trans_toOpenPartialHomeomorph — Mathlib

English

A Homeomorph induces equality of its OpenPartialHomeomorphical images with the corresponding trans under composition.

Русский

Гомеоморфизм порождает равенство OpenPartialHomeomorph через композицию.

LaTeX

$$$(e: X \simeq Y).transOpenPartialHomeomorph f' = e.toOpenPartialHomeomorph.trans f'$$$

Lean4

@[simp, mfld_simps]
theorem trans_toOpenPartialHomeomorph :
    (e.trans e').toOpenPartialHomeomorph = e.toOpenPartialHomeomorph.trans e'.toOpenPartialHomeomorph :=
  OpenPartialHomeomorph.toPartialEquiv_injective <| Equiv.trans_toPartialEquiv _ _

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