intuition.
inversion H; clear H; subst.
eapply getSupport_In_evalDet_steps; eauto.
Qed.
(* The following predicate makes it easier for us to do induction on the number of loop iterations. *)
Inductive evalDet_repeat_steps (A : Set)(P : A -> bool) : comp_state A -> comp_state A -> Prop :=
| evalDet_repeat_steps_done :
forall c s a s',
evalDet_steps (cs_more c s) (cs_done a s') ->
P a = true ->
evalDet_repeat_steps P (cs_more c s) (cs_done a s')
| evalDet_repeat_steps_eof :
forall c s,
evalDet_steps (cs_more c s) (@cs_eof A) ->
evalDet_repeat_steps P (cs_more c s) (@cs_eof A)
| evalDet_repeat_steps_step :
forall c s a s' y,
evalDet_steps (cs_more c s) (cs_done a s') ->
P a = false ->
evalDet_repeat_steps P (cs_more c s') y ->
evalDet_repeat_steps P (cs_more c s) y.
Inductive evalDet_repeat(A : Set)(P : A -> bool)(c : Comp A)(s : Blist) : comp_answer A -> Prop :=
| evalDet_repeat_done : forall a s',
evalDet_repeat_steps P (cs_more c s) (cs_done a s') ->
evalDet_repeat P c s (ca_done a)
| evalDet_repeat_eof :
evalDet_repeat_steps P (cs_more c s) (@cs_eof A) ->
evalDet_repeat P c s (@ca_eof A).

Lemma list_skipn_strong_ind_h : forall (A : Type) l (P : list A -> Prop) ,
P nil ->
(forall x, (forall n, n > 0 -> P (skipn n x)) -> P x) ->
(forall n, P (skipn n l)).