preimage_coe_Ici — Mathlib

English

For any real x, the preimage of Ici(x) under Real.toEReal equals Ici(x).

Русский

Для любого вещественного xabelle предобраз Ici(x) под Real.toEReal равен Ici(x).

LaTeX

$$$\\\\operatorname{Real.toEReal}^{-1}(\\\\mathrm{Ici}(x)) = \\mathrm{Ici}(x)$$$

Lean4

@[simp]
theorem preimage_coe_Ici (x : ℝ) : Real.toEReal ⁻¹' Ici x = Ici x :=
  by
  change (WithBot.some ∘ WithTop.some) ⁻¹' (Ici (WithBot.some (WithTop.some x))) = _
  refine preimage_comp.trans ?_
  simp only [WithBot.preimage_coe_Ici, WithTop.preimage_coe_Ici]

Похожие утверждения