Theorems · Theorem · group theory

AddSubmonoid.LocalizationMap.map_surjective_of_surjOn

∀ {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} {T : AddSubmonoid P} (hy : ∀ (y : ↥S), g ↑y ∈ T)
  {Q : Type u_4} [inst_3 : AddCommMonoid Q] {k : T.LocalizationMap Q},
  Set.SurjOn ⇑g ↑S ↑T → Function.Surjective ⇑g → Function.Surjective ⇑(f.map hy k)

Defined in

Mathlib.GroupTheory.MonoidLocalization.Maps

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoid