Theorems · Theorem · commutative algebra
IsCoprime.ne_zero_or_ne_zero
∀ {R : Type u} [inst : CommSemiring R] {x y : R} [Nontrivial R], IsCoprime x y → x ≠ 0 ∨ y ≠ 0- Defined in
- Mathlib.RingTheory.Coprime.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNontrivial
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.
- CommSemiringstatement and proof · cited by 10,911
- Nontrivialstatement and proof · cited by 2,416
- IsCoprimestatement and proof · cited by 321
- not_or_of_impproof · cited by 8
- not_isCoprime_zero_zeroproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ne_zero_or_ne_zero_of_nat_coprimeproof · cited by 0