image_Ioc — Mathlib

English

Let e be an order isomorphism between α and β. Then the image of the open–closed interval Ioc(a,b) under e is Ioc(e(a), e(b)); i.e., e''Ioc(a,b) = Ioc(e(a), e(b)).

Русский

Пусть e — изоморфизм порядка между α и β. Тогда образ промежутка Ioc(a,b) равен Ioc(e(a), e(b)).

LaTeX

$$$$ e'' Ioc(a,b) = Ioc(e(a), e(b)) $$$$

Lean4

@[simp]
theorem image_Ioc (e : α ≃o β) (a b : α) : e '' Ioc a b = Ioc (e a) (e b) := by
  rw [e.image_eq_preimage, e.symm.preimage_Ioc, e.symm_symm]

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