Theorems · Theorem · group theory

AddSubmonoid.LocalizationMap.eq_of_eq

∀ {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},
  (∀ (y : ↥S), IsAddUnit (g ↑y)) → ∀ {x y : M}, f x = f y → g x = g y

Given a Localization map f : M →+ N for an AddSubmonoid S ⊆ M and a map of AddCommMonoids g : M →+ P such that g(S) ⊆ AddUnits P, f x = f y → g x = g y for all x y : M.

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

4 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidAddCommMonoid