Split the development into different directories

FiniteSets/fsets/operations_decidable.v

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+(* Operations on [FSet A] when [A] has decidable equality *)
+Require Import HoTT HitTactics.
+Require Export representations.definition fsets.operations.
+
+Section decidable_A.
+  Context {A : Type}.
+  Context {A_deceq : DecidablePaths A}.
+  Context `{Univalence}.
+
+  Global Instance isIn_decidable : forall (a : A) (X : FSet A), Decidable (isIn a X).
+  Proof.
+    intros a.
+    hinduction ; try (intros ; apply path_ishprop).
+    - apply _.
+    - intros. apply _.
+    - intros. apply _. 
+  Defined.
+
+  Definition isIn_b (a : A) (X : FSet A) :=
+    match dec (isIn a X) with
+    | inl _ => true
+    | inr _ => false
+    end.
+  
+  Global Instance subset_decidable : forall (X Y : FSet A), Decidable (subset X Y).
+  Proof.
+    hinduction ; try (intros ; apply path_ishprop).
+    - intro ; apply _.
+    - intros ; apply _. 
+    - intros ; apply _.
+  Defined.
+
+  Definition subset_b (X Y : FSet A) :=
+    match dec (subset X Y) with
+    | inl _ => true
+    | inr _ => false
+    end.
+
+  Definition intersection (X Y : FSet A) : FSet A := comprehension (fun a => isIn_b a Y) X. 
+
+End decidable_A.