Theorems · Theorem · commutative algebra
MulEquiv.prime_iff
∀ {M : Type u_1} {N : Type u_2} [inst : CommMonoidWithZero M] [inst_1 : CommMonoidWithZero N] {p : M} {E : Type u_5}
[inst_2 : EquivLike E M N] [MulEquivClass E M N] (e : E), Prime (e p) ↔ Prime p- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MulEquivproof · cited by 1,142
- CommMonoidWithZerostatement and proof · cited by 913
- MulEquiv.symmproof · cited by 482
- Primestatement and proof · cited by 277
- EquivLikestatement and proof · cited by 165
- MulEquivClass.toMulEquivproof · cited by 57
- MulEquiv.apply_symm_applyproof · cited by 37
- MulEquivClassstatement and proof · cited by 30
- MulEquiv.symm_apply_applyproof · cited by 17
- comap_primeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MulEquiv.uniqueFactorizationMonoidproof · cited by 3