Section BlockMatrixRec.
Local Notation e := (mxsize_recl, mxsize_recl).
Local Notation l0 := (lift ord0).
Context {T : Type}.

Lemma mxblock_recu {p q : nat} {p_ : 'I_p.+1 -> nat} {q_ : 'I_q -> nat}
(B_ : forall i j, 'M[T]_(p_ i, q_ j)) :
\mxblock_(i, j) B_ i j = castmx (mxsize_recl, erefl) (col_mx
(\mxrow_j B_ ord0 j)
(\mxblock_(i, j) B_ (l0 i) j)).