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

Lemma mulmx_block m1 m2 n1 n2 p1 p2 (Aul : 'M_(m1, n1)) (Aur : 'M_(m1, n2)) (Adl : 'M_(m2, n1)) (Adr : 'M_(m2, n2)) (Bul : 'M_(n1, p1)) (Bur : 'M_(n1, p2)) (Bdl : 'M_(n2, p1)) (Bdr : 'M_(n2, p2)) : block_mx Aul Aur Adl Adr *m block_mx Bul Bur Bdl Bdr = block_mx (Aul *m Bul + Aur *m Bdl) (Aul *m Bur + Aur *m Bdr) (Adl *m Bul + Adr *m Bdl) (Adl *m Bur + Adr *m Bdr).