finsetImage_natAdd_uIcc — Mathlib

English

For i, j ∈ Fin n, image of uIcc i j under natAdd m equals uIcc (natAdd m i) (natAdd m j).

Русский

Для i, j ∈ Fin n образ uIcc i j под natAdd m равен uIcc (natAdd m i) (natAdd m j).

LaTeX

$$$$(\\mathrm{uIcc}\\ i\\ j).\\operatorname{image}(\\mathrm{natAdd}\\ m) = \\mathrm{uIcc}(\\mathrm{natAdd}\\ m\,i, \\mathrm{natAdd}\\ m\,j)$$$$

Lean4

@[simp]
theorem finsetImage_natAdd_uIcc (m) (i j : Fin n) : (uIcc i j).image (natAdd m) = uIcc (natAdd m i) (natAdd m j) := by
  simp [← coe_inj]

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