theorem Th2:
  for M being Matrix of REAL st [i,j] in Indices M holds (-M)*(i,j) =-(M*(i,j))
proof
  let M be Matrix of REAL;
  assume [i,j] in Indices M;
  then (-M)*(i,j)= -((MXR2MXF M)*(i,j)) by MATRIX_3:def 2,VECTSP_1:def 5;
  hence thesis by VECTSP_1:def 5;
end;
