let C be compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: for n being Nat holds (Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) = E-max (L~ (Cage (C,n)))
let n be Nat; :: thesis: (Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) = E-max (L~ (Cage (C,n)))
A1: ( Upper_Seq (C,n) = (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) -: (E-max (L~ (Cage (C,n)))) & rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) = rng (Cage (C,n)) ) by FINSEQ_6:90, JORDAN1E:def 1, SPRECT_2:43;
then len (Upper_Seq (C,n)) = (E-max (L~ (Cage (C,n)))) .. (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) by FINSEQ_5:42, SPRECT_2:46;
hence (Upper_Seq (C,n)) /. (len (Upper_Seq (C,n))) = E-max (L~ (Cage (C,n))) by A1, FINSEQ_5:45, SPRECT_2:46; :: thesis: verum