decimals. - S077 · premise_and_result_audit — Recompute Exp convolution left3 factorial step3 with exact rational arithmetic, not rounded decimals. - S076 · premise_and_result_audit — Recompute Exp convolution left3 factorial step2 with exact rational arithmetic, not rounded decimals. - S075 · premise_and_result_audit — Recompute Exp convolution left3 factorial step1 with exact rational arithmetic, not rounded decimals. - S074 · premise_and_result_audit — Recompute Exp convolution numerator3 with exact rational arithmetic, not rounded decimals. - S073 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S072 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S071 · premise_and_result_audit — Recompute Exp convolution coefficient term2 with exact rational arithmetic, not rounded decimals. - S070 · premise_and_result_audit — Recompute Exp convolution denominator2 with exact rational arithmetic, not rounded decimals. - S069 · premise_and_result_audit — Recompute Exp convolution right2 factorial step16 with exact rational arithmetic, not rounded decimals. - S068 · premise_and_result_audit — Recompute Exp convolution right2 factorial step15 with exact rational arithmetic, not rounded decimals. - S067 · premise_and_result_audit — Recompute Exp convolution right2 factorial step14 with exact rational arithmetic, not rounded decimals. - S066 · premise_and_result_audit — Recompute Exp convolution right2 factorial step13 with exact rational arithmetic, not rounded decimals. - S065 · premise_and_result_audit — Recompute Exp convolution right2 factorial step12 with exact rational arithmetic, not rounded decimals. - S064 · premise_and_result_audit — Recompute Exp convolution right2 factorial step11 with exact rational arithmetic, not rounded decimals. - S063 · premise_and_result_audit — Recompute Exp convolution right2 factorial step10 with exact rational arithmetic, not rounded decimals. - S062 · premise_and_result_audit — Recompute Exp convolution right2 factorial step9 with exact rational arithmetic, not rounded decimals. - S061 · premise_and_result_audit — Recompute Exp convolution right2 factorial step8 with exact rational arithmetic, not rounded decimals. - S060 · premise_and_result_audit — Recompute Exp convolution right2 factorial step7 with exact rational arithmetic, not rounded decimals. - S059 · premise_and_result_audit — Recompute Exp convolution right2 factorial step6 with exact rational arithmetic, not rounded decimals. - S058 · premise_and_result_audit — Recompute Exp convolution right2 factorial step5 with exact rational arithmetic, not rounded decimals. - S057 · premise_and_result_audit — Recompute Exp convolution right2 factorial step4 with exact rational arithmetic, not rounded decimals. - S056 · premise_and_result_audit — Recompute Exp convolution right2 factorial step3 with exact rational arithmetic, not rounded decimals. - S055 · premise_and_result_audit — Recompute Exp convolution right2 factorial step2 with exact rational arithmetic, not rounded decimals. - S054 · premise_and_result_audit — Recompute Exp convolution right2 factorial step1 with exact rational arithmetic, not rounded decimals. - S053 · premise_and_result_audit — Recompute Exp convolution left2 factorial step2 with exact rational arithmetic, not rounded decimals. - S052 · premise_and_result_audit — Recompute Exp convolution left2 factorial step1 with exact rational arithmetic, not rounded decimals. - S051 · premise_and_result_audit — Recompute Exp convolution numerator2 with exact rational arithmetic, not rounded decimals. - S050 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S049 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S048 · premise_and_result_audit — Recompute Exp convolution coefficient term1 with exact rational arithmetic, not rounded decimals. - S047 · premise_and_result_audit — Recompute Exp convolution denominator1 with exact rational arithmetic, not rounded decimals. - S046 · premise_and_result_audit — Recompute Exp convolution right1 factorial step17 with exact rational arithmetic, not rounded decimals. - S045 · premise_and_result_audit — Recompute Exp convolution right1 factorial step16 with exact rational arithmetic, not rounded decimals. - S044 · premise_and_result_audit — Recompute Exp convolution right1 factorial step15 with exact rational arithmetic, not rounded decimals. - S043 · premise_and_result_audit — Recompute Exp convolution right1 factorial step14 with exact rational arithmetic, not rounded decimals. - S042 · premise_and_result_audit — Recompute Exp convolution right1 factorial step13 with exact rational arithmetic, not rounded decimals. - S041 · premise_and_result_audit — Recompute Exp convolution right1 factorial step12 with exact rational arithmetic, not rounded decimals. - S040 · premise_and_result_audit — Recompute Exp convolution right1 factorial step11 with exact rational arithmetic, not rounded decimals. - S039 · premise_and_result_audit — Recompute Exp convolution right1 factorial step10 with exact rational arithmetic, not rounded decimals. - S038 · premise_and_result_audit — Recompute Exp convolution right1 factorial step9 with exact rational arithmetic, not rounded decimals. - S037 · premise_and_result_audit — Recompute Exp convolution right1 factorial step8 with exact rational arithmetic, not rounded decimals. - S036 · premise_and_result_audit — Recompute Exp convolution right1 factorial step7 with exact rational arithmetic, not rounded decimals. - S035 · premise_and_result_audit — Recompute Exp convolution right1 factorial step6 with exact rational arithmetic, not rounded decimals. - S034 · premise_and_result_audit — Recompute Exp convolution right1 factorial step5 with exact rational arithmetic, not rounded decimals. - S033 · premise_and_result_audit — Recompute Exp convolution right1 factorial step4 