Theorems · Theorem · commutative algebra
map_dvd_iff_dvd_symm
∀ {α : Type u_1} {β : Type u_2} [inst : Semigroup α] [inst_1 : Semigroup β] {F : Type u_3} [inst_2 : EquivLike F α β]
[inst_3 : MulEquivClass F α β] (f : F) {a : α} {b : β}, f a ∣ b ↔ a ∣ (↑f).symm b- Defined in
- Mathlib.Algebra.Ring.Divisibility.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- MulEquivstatement · cited by 1,142
- MulEquiv.symmstatement · cited by 482
- Semigroupstatement and proof · cited by 202
- EquivLikestatement and proof · cited by 165
- MulEquivClass.toMulEquivstatement · cited by 57
- MulEquivClassstatement and proof · cited by 30
- EquivLike.surjectiveproof · cited by 24
- MulEquivClass.coe_symm_apply_applyproof · cited by 3
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