Theorems · Theorem · group theory
AddSubmonoid.LocalizationMap.map_injective_of_surjOn_or_injective
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N] {P : Type u_3}
[inst_2 : AddCommMonoid P] (f : S.LocalizationMap N) {g : M →+ P} {T : AddSubmonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T)
{Q : Type u_4} [inst_3 : AddCommMonoid Q] {k : T.LocalizationMap Q},
Set.SurjOn ⇑g ↑S ↑T ∨ Function.Injective ⇑k → Function.Injective ⇑g → Function.Injective ⇑(f.map hy k)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- SetLike.coestatement and proof · cited by 8,199
- AddMonoidHomstatement and proof · cited by 3,230
- AddSubmonoidstatement and proof · cited by 1,178
- map_addproof · cited by 964
- Set.SurjOnstatement and proof · cited by 186
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- AddSubmonoid.LocalizationMap.map_addUnitsproof · cited by 36
- AddSubmonoid.LocalizationMap.mapstatement and proof · cited by 15
- IsAddUnit.add_left_injproof · cited by 8
- AddSubmonoid.LocalizationMap.eq_iff_existsproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.map_injective_of_injectiveproof · cited by 0