E-max (L~ (Cage (C,n))) in rng (Cage (C,n)) by SPRECT_2:50;
then A1: E-max (L~ (Cage (C,n))) in rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) by FINSEQ_6:96, SPRECT_2:47;
len (Upper_Seq (C,n)) = (E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) by Th12;
hence not Upper_Seq (C,n) is empty by A1, FINSEQ_4:31; :: thesis: verum