Mathlib Map

Theorems · Theorem · commutative algebra

Multiset.gcd_singleton

∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {a : α}, {a}.gcd = normalize a
Defined in
Mathlib.Algebra.GCDMonoid.Multiset
Cited by
2 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidWithZeroNormalizedGCDMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.gcd_singleton · cited by 4Finset.gcd_singletonMultiset.extract_gcd · cited by 0Multiset.extract_gcdMultiset · cited by 2627MultisetCommMonoidWithZero · cited by 913CommMonoidWithZeroNormalizedGCDMonoid · cited by 159NormalizedGCDMonoidGCDMonoid.gcd · cited by 143GCDMonoid.gcdnormalize · cited by 137normalizeMultiset.gcd · cited by 21Multiset.gcdgcd_zero_right · cited by 3gcd_zero_rightMultiset.fold_singleton · cited by 2Multiset.fold_singletonMultiset.gcd_singletonCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.