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

theorem
  a in REAL & c in REAL & a <= b & b <= c implies b in REAL
proof
  assume that
A1: a in REAL and
A2: c in REAL and
A3: a <= b and
A4: b <= c;
  b in REAL or b = +infty by A1,A3,Th10;
  hence thesis by A2,A4,Th13;
end;
