Section SquareBlockMatrixZmod.
Context {V : zmodType} {p : nat} {p_ : 'I_p -> nat}.
Notation sp := (\sum_i p_ i)%N.
Implicit Type (s : 'I_sp).

Lemma is_trig_mxblock (B_ : forall i j, 'M[V]_(p_ i, p_ j)) :
is_trig_mx (\mxblock_(i, j) B_ i j) =
([forall i : 'I_p, forall j : 'I_p, (i < j)%N ==> (B_ i j == 0)] &&
[forall i, is_trig_mx (B_ i i)]).