English
If each block is the identity matrix, then blockDiagonal' of the identity equals the identity matrix (on the block-structured space).
Русский
Если каждая блок-матрица равна единичной, то блочно-диагональная матрица единична на соответствующей размерности.
LaTeX
$$$ \\mathrm{blockDiagonal}' \\bigl( 1 \\bigr) = 1 $$$
Lean4
@[simp]
theorem blockDiagonal'_one [∀ i, DecidableEq (m' i)] [One α] : blockDiagonal' (1 : ∀ i, Matrix (m' i) (m' i) α) = 1 :=
show (blockDiagonal' fun i : o => diagonal fun _ : m' i => (1 : α)) = diagonal fun _ => 1 by
rw [blockDiagonal'_diagonal]