theorem Th12:
  x in ].p,q.] implies x in [.p,q.] & x <> p
proof
  assume
A1: x in ].p,q.];
  then reconsider s = x as ExtReal;
A2: p < s by A1,Th2;
  s <= q by A1,Th2;
  hence thesis by A2,Th1;
end;
