reserve A,A1,A2,B,C,D for Ordinal,
  X,Y for set,
  x,y,a,b,c for object,
  L,L1,L2,L3 for Sequence,
  f for Function;

theorem
  A in X & X c= Y implies inf Y c= inf X
proof
  assume A in X;
  then
A1: On X <> 0 by ORDINAL1:def 9;
  assume X c= Y;
  then On X c= On Y by Th9;
  hence thesis by A1,SETFAM_1:6;
end;
