Theorems · Theorem · group theory

MonoidHom.eqOn_closureM

∀ {M : Type u_1} {N : Type u_2} [inst : MulOneClass M] [inst_1 : MulOneClass N] {f g : M →* N} {s : Set M},
  Set.EqOn (⇑f) (⇑g) s → Set.EqOn ⇑f ⇑g ↑(Submonoid.closure s)

If two monoid homomorphisms are equal on a set, then they are equal on its submonoid closure.

Defined in

Mathlib.Algebra.Group.Submonoid.Basic

Cited by

1 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MulOneClassMulOneClass