Theorems · Theorem · group theory
AddSubmonoid.LocalizationMap.eq_iff_exists
∀ {M : Type u_1} [inst : AddCommMonoid M] {S : AddSubmonoid M} {N : Type u_2} [inst_1 : AddCommMonoid N]
(f : S.LocalizationMap N) {x y : M}, f x = f y ↔ ∃ c, ↑c + x = ↑c + y- Cited by
- 8 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
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
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- map_addproof · cited by 964
- AddSubmonoid.LocalizationMapstatement and proof · cited by 119
- AddSubmonoid.LocalizationMap.map_addUnitsproof · cited by 36
- IsAddUnit.add_right_injproof · cited by 7
- AddSubmonoid.IsLocalizationMap.exists_of_eqproof · cited by 5
- AddSubmonoid.LocalizationMap.isLocalizationMapproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- AddSubmonoid.LocalizationMap.eq_of_eqproof · cited by 4
- AddSubmonoid.LocalizationMap.map_isAddRegularproof · cited by 1
- AddSubmonoid.LocalizationMap.eqproof · cited by 1
- AddSubmonoid.LocalizationMap.injective_iffproof · cited by 1
- AddSubmonoid.LocalizationMap.map_injective_of_surjOn_or_injectiveproof · cited by 1
- AddSubmonoid.LocalizationMap.eq_iff_eqproof · cited by 0
- AddSubmonoid.LocalizationMap.mk'_eq_of_sameproof · cited by 0
- AddSubmonoid.LocalizationMap.exists_of_sec_mk'proof · cited by 0