reserve i,j,k,n,m for Nat;
reserve p,q for Point of TOP-REAL 2;
reserve G for Go-board;
reserve C for Subset of TOP-REAL 2;

theorem
  for g being FinSequence of TOP-REAL 2, p,q being Point of TOP-REAL 2
  st <*p,q*> is_in_the_area_of g holds <*1/2*(p+q)*> is_in_the_area_of g
proof
  let g be FinSequence of TOP-REAL 2, p,q be Point of TOP-REAL 2;
  1/2*(p+q) = (1 - 1/2)*p + 1/2*q by RLVECT_1:def 5;
  hence thesis by Th44;
end;
