let p1, p2 be Point of (TOP-REAL 2); :: thesis: |.(p1 - p2).| <= |.((p1 `1) - (p2 `1)).| + |.((p1 `2) - (p2 `2)).|
( (p1 `1) - (p2 `1) = (p1 - p2) `1 & (p1 `2) - (p2 `2) = (p1 - p2) `2 ) by TOPREAL3:3;
hence |.(p1 - p2).| <= |.((p1 `1) - (p2 `1)).| + |.((p1 `2) - (p2 `2)).| by Th31; :: thesis: verum