Theorems · Theorem · commutative algebra
Prime.coprime_iff_not_dvd
∀ {R : Type u} [inst : CommRing R] [IsBezout R] [IsDomain R] {p n : R}, Prime p → (IsCoprime p n ↔ ¬p ∣ n)- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsDomainstatement and proof · cited by 2,196
- IsCoprimestatement · cited by 321
- Primestatement and proof · cited by 277
- Prime.irreducibleproof · cited by 54
- IsBezoutstatement and proof · cited by 23
- Irreducible.coprime_iff_not_dvdproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Int.ModEq.pow_card_sub_one_eq_oneproof · cited by 3
- ZMod.eq_zero_iff_gcd_ne_oneproof · cited by 2
- Int.ModEq.pow_eq_powproof · cited by 0