map_add_left_Ico — Mathlib

English

Translating the half-open interval Ico(a,b) by c on the left yields Ico(a+c, b+c).

Русский

Сдвиг 半-интервала Ico(a,b) на c слева дает Ico(a+c, b+c).

LaTeX

$$$\text{Multiset.map} (\lambda x, c+x)\, (\text{Multiset.Ico } a b) = \text{Multiset.Ico } (a+c) (b+c)$$$

Lean4

theorem map_add_left_Ico (a b c : α) : (Ico a b).map (c + ·) = Ico (c + a) (c + b) := by
  classical
    rw [Ico, Ico, ← Finset.image_add_left_Ico, Finset.image_val, ((Finset.nodup _).map <| add_right_injective c).dedup]

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