reserve fi,psi for Ordinal-Sequence,
  A,A1,B,C,D for Ordinal,
  X,Y for set,
  x,y for object;

theorem Th19:
  A in B & (C c= D & D <> {} or C in D) implies A*^C in B*^D
proof
  assume that
A1: A in B and
A2: C c= D & D <> {} or C in D;
A3: C c= D by A2,ORDINAL1:def 2;
  A*^D in B*^D by A1,A2,ORDINAL2:40;
  hence thesis by A3,ORDINAL1:12,ORDINAL2:42;
end;
