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 Th23;
assume that
A2: p <= r and
A3: s <= q ; :: thesis: ].r,s.] c= [.p,q.]
[.r,s.] c= [.p,q.] by A2, A3, Th34;
hence ].r,s.] c= [.p,q.] by A1, XBOOLE_1:1; :: thesis: verum