let p, q, r, s be ExtReal; :: thesis: ( r < s implies [.r,s.[ <> [.p,q.] )
assume that
A1: r < s and
A2: [.r,s.[ = [.p,q.] ; :: thesis: contradiction
A3: not s in [.r,s.[ by Th3;
p <= r by A1, A2, Th52;
then A4: p <= s by A1, XXREAL_0:2;
s <= q by A1, A2, Th52;
hence contradiction by A2, A3, A4, Th1; :: thesis: verum