image_coe_Iic — Mathlib

English

For real x, the image of Iic(x) under Real.toEReal is Ioc(⊥, x.toEReal) in EReal.

Русский

Пусть x — вещественное число. Образ Iic(x) при Real.toEReal равен Ioc(⊥, x.toEReal) в EReal.

LaTeX

$$$\\\\operatorname{Set.image}(\\\\operatorname{Real.toEReal}, \\\\mathrm{Iic}(x)) = \\\\mathrm{Ioc}(\\\\bot, \\\\operatorname{Real.toEReal}(x))$$$

Lean4

@[simp]
theorem image_coe_Iic (x : ℝ) : Real.toEReal '' Iic x = Ioc ⊥ ↑x :=
  by
  refine (image_comp WithBot.some WithTop.some _).trans ?_
  rw [WithTop.image_coe_Iic, WithBot.image_coe_Iic]
  rfl

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