theorem Th35:
  for X being finite set st X c= O holds order_type_of RelIncl X =
  card X
proof
  let X be finite set;
  assume
A1: X c= O;
  then order_type_of RelIncl X is finite by Lm4;
  then reconsider o = order_type_of RelIncl X as Nat;
  card X = card order_type_of RelIncl X by A1,Th7;
  then o = card X;
  hence thesis;
end;
