let r, s, p, q be ext-real number ; :: thesis: ].r,s.] \/ ].p,q.] c= ].(min r,p),(max s,q).]
let t be ext-real number ; :: according to MEMBERED:def 8 :: thesis: ( not t in ].r,s.] \/ ].p,q.] or t in ].(min r,p),(max s,q).] )
assume t in ].r,s.] \/ ].p,q.] ; :: thesis: t in ].(min r,p),(max s,q).]
then ( t in ].r,s.] or t in ].p,q.] ) by XBOOLE_0:def 3;
then A1: ( ( r < t & t <= s ) or ( p < t & t <= q ) ) by Th2;
then A2: min r,p < t by XXREAL_0:22;
t <= max s,q by A1, XXREAL_0:31;
hence t in ].(min r,p),(max s,q).] by A2, Th2; :: thesis: verum