Section bt_rect'.
(* When we inspect bt as lists, we can switch to this principle  In fact, btrees code HF-sets like this  {x1,...,xn} = x1⪧...⪧xn⪧∅  We could also use rose-trees but may be this would be more difficult ? *)
Variables (P : bt -> Type)
(HP0 : P ∅)
(HP1 : forall x t, P t -> P (x⪧t)).

Theorem bt_rect' t : P t.