reserve i,j for Nat;

theorem
  for A being Matrix of REAL holds A+A=2*A
proof
  set e2=(1_F_Real) + (1_F_Real);
  let A be Matrix of REAL;
A1: (1_F_Real)*(MXR2MXF A)= MXR2MXF A by MATRIX_5:9;
  2*A = MXF2MXR (e2*(MXR2MXF A)) by Def7
    .= MXF2MXR ((MXR2MXF A)+(MXR2MXF A)) by A1,MATRIX_5:12;
  hence thesis;
end;
