finsetImage_natAdd_Icc — Mathlib

English

For any natural m and i, j ∈ Fin n, the image of Icc i j under natAdd m equals Icc (natAdd m i) (natAdd m j).

Русский

Для любого натурального m и i, j ∈ Fin n образ Icc i j под natAdd m равен Icc (natAdd m i) (natAdd m j).

LaTeX

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

Lean4

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

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