let p, q, r, s be ExtReal; :: thesis: ( r < p & r <= s implies not [.r,s.] c= [.p,q.[ )
assume that
A1: r < p and
A2: r <= s ; :: thesis: not [.r,s.] c= [.p,q.[
take t = r; :: according to MEMBERED:def 8 :: thesis: ( t in [.r,s.] & not t in [.p,q.[ )
thus t in [.r,s.] by A2, Th1; :: thesis: not t in [.p,q.[
thus not t in [.p,q.[ by A1, Th3; :: thesis: verum