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 Th33:
  p1 - p2 = |[ p1`1 - p2`1, p1`2 - p2`2]|
proof
  -p2 = |[ -p2`1, -p2`2]| by Th31;
  then (-p2)`1 = -p2`1 & (-p2)`2 = -p2`2 by FINSEQ_1:44;
  hence p1 - p2 = |[ p1`1 + -p2`1, p1`2 + -p2`2]| by Th27
    .= |[ p1`1 - p2`1, p1`2 - p2`2]|;
end;
