reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;
reserve m,n for Nat;
reserve x1,x2,x3,x4,x5,x6,x7,x8 for object;
reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;

theorem
  Rank n is finite
proof
  defpred P[Nat] means Rank $1 is finite;
A1: P[0] by CLASSES1:29;
A2: for n st P[n] holds P[n+1] by Lm7;
  for n holds P[n] from NAT_1:sch 2(A1,A2);
  hence thesis;
end;
