reserve x,y for set;
reserve G for Graph;
reserve vs,vs9 for FinSequence of the carrier of G;
reserve IT for oriented Chain of G;
reserve N for Nat;
reserve n,m,k,i,j for Nat;
reserve r,r1,r2 for Real;
reserve X for non empty set;
reserve p,p1,p2 for Point of TOP-REAL N;

theorem Th32:
  for p1,p2 being Point of TOP-REAL 2
  holds |.p1-p2.|<=|.p1`1-p2`1.|+|.p1`2-p2`2.|
proof
  let p1,p2 be Point of TOP-REAL 2;
  p1`1-p2`1=(p1-p2)`1 & p1`2-p2`2=(p1-p2)`2 by TOPREAL3:3;
  hence thesis by Th31;
end;
