Theorems · Theorem · group theory

AddMonoid.Coprod.hom_ext

∀ {M : Type u_1} {N : Type u_2} {P : Type u_5} [inst : AddZeroClass M] [inst_1 : AddZeroClass N]
  [inst_2 : AddZeroClass P] {f g : AddMonoid.Coprod M N →+ P},
  f.comp AddMonoid.Coprod.inl = g.comp AddMonoid.Coprod.inl →
    f.comp AddMonoid.Coprod.inr = g.comp AddMonoid.Coprod.inr → f = g

Extensionality lemma for additive monoid homomorphisms AddMonoid.Coprod M N →+ P. If two homomorphisms agree on the ranges of AddMonoid.Coprod.inl and AddMonoid.Coprod.inr, then they are equal.

Defined in

Mathlib.GroupTheory.Coprod.Basic

Cited by

12 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddZeroClassAddZeroClassAddZeroClass