let p, r, s, q be ext-real number ; :: thesis: ( p < r & s <= q implies [.r,s.[ c= ].p,q.] )
A1: [.r,s.[ c= [.r,s.] by Th24;
assume ( p < r & s <= q ) ; :: thesis: [.r,s.[ c= ].p,q.]
then [.r,s.] c= ].p,q.] by Th39;
hence [.r,s.[ c= ].p,q.] by A1, XBOOLE_1:1; :: thesis: verum