Theorems · Theorem · group theory

AddCon.lift_range

∀ {M : Type u_1} {P : Type u_3} [inst : AddZeroClass M] [inst_1 : AddZeroClass P] {c : AddCon M} {f : M →+ P}
  (H : c ≤ AddCon.ker f), AddMonoidHom.mrange (c.lift f H) = AddMonoidHom.mrange f

Given an additive congruence relation c on an AddMonoid and a homomorphism f constant on c's equivalence classes, f has the same image as the homomorphism that f induces on the quotient.

Defined in

Mathlib.GroupTheory.Congruence.Basic

Cited by

1 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddZeroClassAddZeroClass