{"slug":"formal-or-commutativity-magnitude-distinct","identifier":"formal-or-commutativity-magnitude-distinct","title":"OR Commutativity (magnitude distinct)","author":"Maclain Hunter","sourceSha256":"f8adb9da481011e9f218974a409c94ed6c905eddd1691e67b560e0befa5f9151","sourceKind":"formal-theorem","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:48.702Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.distinct_magnitude_or_commutative"],"units":[{"id":"distinct_magnitude_or_commutative","sourceStatement":"Formal statement: ∀a,b ∈ MCBExponent, |a| ≠ |b|: OR(a,b) = OR(b,a)","sourceOffset":0,"scope":"Exact value selection by dominant integer magnitude with the authored first-operand tie behavior. The theorem retains the distinct-magnitude premise.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"def dominantValue (a b : Int) : Int := if a.natAbs < b.natAbs then b else a\ntheorem distinct_magnitude_or_commutative (a b : Int) (distinct : a.natAbs ≠ b.natAbs) :\n    dominantValue a b = dominantValue b a := by\n  unfold dominantValue\n  cases Nat.lt_or_gt_of_ne distinct with\n  | inl h =>\n    rw [if_pos h, if_neg (Nat.not_lt_of_ge (Nat.le_of_lt h))]\n  | inr h =>\n    rw [if_neg (Nat.not_lt_of_ge (Nat.le_of_lt h)), if_pos h]\n#print axioms distinct_magnitude_or_commutative\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.distinct_magnitude_or_commutative"}],"files":{"source.json":{"sha256":"6c1b82aa2e0e0873c4b38fc18a8b7db4908e0b5acad499b28a0568fe22ce6e13","bytes":808},"Proof.lean":{"sha256":"b0c15317a2d9e62e23680b67fcc32fc49c6ec4b063f5a507e8855de82d151c35","bytes":766},"lean-check.txt":{"sha256":"5116ad4c433e048236e59be62f2dcb314a2a657cdb57bd38e0d255d32350c165","bytes":137}},"boundary":"Lean establishes the listed formal statements and dependencies. 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