Theorems · Theorem · commutative algebra
Finset.gcd_image
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α]
{f : β → α} [inst_2 : DecidableEq β] {g : γ → β} (s : Finset γ), (Finset.image g s).gcd f = s.gcd (f ∘ g)- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.imagestatement and proof · cited by 910
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdproof · cited by 143
- Finset.inductionproof · cited by 108
- Finset.gcdstatement and proof · cited by 49
- Finset.image_insertproof · cited by 14
- Finset.gcd_insertproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Finset.gcd_eq_gcd_imageproof · cited by 2