reserve k,n for Nat,
  x,y,z,y1,y2 for object,X,Y for set,
  f,g for Function;
reserve p,q,r,s,t for XFinSequence;
reserve D for set;
reserve i for Nat;
reserve m for Nat,
        D for non empty set;
reserve l for Nat;
reserve M for Nat;
reserve m,n for Nat;
reserve x1,x2,x3,x4 for object;
reserve e,u for object;

theorem
  for p being XFinSequence, x being object holds last(p^<%x%>) = x
proof
  let p be XFinSequence, x be object;
  dom(p^<%x%>) = len(p^<%x%>)
    .= len p + 1 by Th72
    .= len p +^ 1 by CARD_2:36
    .= succ len p by ORDINAL2:31;
  hence last(p^<%x%>) = (p^<%x%>).len p by ORDINAL2:6
    .= x by Th33;
end;
