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 Th31:
  -p = |[ -p`1, -p`2]|
proof
  thus -p = (-1)*p .= |[ (-1)*p`1, (-1)*p`2]| by Th29
    .= |[ -p`1, -p`2]|;
end;
