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;
reserve S for Sequence;

theorem
  A <> {} & A is limit_ordinal implies for S st dom S = A & for B st B
  in A holds S.B = aleph B holds aleph A = card sup S by Lm1;
