let n be Nat; :: thesis: for p1, p2, p3 being Point of (TOP-REAL n) holds |((p1 + p2),p3)| = |(p1,p3)| + |(p2,p3)|
let p1, p2, p3 be Point of (TOP-REAL n); :: thesis: |((p1 + p2),p3)| = |(p1,p3)| + |(p2,p3)|
reconsider f1 = p1, f2 = p2, f3 = p3 as FinSequence of REAL by EUCLID:27;
len f2 = n by EUCLID:28;
then ( len f1 = len f2 & len f2 = len f3 ) by EUCLID:28;
hence |((p1 + p2),p3)| = |(p1,p3)| + |(p2,p3)| by Th19; :: thesis: verum