Theorems · Theorem · group theory

Monoid.Coprod.hom_ext

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

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

Defined in

Mathlib.GroupTheory.Coprod.Basic

Cited by

14 results in Mathlib

Foundations

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

Assumes

MulOneClassMulOneClassMulOneClass