{"slug":"hunter-necessary-entailment","identifier":"hunter-necessary-entailment","title":"Necessary Entailment by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"7e101488b48dd99fff8e338b62c9bb1063d1a010bcb693cfe3635a8de298b990","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T18:42:14.750Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:32.439Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.inference_2","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{MP, MP <-> RP, RP <-> G, G <-> G, G} |= ((MP <-> RP) & (MP & RP)) & G","sourceOffset":1741,"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":["G","MP","RP"],"premises":["MP","MP <-> RP","RP <-> G","G <-> G","G"],"conclusion":"((MP <-> RP) & (MP & RP)) & G","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 : Bool) :\n    ((!((((v1 && (v1 == v2)) && (v2 == v0)) && (v0 == v0)) && v0)) || (((v1 == v2) && (v1 && v2)) && v0)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"inference_2","sourceStatement":"{MP, MP <-> RP, MP <-> MB, RP <-> RB, MB <-> RB, MB <-> RP, MP <-> RB, MP <-> RP, RP <-> C, MP <-> C, C <-> G, G <-> G, MP, MB, RP, RB, C, G} |= (((MP & RP) & (MB & RB)) & C) & G","sourceOffset":1980,"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":["C","G","MB","MP","RB","RP"],"premises":["MP","MP <-> RP","MP <-> MB","RP <-> RB","MB <-> RB","MB <-> RP","MP <-> RB","MP <-> RP","RP <-> C","MP <-> C","C <-> G","G <-> G","MP","MB","RP","RB","C","G"],"conclusion":"(((MP & RP) & (MB & RB)) & C) & G","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 v3 v4 v5 : Bool) :\n    ((!(((((((((((((((((v3 && (v3 == v5)) && (v3 == v2)) && (v5 == v4)) && (v2 == v4)) && (v2 == v5)) && (v3 == v4)) && (v3 == v5)) && (v5 == v0)) && (v3 == v0)) && (v0 == v1)) && (v1 == v1)) && v3) && v2) && v5) && v4) && v0) && v1)) || ((((v3 && v5) && (v2 && v4)) && v0) && v1)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"},{"id":"source_identity_rule","sourceStatement":"A is A","sourceOffset":1626,"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":"01f2189751813e38b68e616cad7f6823b262be331579d073c450d4e9c7385800","bytes":3517},"Proof.lean":{"sha256":"2bc4106aa4210f762b50eadc54e783f6545e4bf9fa44e8e4936921cae95c7095","bytes":1082},"lean-check.txt":{"sha256":"40b7da001d5d78d36b6960c8ae1b7c13a2ea6cf5f9da51ea55e40e490d78ea16","bytes":242}},"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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The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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