New class `SetUnfoldElemOf` that specializes `SetUnfold` to improve performance.

theories/fin_sets.v

@@ -60,8 +60,8 @@ Defined.
 
 (** * The [elements] operation *)
 Global Instance set_unfold_elements X x P :
-  SetUnfold (x ∈ X) P → SetUnfold (x ∈ elements X) P.
-Proof. constructor. by rewrite elem_of_elements, (set_unfold (x ∈ X) P). Qed.
+  SetUnfoldElemOf x X P → SetUnfoldElemOf x (elements X) P.
+Proof. constructor. by rewrite elem_of_elements, (set_unfold_elem_of x X P). Qed.
 
 Global Instance elements_proper: Proper ((≡) ==> (≡ₚ)) (elements (C:=C)).
 Proof.
@@ -278,9 +278,9 @@ Section filter.
     by rewrite elem_of_list_to_set, elem_of_list_filter, elem_of_elements.
   Qed.
   Global Instance set_unfold_filter X Q :
-    SetUnfold (x ∈ X) Q → SetUnfold (x ∈ filter P X) (P x ∧ Q).
+    SetUnfoldElemOf x X Q → SetUnfoldElemOf x (filter P X) (P x ∧ Q).
   Proof.
-    intros ??; constructor. by rewrite elem_of_filter, (set_unfold (x ∈ X) Q).
+    intros ??; constructor. by rewrite elem_of_filter, (set_unfold_elem_of x X Q).
   Qed.
 
   Lemma filter_empty : filter P (∅:C) ≡ ∅.
@@ -316,8 +316,8 @@ Section map.
     by setoid_rewrite elem_of_elements.
   Qed.
   Global Instance set_unfold_map (f : A → B) (X : C) (P : A → Prop) :
-    (∀ y, SetUnfold (y ∈ X) (P y)) →
-    SetUnfold (x ∈ set_map (D:=D) f X) (∃ y, x = f y ∧ P y).
+    (∀ y, SetUnfoldElemOf y X (P y)) →
+    SetUnfoldElemOf x (set_map (D:=D) f X) (∃ y, x = f y ∧ P y).
   Proof. constructor. rewrite elem_of_map; naive_solver. Qed.
 
   Global Instance set_map_proper :

theories/gmultiset.v

@@ -136,10 +136,11 @@ Lemma gmultiset_elem_of_disj_union X Y x : x ∈ X ⊎ Y ↔ x ∈ X ∨ x ∈ Y
 Proof. rewrite !elem_of_multiplicity, multiplicity_disj_union. lia. Qed.
 
 Global Instance set_unfold_gmultiset_disj_union x X Y P Q :
-  SetUnfold (x ∈ X) P → SetUnfold (x ∈ Y) Q → SetUnfold (x ∈ X ⊎ Y) (P ∨ Q).
+  SetUnfoldElemOf x X P → SetUnfoldElemOf x Y Q →
+  SetUnfoldElemOf x (X ⊎ Y) (P ∨ Q).
 Proof.
   intros ??; constructor. rewrite gmultiset_elem_of_disj_union.
-  by rewrite <-(set_unfold (x ∈ X) P), <-(set_unfold (x ∈ Y) Q).
+  by rewrite <-(set_unfold_elem_of x X P), <-(set_unfold_elem_of x Y Q).
 Qed.
 
 (* Algebraic laws *)

theories/propset.v

@@ -44,10 +44,10 @@ Instance propset_join : MJoin propset := λ A (XX : propset (propset A)),
 Instance propset_monad_set : MonadSet propset.
 Proof. by split; try apply _. Qed.
 
-Instance set_unfold_propset_top {A} (x : A) : SetUnfold (x ∈ (⊤ : propset A)) True.
+Instance set_unfold_propset_top {A} (x : A) : SetUnfoldElemOf x (⊤ : propset A) True.
 Proof. by constructor. Qed.
 Instance set_unfold_PropSet {A} (P : A → Prop) x Q :
-  SetUnfoldSimpl (P x) Q → SetUnfold (x ∈ PropSet P) Q.
+  SetUnfoldSimpl (P x) Q → SetUnfoldElemOf x (PropSet P) Q.
 Proof. intros HPQ. constructor. apply HPQ. Qed.
 
 Global Opaque propset_elem_of propset_top propset_empty propset_singleton.