toContinuousMap_injective — Mathlib

English

The underlying monoid homomorphism of a continuous monoid homomorphism obtained from f equals the same MonoidHom as f.

Русский

Подлежащее моноид-гомоморфизм f сохраняет свою моноид-гомоморфическую природу при преобразовании.

LaTeX

$$$(MonoidHomClass.toMonoidHom (ContinuousMonoidHom.toContinuousMonoidHom f)) = MonoidHomClass.toMonoidHom f$$$

Lean4

@[to_additive]
theorem toContinuousMap_injective : Injective (toContinuousMap : _ → C(A, B)) := fun f g h =>
  ext <| by convert DFunLike.ext_iff.1 h

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