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

theorem Th18:
  x - y = +infty implies (x = +infty or y = -infty)
proof
  assume
A1: x - y = +infty;
  assume ( not x = +infty)& not y = -infty;
  then x in REAL & y in REAL or x in REAL & y = +infty or x = -infty & y in
  REAL or x = -infty & y = +infty by XXREAL_0:14;
  hence thesis by A1,Th13,Th14;
end;
