English
Similarly, snd ∘ diag = id, i.e., the right projection after diagonalization returns the original vector.
Русский
Аналогично, snd ∘ diag = id; правая проекция после диагонализации возвращает исходный вектор.
LaTeX
$$$\\mathrm{snd} \\circ \\mathrm{diag} = \\mathrm{id}$$$
Lean4
theorem snd_diag {α : TypeVec n} : TypeVec.prod.snd ⊚ (prod.diag : α ⟹ _) = id := by funext i;
induction i with
| fz => rfl
| fs _ i_ih => apply i_ih