Theorems · Theorem · commutative algebra
Finset.gcd_eq_zero_iff
∀ {α : Type u_2} {β : Type u_3} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] {s : Finset β}
{f : β → α}, s.gcd f = 0 ↔ ∀ x ∈ s, f x = 0- Defined in
- Mathlib.Algebra.GCDMonoid.Finset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- NormalizedGCDMonoidstatement and proof · cited by 159
- Finset.gcdstatement and proof · cited by 49
- Finset.cons_induction_onproof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.content_eq_zero_iffproof · cited by 7
- Rat.mulHeight_eq_max_abs_of_gcd_eq_oneproof · cited by 2
- Finset.gcd_div_eq_oneproof · cited by 1
- Finset.extract_gcdproof · cited by 1
- Finset.extract_gcd'proof · cited by 1