reserve x for set;
reserve a,b,c,d for ExtReal;

theorem Th9:
  a in REAL implies +infty > a
proof
  assume a in REAL;
  then
A1: a <> +infty by Lm0;
  +infty >= a by Def5,Lm3,Lm5;
  hence thesis by A1,Th1;
end;
