theorem :: TH87
  for G being finite Group
  for x being Element of G
  holds 0 < ord x & ord x <= card G
proof
  let G be finite Group;
  let x be Element of G;
  not x is being_of_order_0 by GR_CY_1:6;
  then 0 <> ord x by GROUP_1:def 11;
  hence 0 < ord x;
  ord x divides card G by GR_CY_1:8;
  hence ord x <= card G by NAT_D:7;
end;
