Theorems · Theorem · commutative algebra
Multiset.gcd_eq_zero_iff
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizedGCDMonoid α] (s : Multiset α),
s.gcd = 0 ↔ ∀ x ∈ s, x = 0- Defined in
- Mathlib.Algebra.GCDMonoid.Multiset
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement and proof · cited by 2,627
- CommMonoidWithZerostatement and proof · cited by 913
- Multiset.consproof · cited by 313
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdproof · cited by 143
- Multiset.induction_onproof · cited by 109
- Multiset.mem_cons_selfproof · cited by 44
- Multiset.mem_cons_of_memproof · cited by 35
- Multiset.gcdstatement and proof · cited by 21
- normalize_zeroproof · cited by 16
- eq_zero_of_zero_dvdproof · cited by 13
- gcd_sameproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.extract_gcd'proof · cited by 1
- Multiset.extract_gcdproof · cited by 0