let n be Nat; :: thesis: for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2) holds (W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) = (W-bound C) + (E-bound C)

let C be connected compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: (W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) = (W-bound C) + (E-bound C)

thus (W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) = (W-bound (L~ (Cage (C,n)))) + ((E-bound C) + (((E-bound C) - (W-bound C)) / (2 |^ n))) by JORDAN1A:64

.= ((W-bound C) - (((E-bound C) - (W-bound C)) / (2 |^ n))) + ((E-bound C) + (((E-bound C) - (W-bound C)) / (2 |^ n))) by JORDAN1A:62

.= (W-bound C) + (E-bound C) ; :: thesis: verum

let C be connected compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: (W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) = (W-bound C) + (E-bound C)

thus (W-bound (L~ (Cage (C,n)))) + (E-bound (L~ (Cage (C,n)))) = (W-bound (L~ (Cage (C,n)))) + ((E-bound C) + (((E-bound C) - (W-bound C)) / (2 |^ n))) by JORDAN1A:64

.= ((W-bound C) - (((E-bound C) - (W-bound C)) / (2 |^ n))) + ((E-bound C) + (((E-bound C) - (W-bound C)) / (2 |^ n))) by JORDAN1A:62

.= (W-bound C) + (E-bound C) ; :: thesis: verum