Theorems · Theorem · group theory
Submonoid.LocalizationMap.injective_iff
∀ {M : Type u_1} {N : Type u_2} [inst : CommMonoid M] {S : Submonoid M} [inst_1 : CommMonoid N]
(f : S.LocalizationMap N), Function.Injective ⇑f ↔ ∀ ⦃x : M⦄, x ∈ S → IsRegular x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Commute.allproof · cited by 119
- IsRegularstatement · cited by 116
- CommMagmaproof · cited by 57
- forall₂_commproof · cited by 28
- Commute.isRegular_iffproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.injective_iff_isRegularproof · cited by 1
- IsLocalization.injectiveₛproof · cited by 1