Require Export VST.msl.Extensionality.
(*  These three hints are considered "dangerous" because they make proofs noncomputational, which is an issue for things we want to solve with "compute". *)
(* Can't use "Hint Resolve" because a bug in "apply proof_irr" matches things that are not Props, which leads the Qed to fail (later) *)
Hint Extern 1 (@eq _ _ _) => exact (proof_irr _ _) : extensionality.
(* Can't use "Hint Resolve" because it doesn't seem to do anything... *)
Hint Extern 2 (eq _ _)  => apply exist_ext : extensionality.
(* Can't use "Hint Resolve" because it doesn't seem to do anything... *)
Hint Extern 2 (@eq _ (@existT _ _ _ _) (@existT _ _ _ _))  => apply existT_ext : extensionality.
Tactic Notation "forget" constr(X) "as" ident(y) :=
set (y:=X) in *; clearbody y.
Ltac proof_irr := match goal with H: ?A, H' : ?A |- _ => generalize (proof_irr H H'); intro; subst H' end.
Ltac inversion2 H1 H2 :=
rewrite H1 in H2; symmetry in H2; inv H2.
Ltac invT H :=
match type of H  with
| existT _ ?a ?b = existT _ ?a ?c =>
generalize (inj_pair2 _ _ a b c H); clear H; intro H; invT H
| existT _ _ _ = existT _ _ _ =>
let HH := fresh in (injection H; intros _ HH; invT HH; invT H)
| _ => inv H
end.
Ltac invSome :=
match goal with
| H: match ?A with Some _ =>  _ | None => None end = Some _ |- _ =>
let Hx := fresh in
(revert H; case_eq A; [intros ? H Hx | intros H Hx]; inv Hx)
| H: match ?A with Some _ => _  | None => False end |- _ =>
(revert H; case_eq A; [intros ? H ? | intros; contradiction])
| H: match ?A return _ with Some _ =>  _ | None => _ end eq_refl = Some _ |- _ =>
let Hx := fresh in
(revert H; generalize (eq_refl A); pattern A at 1 3; destruct A;
[ intros Hx H | intros ? H; discriminate H])
end.
Ltac split3 := split; [|split].

Lemma if_false: forall (A: Prop) (E: {A}+{~A}) (T: Type) (B C: T), ~A -> (if E then B else C) = C.