let p be Point of (TOP-REAL 2); for C being Subset of (TOP-REAL 2) holds LSeg ((North-Bound (p,C)),(South-Bound (p,C))) is vertical
let C be Subset of (TOP-REAL 2); LSeg ((North-Bound (p,C)),(South-Bound (p,C))) is vertical
( (North-Bound (p,C)) `1 = p `1 & (South-Bound (p,C)) `1 = p `1 )
by EUCLID:52;
hence
LSeg ((North-Bound (p,C)),(South-Bound (p,C))) is vertical
by SPPOL_1:16; verum