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Theorems · Theorem · group theory

AddSubmonoid.IsLocalizationMap.exists_of_eq

∀ {M : Type u_1} [inst : AddCommMonoid M] {N : Type u_2} [inst_1 : AddCommMonoid N] {S : AddSubmonoid M} {f : M → N},
  S.IsLocalizationMap f → ∀ {x y : M}, f x = f y → ∃ c, ↑c + x = ↑c + y
Defined in
Mathlib.GroupTheory.MonoidLocalization.Basic
Cited by
5 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
AddCommMonoidAddCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubmonoid.LocalizationMap.eq_iff_exists · cited by 8LocalizationMap.eq_iff_ex…AddSubmonoid.LocalizationMap.exists_of_eq · cited by 1LocalizationMap.exists_of…AddSubmonoid.isLocalizationMap_iff_bijective · cited by 1AddSubmonoid.isLocalizati…AddSubmonoid.IsLocalizationMap.pi · cited by 0IsLocalizationMap.piAddSubmonoid.IsLocalizationMap.addEquiv_comp · cited by 0IsLocalizationMap.addEqui…AddCommMonoid · cited by 12281AddCommMonoidAddSubmonoid · cited by 1178AddSubmonoidAddSubmonoid.IsLocalizationMap · cited by 18AddSubmonoid.IsLocalizati…IsLocalizationMap.exists_of_eqCITED BYCITES

Cites3

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Cited by5

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