{"slug":"hunter-predicated-propositions","identifier":"hunter-predicated-propositions","title":"Predicated Propositions by Maclain Hunter","author":"Maclain Hunter","sourceSha256":"1fc220556e7ee9cb2acad47b8d76fed95f0130786811ccfc768e7637c5bdd0c1","sourceKind":"authored-foundational-record","recordedAt":"2026-10-02T16:41:32.429Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:53.955Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_2","HunterAuthored.inference_3","HunterAuthored.inference_4","HunterAuthored.inference_5","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{a} |= ~a","sourceOffset":2048,"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":["a"],"premises":["a"],"conclusion":"~a","status":"countermodel","countermodel":{"a":true},"reason":"The written sequent alone has a countermodel. No authored wording or unstated premise was changed.","kernelStatus":"not_checked"},{"id":"inference_2","sourceStatement":"{P, P -> Q, Q <-> R, R -> S} |= (P & Q) & (R & S)","sourceOffset":3900,"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"],"premises":["P","P -> Q","Q <-> R","R -> S"],"conclusion":"(P & Q) & (R & S)","status":"candidate","leanStatement":"theorem inference_2 (v0 v1 v2 v3 : Bool) :\n    ((!(((v0 && ((!v0) || v1)) && (v1 == v2)) && ((!v2) || v3))) || ((v0 && v1) && (v2 && v3))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_2\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_2"},{"id":"inference_3","sourceStatement":"{Q, Q -> R, R <-> S, S -> P} |= (Q & R) & (S & P)","sourceOffset":3951,"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"],"premises":["Q","Q -> R","R <-> S","S -> P"],"conclusion":"(Q & R) & (S & P)","status":"candidate","leanStatement":"theorem inference_3 (v0 v1 v2 v3 : Bool) :\n    ((!(((v1 && ((!v1) || v2)) && (v2 == v3)) && ((!v3) || v0))) || ((v1 && v2) && (v3 && v0))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_3\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_3"},{"id":"inference_4","sourceStatement":"{R, R -> S, S <-> P, P -> Q} |= (R & S) & (P & Q)","sourceOffset":4002,"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"],"premises":["R","R -> S","S <-> P","P -> Q"],"conclusion":"(R & S) & (P & Q)","status":"candidate","leanStatement":"theorem inference_4 (v0 v1 v2 v3 : Bool) :\n    ((!(((v2 && ((!v2) || v3)) && (v3 == v0)) && ((!v0) || v1))) || ((v2 && v3) && (v0 && v1))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_4\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_4"},{"id":"inference_5","sourceStatement":"{S, S -> P, P <-> Q, Q -> R} |= (S & P) & (Q & R)","sourceOffset":4053,"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"],"premises":["S","S -> P","P <-> Q","Q -> R"],"conclusion":"(S & P) & (Q & R)","status":"candidate","leanStatement":"theorem inference_5 (v0 v1 v2 v3 : Bool) :\n    ((!(((v3 && ((!v3) || v0)) && (v0 == v1)) && ((!v1) || v2))) || ((v3 && v0) && (v1 && v2))) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide\n#print axioms inference_5\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_5"},{"id":"source_identity_rule","sourceStatement":"a is a","sourceOffset":6982,"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":"885b4313e961fc292f6e27630c2683218590382c8fe4ba735b8f32b19417ff6b","bytes":10307},"Proof.lean":{"sha256":"156e8e59d7360d952f71fd620f8992c16b0e0cef536343e1faea340e5702a794","bytes":1353},"lean-check.txt":{"sha256":"502dfa0a316bec1881f2633a0810a079ab7a3c28d21ca804fa523d4be041735d","bytes":360}},"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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