reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for FinSequence;
reserve D for set;

theorem Th42:
  for x being object holds (p^<*x*>).(len p + 1)=x
proof let x be object;
  dom <*x*> = Seg 1 by Def8;
  then 1 in dom <*x*>;
  hence (p^<*x*>).(len p + 1) = <*x*>.1 by Def7
    .=x;
end;