with exact rational arithmetic, not rounded decimals. - S032 · premise_and_result_audit — Recompute Exp convolution right1 factorial step3 with exact rational arithmetic, not rounded decimals. - S031 · premise_and_result_audit — Recompute Exp convolution right1 factorial step2 with exact rational arithmetic, not rounded decimals. - S030 · premise_and_result_audit — Recompute Exp convolution right1 factorial step1 with exact rational arithmetic, not rounded decimals. - S029 · premise_and_result_audit — Recompute Exp convolution left1 factorial step1 with exact rational arithmetic, not rounded decimals. - S028 · premise_and_result_audit — Recompute Exp convolution numerator1 with exact rational arithmetic, not rounded decimals. - S027 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S025 · premise_and_result_audit — Recompute Exp convolution coefficient term0 with exact rational arithmetic, not rounded decimals. - S024 · premise_and_result_audit — Recompute Exp convolution denominator0 with exact rational arithmetic, not rounded decimals. - S023 · premise_and_result_audit — Recompute Exp convolution right0 factorial step18 with exact rational arithmetic, not rounded decimals. - S022 · premise_and_result_audit — Recompute Exp convolution right0 factorial step17 with exact rational arithmetic, not rounded decimals. - S021 · premise_and_result_audit — Recompute Exp convolution right0 factorial step16 with exact rational arithmetic, not rounded decimals. - S020 · premise_and_result_audit — Recompute Exp convolution right0 factorial step15 with exact rational arithmetic, not rounded decimals. - S019 · premise_and_result_audit — Recompute Exp convolution right0 factorial step14 with exact rational arithmetic, not rounded decimals. - S018 · premise_and_result_audit — Recompute Exp convolution right0 factorial step13 with exact rational arithmetic, not rounded decimals. - S017 · premise_and_result_audit — Recompute Exp convolution right0 factorial step12 with exact rational arithmetic, not rounded decimals. - S016 · premise_and_result_audit — Recompute Exp convolution right0 factorial step11 with exact rational arithmetic, not rounded decimals. - S015 · premise_and_result_audit — Recompute Exp convolution right0 factorial step10 with exact rational arithmetic, not rounded decimals. - S014 · premise_and_result_audit — Recompute Exp convolution right0 factorial step9 with exact rational arithmetic, not rounded decimals. - S013 · premise_and_result_audit — Recompute Exp convolution right0 factorial step8 with exact rational arithmetic, not rounded decimals. - S012 · premise_and_result_audit — Recompute Exp convolution right0 factorial step7 with exact rational arithmetic, not rounded decimals. - S011 · premise_and_result_audit — Recompute Exp convolution right0 factorial step6 with exact rational arithmetic, not rounded decimals. - S010 · premise_and_result_audit — Recompute Exp convolution right0 factorial step5 with exact rational arithmetic, not rounded decimals. - S009 · premise_and_result_audit — Recompute Exp convolution right0 factorial step4 with exact rational arithmetic, not rounded decimals. - S008 · premise_and_result_audit — Recompute Exp convolution right0 factorial step3 with exact rational arithmetic, not rounded decimals. - S007 · premise_and_result_audit — Recompute Exp convolution right0 factorial step2 with exact rational arithmetic, not rounded decimals. - S006 · premise_and_result_audit — Recompute Exp convolution right0 factorial step1 with exact rational arithmetic, not rounded decimals. - S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S004 · premise_and_result_audit — Recompute Exp convolution numerator0 with exact rational arithmetic, not rounded decimals. - S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. ## Result (19/20, -20/21, 18, [[0, 32000000000000000/493058422447458087543290824655799], [1, -3040000000000000/2608774721944222685414237167491], [2, 72200000000000/7307492218331155981552485063], [3, -54872000000000/1043927459761593711650355009], [4, 3258025000000/16570277139072916057942143], [5, -61902475000/112722973735189905156069], [6, 5880735125/4954855988359995831036], [7, -4469358695/2202158217048887036016], [8, 16983563041/6101217571044535511040], [9, -322687697779/104592301217906323046400], [10, 6131066257801/2213593676569445990400000], [11, -116490258898219/57975072481580728320000000], [12, 2213314919066161/1893063591235289088000000000], [13, -42052983462257059/78126433923996057600000000000], [14, 799006685782884121/4166743142613123072000000000000], [15, -15181127029874798299/297624510186651648000000000000000], [16, 288441413567621167681/30234870876104294400000000000000000], [17, -5480386857784802185939/4895169570416885760000000000000000000], [18, 104127350297911241532841/1678343852714360832000000000000000000000]], 1/1058834899714592382164569538056763580874752000000000000000000000, 1/1058834899714592382164569538056763580874752000000000000000000000, Yes, binomial_convolution_matches_the_declared_degree;the_general_addition_law_requires_all_degrees_plus_absolute_convergence_for_Cauchy_product_rearrangement) The full substitutions and premise checks give the original answer; source identity,format and status are unchanged. ## This question review and source binding Review date: 2026-10-26 Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: c6a3353662dbbb75f71a71548cd65c303de2eaf033a4bbe196d50f63e67731fa - candidate record SHA-256: 695ef415a0a245ed49bf6dfd0f04f07062738b38979685e354c1e171954c412b - semantic review receipt SHA-256: 9b43b9823e9bd2478d6caa5b57ffed161c2c8956af86974e901d5662ad994386 - question-first witness SHA-256: eb97596068e2d5648033bab2b8f6ca9b653bbe8cb77c0f8e1d16d0c40e46f50b - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261113-r02-real-exponential-function-0069.json)