let n be Nat; :: thesis: for C being compact non horizontal non vertical Subset of (TOP-REAL 2) holds Lower_Seq (C,n) is_in_the_area_of Cage (C,n)

let C be compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: Lower_Seq (C,n) is_in_the_area_of Cage (C,n)

E-max (L~ (Cage (C,n))) in rng (Cage (C,n)) by SPRECT_2:46;

then E-max (L~ (Cage (C,n))) in rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) by FINSEQ_6:90, SPRECT_2:43;

hence Lower_Seq (C,n) is_in_the_area_of Cage (C,n) by Th2, JORDAN1B:10; :: thesis: verum

let C be compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: Lower_Seq (C,n) is_in_the_area_of Cage (C,n)

E-max (L~ (Cage (C,n))) in rng (Cage (C,n)) by SPRECT_2:46;

then E-max (L~ (Cage (C,n))) in rng (Rotate ((Cage (C,n)),(W-min (L~ (Cage (C,n)))))) by FINSEQ_6:90, SPRECT_2:43;

hence Lower_Seq (C,n) is_in_the_area_of Cage (C,n) by Th2, JORDAN1B:10; :: thesis: verum