Theorems · Theorem · group theory
AddSubmonoid.IsLocalizationMap.map_zero
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N] {F : Type u_4}
[inst_2 : FunLike F M N] [AddHomClass F M N] {f : F}, S.IsLocalizationMap ⇑f → f 0 = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
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
- add_zeroproof · cited by 2,707
- FunLikestatement and proof · cited by 2,560
- AddSubmonoidstatement and proof · cited by 1,178
- map_addproof · cited by 964
- AddHomClassstatement and proof · cited by 65
- AddSubmonoid.IsLocalizationMapstatement and proof · cited by 18
- IsAddUnit.add_right_injproof · cited by 7
- AddSubmonoid.IsLocalizationMap.map_addUnitsproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.isLocalizationMap_iff_bijectiveproof · cited by 1