Generalize `gset_to_propset` to `set_to_propset` for any SemiSet.

This closes issue #25.

theories/gmap.v

@@ -237,11 +237,6 @@ Section gset.
   Global Instance gset_dom {A} : Dom (gmap K A) (gset K) := mapset_dom.
   Global Instance gset_dom_spec : FinMapDom K (gmap K) (gset K) := mapset_dom_spec.
 
-  Definition gset_to_propset (X : gset K) : propset K :=
-    {[ x | x ∈ X ]}.
-  Lemma elem_of_gset_to_propset (X : gset K) x : x ∈ gset_to_propset X ↔ x ∈ X.
-  Proof. done. Qed.
-
   Definition gset_to_gmap {A} (x : A) (X : gset K) : gmap K A :=
     (λ _, x) <$> mapset_car X.
 

theories/propset.v

@@ -34,6 +34,12 @@ Lemma top_subseteq {A} (X : propset A) : X ⊆ ⊤.
 Proof. done. Qed.
 Hint Resolve top_subseteq : core.
 
+Definition set_to_propset `{ElemOf A C} (X : C) : propset A :=
+  {[ x | x ∈ X ]}.
+Lemma elem_of_set_to_propset `{SemiSet A C} x (X : C) :
+  x ∈ set_to_propset X ↔ x ∈ X.
+Proof. done. Qed.
+
 Instance propset_ret : MRet propset := λ A (x : A), {[ x ]}.
 Instance propset_bind : MBind propset := λ A B (f : A → propset B) (X : propset A),
   PropSet (λ b, ∃ a, b ∈ f a ∧ a ∈ X).