reserve f for non empty FinSequence of TOP-REAL 2,
  i,j,k,k1,k2,n,i1,i2,j1,j2 for Nat,
  r,s,r1,r2 for Real,
  p,q,p1,q1 for Point of TOP-REAL 2,
  G for Go-board;

theorem Th3:
  for p,p1,q being Point of TOP-REAL n st p + p1 = q + p1 holds p = q
proof
  let p,p1,q be Point of TOP-REAL n such that
A1: p + p1 = q + p1;
  thus p = p + 0.TOP-REAL n by RLVECT_1:4
    .= p + (p1 - p1) by RLVECT_1:5
    .= p + p1 - p1 by RLVECT_1:def 3
    .= q + (p1 - p1) by A1,RLVECT_1:def 3
    .= q + 0.TOP-REAL n by RLVECT_1:5
    .= q by RLVECT_1:4;
end;
