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(* Check the synthesis of predicate from a cast in case of matching of
the first component (here [list bool]) of a dependent type (here [sigS])
(Simplification of an example from file parsing2.v of the Coq'Art
exercises) *)
Require Import PolyList.
Variable parse_rel : (list bool) -> (list bool) -> nat -> Prop.
Variables l0:(list bool); rec:(l' : (list bool))
(le (length l') (S (length l0))) ->
{l'' : (list bool) &
{t : nat | (parse_rel l' l'' t) /\ (le (length l'') (length l'))}} +
{(l'' : (list bool))(t : nat)~ (parse_rel l' l'' t)}.
Axiom HHH : (A:Prop)A.
Check (Cases (rec l0 (HHH ?)) of
| (inleft (existS (cons false l1) _)) => (inright ? ? (HHH ?))
| (inleft (existS (cons true l1) (exist t1 (conj Hp Hl)))) =>
(inright ? ? (HHH ?))
| (inleft (existS _ _)) => (inright ? ? (HHH ?))
| (inright Hnp) => (inright ? ? (HHH ?))
end ::
{l'' : (list bool) &
{t : nat | (parse_rel (cons true l0) l'' t) /\ (le (length l'') (S (length l0)))}} +
{(l'' : (list bool)) (t : nat) ~ (parse_rel (cons true l0) l'' t)}).
(* The same but with relative links to l0 and rec *)
Check [l0:(list bool);rec:(l' : (list bool))
(le (length l') (S (length l0))) ->
{l'' : (list bool) &
{t : nat | (parse_rel l' l'' t) /\ (le (length l'') (length l'))}} +
{(l'' : (list bool)) (t : nat) ~ (parse_rel l' l'' t)}]
(Cases (rec l0 (HHH ?)) of
| (inleft (existS (cons false l1) _)) => (inright ? ? (HHH ?))
| (inleft (existS (cons true l1) (exist t1 (conj Hp Hl)))) =>
(inright ? ? (HHH ?))
| (inleft (existS _ _)) => (inright ? ? (HHH ?))
| (inright Hnp) => (inright ? ? (HHH ?))
end ::
{l'' : (list bool) &
{t : nat | (parse_rel (cons true l0) l'' t) /\ (le (length l'') (S (length l0)))}} +
{(l'' : (list bool)) (t : nat) ~ (parse_rel (cons true l0) l'' t)}).
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