Theorems · Theorem · commutative algebra
ne_zero_or_ne_zero_of_nat_coprime
∀ {A : Type u} [inst : CommRing A] [Nontrivial A] {a b : ℕ}, a.Coprime b → ↑a ≠ 0 ∨ ↑b ≠ 0- Defined in
- Mathlib.RingTheory.Coprime.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNontrivial
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Nontrivialstatement and proof · cited by 2,416
- IsCoprimeproof · cited by 321
- Int.castRingHomproof · cited by 254
- map_natCastproof · cited by 134
- Nat.Coprime.isCoprimeproof · cited by 6
- IsCoprime.mapproof · cited by 2
- IsCoprime.ne_zero_or_ne_zeroproof · cited by 1
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