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 TOPREAL3:8;
hence |.(p1 - p2).| <= (abs ((p1 `1 ) - (p2 `1 ))) + (abs ((p1 `2 ) - (p2 `2 ))) by Th48; :: thesis: verum