Commit cde5b548 authored by Ralf Jung's avatar Ralf Jung

Merge branch 'master' of https://gitlab.mpi-sws.org/FP/iris-coq

parents b40dca66 ed90ff31
......@@ -39,11 +39,15 @@ Section definitions.
let (X) := X in let (Y) := Y in
GMultiSet $ difference_with (λ x y,
let z := x - y in guard (0 < z); Some (pred z)) X Y.
Instance gmultiset_dom : Dom (gmultiset A) (gset A) := λ X,
let (X) := X in dom _ X.
End definitions.
Typeclasses Opaque gmultiset_elem_of gmultiset_subseteq.
Typeclasses Opaque gmultiset_elements gmultiset_size gmultiset_empty.
Typeclasses Opaque gmultiset_singleton gmultiset_union gmultiset_difference.
Typeclasses Opaque gmultiset_dom.
(** These instances are declared using [Hint Extern] to avoid too
eager type class search. *)
......@@ -63,6 +67,8 @@ Hint Extern 1 (Elements _ (gmultiset _)) =>
eapply @gmultiset_elements : typeclass_instances.
Hint Extern 1 (Size (gmultiset _)) =>
eapply @gmultiset_size : typeclass_instances.
Hint Extern 1 (Dom (gmultiset _) _) =>
eapply @gmultiset_dom : typeclass_instances.
Section lemmas.
Context `{Countable A}.
......@@ -196,6 +202,12 @@ Proof.
exists (x,n); split; [|by apply elem_of_map_to_list].
apply elem_of_replicate; auto with omega.
Qed.
Lemma gmultiset_elem_of_dom x X : x dom (gset A) X x X.
Proof.
unfold dom, gmultiset_dom, elem_of at 2, gmultiset_elem_of, multiplicity.
destruct X as [X]; simpl; rewrite elem_of_dom, <-not_eq_None_Some.
destruct (X !! x); naive_solver omega.
Qed.
(* Properties of the size operation *)
Lemma gmultiset_size_empty : size ( : gmultiset A) = 0.
......
......@@ -478,8 +478,13 @@ Tactic Notation "naive_solver" tactic(tac) :=
| |- _, _ => intro
(**i simplification of assumptions *)
| H : False |- _ => destruct H
| H : _ _ |- _ => destruct H
| H : _, _ |- _ => destruct H
| H : _ _ |- _ =>
(* Work around bug https://coq.inria.fr/bugs/show_bug.cgi?id=2901 *)
let H1 := fresh in let H2 := fresh in
destruct H as [H1 H2]; try clear H
| H : _, _ |- _ =>
let x := fresh in let Hx := fresh in
destruct H as [x Hx]; try clear H
| H : ?P ?Q, H2 : ?P |- _ => specialize (H H2)
| H : Is_true (bool_decide _) |- _ => apply (bool_decide_unpack _) in H
| H : Is_true (_ && _) |- _ => apply andb_True in H; destruct H
......@@ -491,7 +496,8 @@ Tactic Notation "naive_solver" tactic(tac) :=
| |- _ _ => split
| |- Is_true (bool_decide _) => apply (bool_decide_pack _)
| |- Is_true (_ && _) => apply andb_True; split
| H : _ _ |- _ => destruct H
| H : _ _ |- _ =>
let H1 := fresh in destruct H as [H1|H1]; try clear H
(**i solve the goal using the user supplied tactic *)
| |- _ => solve [tac]
end;
......
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