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

theorem
  a in REAL & a <= b & b < c implies b in REAL
proof
  assume that
A1: a in REAL & a <= b and
A2: b < c;
  b in REAL or b = +infty by A1,Th10;
  hence thesis by A2,Lm9;
end;
