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

theorem Th13:
  x <> +infty implies +infty - x = +infty & x - +infty = -infty
proof
  assume
A1: x <> +infty;
  then -x <> -infty by Th5;
  hence +infty - x = +infty by Def2;
  - +infty = -infty by Def3;
  hence thesis by A1,Def2;
end;
