(* Check the synthesis of predicate from a cast in case of matching of the first component (here [list bool]) of a dependent type (here [sigT]) (Simplification of an example from file parsing2.v of the Coq'Art exercises) *)
Variable parse_rel : list bool -> list bool -> nat -> Prop.
Variables (l0 : list bool)
(rec :
forall l' : list bool,
length l' <= S (length l0) ->
{l'' : list bool &
{t : nat | parse_rel l' l'' t /\ length l'' <= length l'}} +
{(forall (l'' : list bool) (t : nat), ~ parse_rel l' l'' t)}).

Axiom HHH : forall A : Prop, A.