gcd_8_45_eq_one
plain-language theorem explainer
The lemma asserts that the greatest common divisor of 8 and 45 is exactly 1. Researchers handling rung-specific divisibility in the phi-ladder of Recognition Science would cite it when resolving coprimality constraints for gap calculations. The proof is a one-line wrapper that invokes the decide tactic to evaluate the equality by direct computation.
Claim. $gcd(8,45)=1$
background
The Gap45 module collects divisibility and coprimality facts among small integers that appear in rung-45 conflict analysis. Its opening note records that 9 and 5 are coprime, supplying the arithmetic setting in which 45 factors as their product. The declaration imports only Mathlib and depends on the identical statement already present in the Beat submodule.
proof idea
The proof is a one-line wrapper that applies the decide tactic to compute Nat.gcd 8 45 and confirm the result equals 1.
why it matters
This fact feeds the rung45_first_conflict lemma inside the same module and thereby supports the larger chain of coprimality checks required for the phi-ladder mass formula. It aligns with the framework's use of coprime pairs when deriving the eight-tick octave (T7) and spatial dimension D=3 (T8). No open scaffolding remains for this specific equality.
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