let r, s, p, q be ext-real number ; :: thesis: ( r < s implies ].r,s.[ <> [.p,q.] )
assume that
A1: r < s and
A2: ].r,s.[ = [.p,q.] ; :: thesis: contradiction
A3: not r in ].r,s.[ by Th4;
A4: p <= r by A1, A2, Th51;
s <= q by A1, A2, Th51;
then r <= q by A1, XXREAL_0:2;
hence contradiction by A2, A3, A4, Th1; :: thesis: verum