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Copyright 2025 The Formal Conjectures Authors.
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-/
module
public import Batteries.Data.Nat.Gcd
public import Mathlib.Algebra.GCDMonoid.Finset
public import Mathlib.Algebra.GCDMonoid.Nat@[expose] public section
A Finset of numbers is coprime, or relatively prime, if its gcd is 1.
@[reducible] def Finset.Coprime (S : Finset ℕ) : Prop := S.gcd id = 1theorem Finset.Coprime_pair_iff (S : Finset ℕ) (a b : ℕ) (h : S = {a, b}) :
S.Coprime ↔ Nat.Coprime a b := S:Finset ℕa:ℕb:ℕh:S = {a, b}⊢ S.Coprime ↔ a.Coprime b
S:Finset ℕa:ℕb:ℕh:S = {a, b}⊢ GCDMonoid.gcd (id a) (id b) = 1 ↔ a.gcd b = 1
All goals completed! 🐙