let W, W1 be Tree; :: thesis: for p, q being FinSequence of NAT st p in W & q in W & not p is_a_prefix_of q holds
q in W with-replacement (p,W1)
let p, q be FinSequence of NAT ; :: thesis: ( p in W & q in W & not p is_a_prefix_of q implies q in W with-replacement (p,W1) )
( not p is_a_prefix_of q implies not p is_a_proper_prefix_of q ) ;
hence ( p in W & q in W & not p is_a_prefix_of q implies q in W with-replacement (p,W1) ) by TREES_1:def 9; :: thesis: verum