English
Let m ∈ ℕ and i, j ∈ Fin(n). The image of uIcc(i, j) under x ↦ x + m is uIcc(i + m, j + m).
Русский
Пусть m ∈ ℕ и i, j ∈ Fin(n). Образ uIcc(i, j) при сдвиге на m равен uIcc(i + m, j + m).
LaTeX
$$$$ \\\\mathrm{Set.image}(\\\\mathrm{Fin.natAdd}(m))(\\\\mathrm{Set.uIcc}(i,j)) = \\\\mathrm{Set.uIcc}(\\\\mathrm{Fin.natAdd}(m)i, \\\\mathrm{Fin.natAdd}(m)j). $$$$
Lean4
@[simp]
theorem image_natAdd_uIcc (m) (i j : Fin n) : natAdd m '' uIcc i j = uIcc (natAdd m i) (natAdd m j) := by
simp [uIcc, ← (strictMono_natAdd m).monotone.map_max, ← (strictMono_natAdd m).monotone.map_min]