Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 checked theorem statements.
Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.
Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.
Source registered: 2026-10-02T18:42:10.003Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:10.288Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 0550ab97e05f6295c562b6ca710f0f354754ea2ef0d58758bbeb6b6a8b112215
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) exitCode=0 'HunterAuthored.inference_1' does not depend on any axioms
{P, Q, R} |= (P & Q) <-> (R -> (P <-> Q))
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.
Everything is Proof by Maclain Hunter
Premises:
P: All things prove something.
Q: Even the complete lack of proof would ironically prove that God (the Logos - the self-evident Logic of Reality that proof comes from) doesn’t exist - thus making it impossible for a complete lack of proof to exist (as it still proves something).
R: Assume the negation of the premises and that everything (or each thing) did not prove everything or something (or each thing). Assume also that the complete lack of proof was both possible and didn’t prove anything (in a paradoxical fashion).
Logical Argument:
{P, Q, R} |= (P & Q) <-> (R -> (P <-> Q))
Conclusion: {P, Q, R}:
All things are proof of something (and everything), in some way, and through some feasible valid argument, even the absurd hypothetical of the “complete lack of proof” (in the Cosmos). We can deduce this with certainty and prove it rigorously through the exploration of the assumption of the negation of the premises P and Q.
This assumption leads not only to the contradiction of logical rules but to the absurdity where “everything” did not include proof for everything or the conceivable/possible concept of everything being proof for everything (and each thing for each thing).
It also leads to the absurdity where you would have to deny this proof is this proof, which is tautological and irrefutable as a matter of identity and calculable logical structure, to accept “not Q”.
This shows why we must accept the premises and their conjunction to satisfy Logic and avoid contradiction - regardless of the positions and subjective views of any other school(s) of thought or individual(s).
Therefore we can conclude that this conclusion not only follows necessarily from the premises “if” the premises are rationally accepted, but that the premises are themselves logical truths that cannot coherently be “rationally denied”.
Truth Table Analysis:
PQR⎪P Q R╞(P&Q)↔(R→(P↔Q))
TTT⎪T T T TTT T TT TTT
TTF⎪T T F TTT T FT TTT
TFT⎪T F T TFF T TF TFF
TFF⎪T F F TFF F FT TFF
FTT⎪F T T FFT T TF FFT
FTF⎪F T F FFT F FT FFT
FFT⎪F F T FFF F TT FTF
FFF⎪F F F FFF F FT FTF
Q.E.D.