gcd_fortyfive_threehundredsixty
plain-language theorem explainer
The declaration establishes that the greatest common divisor of 45 and 360 equals 45. Number theorists handling divisor reductions inside the arithmetic functions layer of Recognition Science would cite this identity during simplification. The proof applies a direct computational decision procedure that evaluates the equality without manual reduction steps.
Claim. $ gcd(45, 360) = 45 $
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. Local conventions keep statements minimal to allow later layering of Dirichlet algebra and inversion once interfaces stabilize. No upstream lemmas are invoked.
proof idea
A one-line wrapper applies the native_decide tactic to compute and verify the gcd equality directly.
why it matters
The identity supplies a basic arithmetic foothold inside the arithmetic functions module. It supports potential divisor simplifications in prime-related contexts without linking to framework landmarks such as the forcing chain steps T5-T8 or the Recognition Composition Law. No downstream theorems reference it.
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