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R0018-09973 · q-20261013-advance-20261019-r07-lean-proof-term-0023
Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h22","type":"P22"},{"name":"q22","type":"Q22"}], term={"kind":"pair","left":{"kind":"var","name":"h22"},"right":{"kind":"var","name":"q22"}}, claimed_type=["and","P22","Q22"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).
G001 — Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Context=[{"name":"h22","type":"P22"},{"name":"q22","type":"Q22"}], term={"kind":"pair","left":{"kind":"var","name":"h22"},"right":{"kind":"var","name":"q22"}}, claimed_type=["and","P22","Q22"]. Atomic types are uppercase names; [imp,A,B] and [and,A,B] are implication and conjunction. Terms use var, lam, app, pair, fst, snd; this toy rule forbids rebinding a context name. Give (inferred type, claimed type, exact type match?).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.
Before
synthetic proposition/term calculus or supplied synthetic receipt
After
no actual Lean build,source-digest check or kernel acceptance
Conditions: none
Apply only the specified small calculus or synthetic receipt protocol.Statement,tactic completion,term presence and kernel acceptance are separate.No Lean is run and the teaching guide is not promoted to a formal proof.
Rule: synthetic_proofterm_not_actual_kernel · Uses: G001
Before
raw context=[{"name":"h22","type":"P22"},{"name":"q22","type":"Q22"}]After
validated English-locale context=[["h22","P22"],["q22","Q22"]]
Conditions: none
Validate every context name and type,reject duplicates,and display in the specified English order without translating opaque names.
Rule: synthetic_whole_context_validation · Uses: G001, S001
Before
path=root/left;term={"kind":"var","name":"h22"};context=[["h22","P22"],["q22","Q22"]]After
variable lookup type=P22
Conditions: none
Look up the exact name in the current lexical context.Do not treat a similar name or a missing binding as an assumption.
Rule: synthetic_variable_typing · Uses: G001, S002
Before
path=root/right;term={"kind":"var","name":"q22"};context=[["h22","P22"],["q22","Q22"]]After
variable lookup type=Q22
Conditions: none
Look up the exact name in the current lexical context.Do not treat a similar name or a missing binding as an assumption.
Rule: synthetic_variable_typing · Uses: G001, S003
Before
path=root;term={"kind":"pair","left":{"kind":"var","name":"h22"},"right":{"kind":"var","name":"q22"}};context=[["h22","P22"],["q22","Q22"]];left type=P22;right type=Q22After
conjunction introduction type=[and, P22, Q22]
Conditions: none
The two subterms have types A and B,so the ordered pair has type A∧B.Preserve component order.
Rule: synthetic_pair_conjunction_intro · Uses: G001, S004
Before
inferred type=[and, P22, Q22];declared claim=[and, P22, Q22]
After
exact structural type match=Yes
Conditions: none
Compare the inferred type structurally with the claim.Do not fill the inference from the claim.A match belongs only to this synthetic calculus.
Rule: synthetic_claim_checked_not_assumed · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.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 — Check against the original data and this step's premises; a one-way implication is not an equivalence.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.([and, P22, Q22], [and, P22, Q22], Yes)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
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.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 30a2a7d32ef79b6cb7384b44d4848b8d73f87b56ff797b6aca76b74058c9d9bacandidate record SHA-256: 5f66dff864b39945d5f97887aa488f227bcd0b82afb63eb5e1023e4e05a44747semantic review receipt SHA-256: bd35da62087a15d6b89b45585dc46e89b9efbe097cba7b3c707b5030496f013cquestion-first witness SHA-256: fab45a10d8ac95c7d61d32e47d1bdd3ca862c17c3289a6bf4b01d4dc9492fbb6Lean: NOT_RUN · human review: NOT_PERFORMED