let n be Nat; :: thesis: for C being compact non horizontal non vertical Subset of (TOP-REAL 2) holds
( E-max (L~ (Cage (C,n))) in rng (Lower_Seq (C,n)) & E-max (L~ (Cage (C,n))) in L~ (Lower_Seq (C,n)) )
let C be compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: ( E-max (L~ (Cage (C,n))) in rng (Lower_Seq (C,n)) & E-max (L~ (Cage (C,n))) in L~ (Lower_Seq (C,n)) )
set p = E-max (L~ (Cage (C,n)));
Lower_Seq (C,n) = (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) :- (E-max (L~ (Cage (C,n)))) by JORDAN1E:def 2;
hence A1: E-max (L~ (Cage (C,n))) in rng (Lower_Seq (C,n)) by FINSEQ_6:61; :: thesis: E-max (L~ (Cage (C,n))) in L~ (Lower_Seq (C,n))
len (Lower_Seq (C,n)) >= 2 by TOPREAL1:def 8;
then rng (Lower_Seq (C,n)) c= L~ (Lower_Seq (C,n)) by SPPOL_2:18;
hence E-max (L~ (Cage (C,n))) in L~ (Lower_Seq (C,n)) by A1; :: thesis: verum