let n be Element of 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_6:66; :: thesis: E-max (L~ (Cage C,n)) in L~ (Lower_Seq C,n)
len (Lower_Seq C,n) >= 2 by TOPREAL1:def 10;
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