theorem
  for M1 be Matrix of n,k,D, M2 be Matrix of m,k,D st i in dom M1 holds
  Line(M1^M2,i) = Line(M1,i)
proof
  let M1 be Matrix of n,k,D;
  let M2 be Matrix of m,k,D such that
A1: i in dom M1;
  reconsider i1=i as Element of NAT by ORDINAL1:def 12;
  dom M1 c= dom (M1^M2) by FINSEQ_1:26;
  hence Line(M1^M2,i) = (M1^M2).i by A1,MATRIX_0:60
    .= M1.i1 by A1,FINSEQ_1:def 7
    .= Line(M1,i) by A1,MATRIX_0:60;
end;
