for K being Field
for A, B being Matrix of K st the_rank_of A = the_rank_of (A ^^ B) & len A = len B holds
for N being finite without_zero Subset of NAT st N c= dom A & ( for i being Nat st i in N holds
Line (A,i) = (width A) |-> (0. K) ) holds
for i being Nat st i in N holds
Line (B,i) = (width B) |-> (0. K)