# Question 35600: Induction Proof Obligations [Return to catalogue page 178](https://ocme.evemisslab.com/en/questions/page/178/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20260914-domain-foundations/#q-20260914-induction-proof-obligation-0005) 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. R0070-35600 · q-20260914-induction-proof-obligation-0005 ## Original question and givens For a proposition family P(n) beginning at 0, a draft supplies base case, induction hypothesis, conclusion and checks 5 finite example(s). Which induction role is missing? - G001 — For a proposition family P(n) beginning at 0, a draft supplies base case, induction hypothesis, conclusion and checks 5 finite example(s). Which induction role is missing? ## 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-mathematical-induction](https://ocme.evemisslab.com/en/mko/mko-mathematical-induction/) ## Step-by-step derivation S001 · impliesBefore source roles = [qf-induction-proof-obligation, [base_index, finite_examples_checked, mode, provided_roles, step_relation, target_role]] After derived = [induction, null, null] Conditions: none Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules. Step identifiers and dependenciesRule: R70_SOURCE_bank_specific_interface · Uses: G001 S002 · impliesBefore source roles = [base_case] After derived = [prove P(0)] Conditions: none Keep induction roles distinct:P(0)is the proved start;the IH for arbitrary fixed n is a CONDITIONAL assumption,not the universal conclusion;the step derives the next case under that assumption;only then apply induction. Step identifiers and dependenciesRule: Induction_DEFINE_each_distinct_proof_obligation · Uses: G001, S001 S003 · impliesBefore source roles = [induction_hypothesis] After derived = [assume P(n) for arbitrary fixed n>=0] Conditions: none Keep induction roles distinct:P(0)is the proved start;the IH for arbitrary fixed n is a CONDITIONAL assumption,not the universal conclusion;the step derives the next case under that assumption;only then apply induction. Step identifiers and dependenciesRule: Induction_DEFINE_each_distinct_proof_obligation · Uses: G001, S002 S004 · impliesBefore source roles = [induction_step] After derived = [under that assumption derive P(n+1)] Conditions: none Keep induction roles distinct:P(0)is the proved start;the IH for arbitrary fixed n is a CONDITIONAL assumption,not the universal conclusion;the step derives the next case under that assumption;only then apply induction. Step identifiers and dependenciesRule: Induction_DEFINE_each_distinct_proof_obligation · Uses: G001, S003 S005 · impliesBefore source roles = [conclusion] After derived = [infer every n>=0 by induction after base and step] Conditions: none Keep induction roles distinct:P(0)is the proved start;the IH for arbitrary fixed n is a CONDITIONAL assumption,not the universal conclusion;the step derives the next case under that assumption;only then apply induction. Step identifiers and dependenciesRule: Induction_DEFINE_each_distinct_proof_obligation · Uses: G001, S004 S006 · impliesBefore source roles = [missing_role, [base_case, induction_hypothesis, conclusion]] After derived = [induction_step] Conditions: none For a missing-role task,subtract the THREE provided roles from all FOUR.For identification,use the SINGLE given clause’s role.Do not copy target_role instead of deriving it. Step identifiers and dependenciesRule: Induction_DERIVE_role_from_provided_draft · Uses: G001, S005 S007 · impliesBefore source roles = [5, induction_step] After derived = [role identified; arbitrary theorem NOT proved] Conditions: none These n FINITE examples neither prove all natural cases nor discharge a missing base/step.This task identifies an obligation;it does not prove an unspecified theorem P. Step identifiers and dependenciesRule: Induction_FINITE_examples_do_NOT_discharge_universal_obligation · Uses: G001, S006 ## Reverse checks - S007 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S006 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S005 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S004 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. - S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved. ## Result induction step 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: 6cdcf83ce1a3b6b39cdab4f8f350d3ff4f948a1cf8380e57160eed2a0bd65e36 - candidate record SHA-256: 72cfd459abd1991d883fa3cdf0f4c32f841f8e4dc460eabcf9856651dd91bab2 - semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80 - question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260914-induction-proof-obligation-0005.json)