reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem Th9:
  for X being non empty set, A being finite Subset of X, R be
  being_linear-order Order of X holds len SgmX(R,A) = card A
proof
  let X being non empty set, A being finite Subset of X, R be
  being_linear-order Order of X;
  field R = X & R linearly_orders field R by ORDERS_1:15,37;
  hence thesis by ORDERS_1:38,PRE_POLY:11;
end;
