theorem Th42:
  for D being non empty set,M being Matrix of D holds for i,j st j
  in dom M & i in Seg width M holds Col(M,i).j = Line(M,j).i
proof
  let D be non empty set,M be Matrix of D;
  let i,j;
  assume that
A1: j in dom M and
A2: i in Seg width M;
  thus Col(M,i).j = M*(j,i) by A1,Def8
    .= Line(M,j).i by A2,Def7;
end;
