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Theorems · Theorem · group theory

Submonoid.LocalizationMap.eq_iff_eq

∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N] {P : Type u_3}
  [inst_2 : CommMonoid P] (f : S.LocalizationMap N) (g : S.LocalizationMap P) {x y : M}, f x = f y ↔ g x = g y
Defined in
Mathlib.GroupTheory.MonoidLocalization.Basic
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
CommMonoidCommMonoidCommMonoid
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IsLocalization.eq_iff_eq · cited by 0IsLocalization.eq_iff_eqDFunLike.coe · cited by 62936DFunLike.coeSubmonoid · cited by 3086SubmonoidCommMonoid · cited by 2264CommMonoidSubmonoid.LocalizationMap · cited by 147Submonoid.LocalizationMapSubmonoid.LocalizationMap.eq_iff_exists · cited by 9LocalizationMap.eq_iff_ex…LocalizationMap.eq_iff_eqCITED BYCITES

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