(* Conversion from list to kn *)
Fixpoint kn2l (n : nat) : kn n -> list K :=
match n return (kn n -> list K) with
| 0 => fun x => nil
| S n1 => fun v => let (a, v1) := v in a :: kn2l n1 v1
end.

Lemma genk_id0 n i : In i (kn2l n (genk n 0%f)) -> i = 0%f.
Inductive eql_t0 : list K -> list K -> Prop :=
eql_t0N: eql_t0 nil nil
| eql_t0Nl: forall l, eql_t0 l nil -> eql_t0 (0%f :: l) nil
| eql_t0Nr: forall l, eql_t0 nil l -> eql_t0 nil (0%f :: l)
| eql_t0R: forall a l1 l2, eql_t0 l1 l2 -> eql_t0 (a :: l1) (a :: l2).