reserve i,j for Nat;

theorem
  for M being Matrix of REAL holds M + 0_Rmatrix(len M,width M) = M
proof
  let M be Matrix of REAL;
A1: len M=len MXR2MXF M & width M=width MXR2MXF M;
  M + 0_Rmatrix(len M,width M) = M +(-0_Rmatrix(len M,width M)) by MATRIX_4:9
    .= M +(-(M-M)) by MATRIX_4:3
    .= MXF2MXR ((MXR2MXF M)-(MXR2MXF M-MXR2MXF M)) by MATRIX_4:def 1
    .= M by A1,MATRIX_4:11;
  hence thesis;
end;
