Definition copid_mx {n} r : 'M_n := 1%:M - pid_mx r.

Lemma mul_block_col m1 m2 n1 n2 p (Aul : 'M_(m1, n1)) (Aur : 'M_(m1, n2)) (Adl : 'M_(m2, n1)) (Adr : 'M_(m2, n2)) (Bu : 'M_(n1, p)) (Bd : 'M_(n2, p)) : block_mx Aul Aur Adl Adr *m col_mx Bu Bd = col_mx (Aul *m Bu + Aur *m Bd) (Adl *m Bu + Adr *m Bd).