Theorems · Theorem · group theory
AddSubmonoid.LocalizationMap.injective_iff
∀ {M : Type u_1} {N : Type u_2} [inst : AddCommMonoid M] {S : AddSubmonoid M} [inst_1 : AddCommMonoid N]
(f : S.LocalizationMap N), Function.Injective ⇑f ↔ ∀ ⦃x : M⦄, x ∈ S → IsAddRegular x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- IsAddRegularstatement · cited by 43
- AddCommMagmaproof · cited by 32
- forall₂_commproof · cited by 28
- AddCommute.allproof · cited by 12
- AddSubmonoid.LocalizationMap.eq_iff_existsproof · cited by 8
- AddCommute.isAddRegular_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.top_injective_iffproof · cited by 0