theorem Th38:
  for M be Matrix of n,m,D,F for k st k in Seg n holds Line(M*F,k) = M.(F.k)
proof
  let M be Matrix of n,m,D,F;
  let k such that
A1: k in Seg n;
  len (M*F)=n by MATRIX_0:def 2;
  then k in dom (M*F) by A1,FINSEQ_1:def 3;
  then (M*F).k=M.(F.k) by FUNCT_1:12;
  hence thesis by A1,MATRIX_0:52;
end;
