reserve A,B,C for Ordinal,
  X,X1,Y,Y1,Z for set,a,b,b1,b2,x,y,z for object,
  R for Relation,
  f,g,h for Function,
  k,m,n for Nat;
reserve M,N for Cardinal;

theorem Th5:
  R is well-ordering implies field R,order_type_of R are_equipotent
proof
  assume R is well-ordering;
  then R,RelIncl order_type_of R are_isomorphic by WELLORD2:def 2;
  then consider f such that
A1: f is_isomorphism_of R,RelIncl order_type_of R by WELLORD1:def 8;
  take f;
  field RelIncl order_type_of R = order_type_of R by WELLORD2:def 1;
  hence thesis by A1,WELLORD1:def 7;
end;
