map_natAddEmb_Ioo — Mathlib

English

For m ∈ Nat, i, j ∈ Fin n, map (natAddEmb m) on Ioc i j equals Ioc (natAdd m i) (natAdd m j).

Русский

Для m ∈ Nat, i, j ∈ Fin n отображение natAddEmb м на Ioc i j даёт Ioc (natAdd m i) (natAdd m j).

LaTeX

$$$$(\\mathrm{Ioc}\\ i\\ j).\\operatorname{map}(\\mathrm{natAddEmb}\\ m) = \\mathrm{Ioc}(\\mathrm{natAdd}\\ m\,i, \\mathrm{natAdd}\\ m\,j)$$$$

Lean4

@[simp]
theorem map_natAddEmb_Ioo (m) (i j : Fin n) : (Ioo i j).map (natAddEmb m) = Ioo (natAdd m i) (natAdd m j) := by
  simp [← coe_inj]

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