reserve x for set,
  p,q,r,s,t,u for ExtReal,
  g for Real,
  a for Element of ExtREAL;

theorem Th15:
  x in ].p,q.[ implies x in ].p,q.] & x <> q
proof
  assume
A1: x in ].p,q.[;
  then reconsider s = x as ExtReal;
A2: p < s by A1,Th4;
  s < q by A1,Th4;
  hence thesis by A2,Th2;
end;
