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......@@ -4,8 +4,8 @@ From stdpp Require Export sets list.
From stdpp Require Import options.
Record listset A := Listset { listset_car: list A }.
Arguments listset_car {_} _ : assert.
Arguments Listset {_} _ : assert.
Global Arguments listset_car {_} _ : assert.
Global Arguments Listset {_} _ : assert.
Section listset.
Context {A : Type}.
......@@ -28,7 +28,7 @@ Lemma listset_empty_alt X : X ≡ ∅ ↔ listset_car X = [].
Proof.
destruct X as [l]; split; [|by intros; simplify_eq/=].
rewrite elem_of_equiv_empty; intros Hl.
destruct l as [|x l]; [done|]. feed inversion (Hl x). left.
destruct l as [|x l]; [done|]. oinversion Hl. left.
Qed.
Global Instance listset_empty_dec (X : listset A) : Decision (X ).
Proof.
......@@ -48,7 +48,7 @@ Global Instance listset_intersection: Intersection (listset A) :=
Global Instance listset_difference: Difference (listset A) :=
λ '(Listset l) '(Listset k), Listset (list_difference l k).
Instance listset_set: Set_ A (listset A).
Local Instance listset_set: Set_ A (listset A).
Proof.
split.
- apply _.
......@@ -66,14 +66,14 @@ Proof.
Qed.
End listset.
Instance listset_ret: MRet listset := λ A x, {[ x ]}.
Instance listset_fmap: FMap listset := λ A B f '(Listset l),
Global Instance listset_ret: MRet listset := λ A x, {[ x ]}.
Global Instance listset_fmap: FMap listset := λ A B f '(Listset l),
Listset (f <$> l).
Instance listset_bind: MBind listset := λ A B f '(Listset l),
Global Instance listset_bind: MBind listset := λ A B f '(Listset l),
Listset (mbind (listset_car f) l).
Instance listset_join: MJoin listset := λ A, mbind id.
Global Instance listset_join: MJoin listset := λ A, mbind id.
Instance listset_set_monad : MonadSet listset.
Global Instance listset_set_monad : MonadSet listset.
Proof.
split.
- intros. apply _.
......
......@@ -7,9 +7,9 @@ From stdpp Require Import options.
Record listset_nodup A := ListsetNoDup {
listset_nodup_car : list A; listset_nodup_prf : NoDup listset_nodup_car
}.
Arguments ListsetNoDup {_} _ _ : assert.
Arguments listset_nodup_car {_} _ : assert.
Arguments listset_nodup_prf {_} _ : assert.
Global Arguments ListsetNoDup {_} _ _ : assert.
Global Arguments listset_nodup_car {_} _ : assert.
Global Arguments listset_nodup_prf {_} _ : assert.
Section list_set.
Context `{EqDecision A}.
......@@ -29,7 +29,7 @@ Global Instance listset_nodup_difference: Difference C :=
λ '(ListsetNoDup l Hl) '(ListsetNoDup k Hk),
ListsetNoDup _ (NoDup_list_difference _ k Hl).
Instance listset_nodup_set: Set_ A C.
Local Instance listset_nodup_set: Set_ A C.
Proof.
split; [split | | ].
- by apply not_elem_of_nil.
......
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......@@ -13,7 +13,7 @@ Section orders.
Lemma reflexive_eq `{!Reflexive R} X Y : X = Y X Y.
Proof. by intros <-. Qed.
Lemma anti_symm_iff `{!PartialOrder R} X Y : X = Y R X Y R Y X.
Proof. split; [by intros ->|]. by intros [??]; apply (anti_symm _). Qed.
Proof. split; [by intros ->|]. by intros [??]; apply (anti_symm R). Qed.
Lemma strict_spec X Y : X Y X Y Y X.
Proof. done. Qed.
Lemma strict_include X Y : X Y X Y.
......
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