let n be Element of 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:85
.= ((W-bound C) - (((E-bound C) - (W-bound C)) / (2 |^ n))) + ((E-bound C) + (((E-bound C) - (W-bound C)) / (2 |^ n))) by JORDAN1A:83
.= (W-bound C) + (E-bound C) ; :: thesis: verum