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