English
The image of the closed-interval Ici i under Fin.castAdd m equals the half-open interval Ico (castAdd m i) (natAdd n 0).
Русский
Изображение непрерывного интервала Ici i под Fin.castAdd m равно полузакрытому интервалу Ico (castAdd m i) (natAdd n 0).
LaTeX
$$$$\\mathrm{Fin.castAdd}\\, m'' \\mathrm{Ici}(i) = \\mathrm{Ico}(\\mathrm{Fin.castAdd}\\, m\\, i)\\, (\\mathrm{Fin.natAdd}\\, n\\, 0).$$$$
Lean4
@[simp]
theorem image_castAdd_Ici (m) [NeZero m] (i : Fin n) : castAdd m '' Ici i = Ico (castAdd m i) (natAdd n 0) :=
val_injective.image_injective <| by simp [← image_comp]