let p1, p2 be Point of (TOP-REAL 2); :: thesis: |.(p1 - p2).| <= (abs ((p1 `1) - (p2 `1))) + (abs ((p1 `2) - (p2 `2)))
( (p1 `1) - (p2 `1) = (p1 - p2) `1 & (p1 `2) - (p2 `2) = (p1 - p2) `2 ) by TOPREAL3:3;
hence |.(p1 - p2).| <= (abs ((p1 `1) - (p2 `1))) + (abs ((p1 `2) - (p2 `2))) by Th48; :: thesis: verum