image_cast_int_Ioo — Mathlib

English

The image of the open upper interval Ioi(a) under Nat.cast is the open upper interval Ioi(a.cast) in ℤ.

Русский

Образ открытого правого интервала Ioi(a) через Nat.cast равен Ioi(a.cast) в ℤ.

LaTeX

$$$ \mathrm{Set.image}(\mathrm{Nat.cast}, \mathrm{Ioi}(a)) = \mathrm{Ioi}(a.cast) $$$

Lean4

theorem image_cast_int_Ioo (a b : ℕ) : (↑) '' Ioo a b = Ioo (a : ℤ) b :=
  (castOrderEmbedding (α := ℤ)).image_Ioo (by simp [ordConnected_Ici]) a b

Похожие утверждения