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)|
|((p1 - p2),p3)| = |(p1,p3)| + |((- p2),p3)| by Th40
.= |(p1,p3)| + (- |(p2,p3)|) by Th43 ;
hence |((p1 - p2),p3)| = |(p1,p3)| - |(p2,p3)| ; :: thesis: verum