reserve x,y,z,w for ExtReal,
  r for Real;
reserve f,g for ExtReal;

theorem Th21:
  not ( x = +infty & y = +infty or x = -infty & y = -infty ) & x -
  y in REAL implies x in REAL & y in REAL
proof
  assume
A1: ( not ( x = +infty & y = +infty or x = -infty & y = -infty ))& x - y
  in REAL;
A2: x in REAL or x = -infty or x = +infty by XXREAL_0:14;
A3: y in REAL or y = -infty or y = +infty by XXREAL_0:14;
  assume not (x in REAL & y in REAL);
  hence thesis by A1,A2,A3,Th13,Th14;
end;
