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Theorems · Theorem · group theory

Submonoid.IsLocalizationMap.exists_of_eq

∀ {M : Type u_1} [inst : CommMonoid M] {N : Type u_2} [inst_1 : CommMonoid N] {S : Submonoid 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
6 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
CommMonoidCommMonoid
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Around this declaration

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

Submonoid.LocalizationMap.eq_iff_exists · cited by 9LocalizationMap.eq_iff_ex…IsLocalization.exists_of_eq · cited by 4IsLocalization.exists_of_…Submonoid.LocalizationMap.exists_of_eq · cited by 2LocalizationMap.exists_of…Submonoid.isLocalizationMap_iff_bijective · cited by 1Submonoid.isLocalizationM…Submonoid.IsLocalizationMap.mulEquiv_comp · cited by 0IsLocalizationMap.mulEqui…Submonoid.IsLocalizationMap.pi · cited by 0IsLocalizationMap.piSubmonoid · cited by 3086SubmonoidCommMonoid · cited by 2264CommMonoidSubmonoid.IsLocalizationMap · cited by 19Submonoid.IsLocalizationM…IsLocalizationMap.exists_of_eqCITED BYCITES

Cites3

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Cited by6

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