Theorems · Theorem · commutative algebra
Finset.gcd_union
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s₁ s₂ : Finset β}
{f : β → α} [inst_2 : DecidableEq β], (s₁ ∪ s₂).gcd f = gcd (s₁.gcd f) (s₂.gcd f)- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.induction_onproof · cited by 167
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdstatement and proof · cited by 143
- Finset.gcdstatement and proof · cited by 49
- Finset.insert_unionproof · cited by 16
- Finset.gcd_insertproof · cited by 9
- Finset.empty_unionproof · cited by 8
- Finset.normalize_gcdproof · cited by 6
- gcd_assocproof · cited by 3
- gcd_zero_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.gcd_eq_gcd_filter_ne_zeroproof · cited by 0