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;
