{"slug":"hunter-logic-says-ergo-i-say","identifier":"hunter-logic-says-ergo-i-say","title":"Logic Says Ergo I Say by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"4b6e16998317bfdf749f11f102a02813253d6a9845198ef6b2582a08d21dd3b7","sourceKind":"authored-foundational-record","recordedAt":"2026-10-03T01:33:20.077Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:39:26.561Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2","HunterAuthored.inference_3","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{P, P <-> Q, Q} |= P & Q","sourceOffset":313,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q"],"premises":["P","P <-> Q","Q"],"conclusion":"P & Q","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 : Bool) :\n    ((!((v0 && (v0 == v1)) && v1)) || (v0 && v1)) = true := by\n  cases v0 <;> cases v1 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{T, P <-> Q, Q <-> R, R <-> S, S <-> T} |= ((P & Q) <-> (R & S)) <-> T","sourceOffset":3210,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q","R","S","T"],"premises":["T","P <-> Q","Q <-> R","R <-> S","S <-> T"],"conclusion":"((P & Q) <-> (R & S)) <-> T","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 v3 v4 : Bool) :\n    ((!((((v4 && (v0 == v1)) && (v1 == v2)) && (v2 == v3)) && (v3 == v4))) || (((v0 && v1) == (v2 && v3)) == v4)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"},{"id":"inference_3","sourceStatement":"{P, Q} |= P <-> Q","sourceOffset":4827,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q"],"premises":["P","Q"],"conclusion":"P <-> Q","status":"candidate","leanStatement":"theorem inference_3 (v0 v1 : Bool) :\n    ((!(v0 && v1)) || (v0 == v1)) = true := by\n  cases v0 <;> cases v1 <;> decide\n#print axioms inference_3\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_3"},{"id":"source_identity_rule","sourceStatement":"A is A","sourceOffset":2580,"scope":"The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.","status":"candidate","variables":[],"premises":[],"conclusion":"∀ (α : Type) (a : α), a = a","leanStatement":"theorem source_identity_rule (α : Type) (a : α) : a = a := rfl\n#print axioms source_identity_rule\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.source_identity_rule"}],"files":{"source.json":{"sha256":"c5b4e951789315ff2c074f44d394a3b741452d0ae94fe2d1e015e22685228dd8","bytes":7130},"Proof.lean":{"sha256":"d6255d5feab752fdee2a475dab56bb3aa49205f21ff63a52d9c88915f0f816ce","bytes":973},"lean-check.txt":{"sha256":"b2a13c78d5e07cc13897edfa6e4ad95b717a32423f43c97d6c342c394c93869c","bytes":301}},"boundary":"Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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