reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;
reserve p,p1,p2,p3 for Point of TOP-REAL n,
  x,x1,x2,y,y1,y2 for Real;
reserve p,p1,p2 for Point of TOP-REAL 2;

theorem
  |[x1, y1]| - |[x2, y2]| = |[ x1 - x2, y1 - y2]|
proof
A1: |[x2, y2]|`1 = x2 & |[x2, y2]|`2 = y2 by FINSEQ_1:44;
  |[x1, y1]|`1 = x1 & |[x1, y1]|`2 = y1 by FINSEQ_1:44;
  hence thesis by A1,Th33;
end;
