diff --git a/lib/coq/set/Cardinal.v b/lib/coq/set/Cardinal.v
index f9338432ed9f5d5a063633bfd0094e6d6f997c44..224efb9acea643cacd29e4f8fed584d44537922f 100644
--- a/lib/coq/set/Cardinal.v
+++ b/lib/coq/set/Cardinal.v
@@ -475,7 +475,7 @@ destruct ClassicalEpsilon.excluded_middle_informative.
   destruct x0. 
   + inversion h1.
   + destruct x0.
-    - simpl in a0. eapply a0 in h2. eapply a0 in H0. intuition. subst. assumption.
+    - simpl in a0. eapply a0 in h2. eapply a0 in H0. intuition. subst. reflexivity.
     - simpl in h1; contradict h1; zify; omega.
 * inversion h1.
 Qed.
@@ -748,4 +748,5 @@ assert (List.length x <= List.length x0).
   - rewrite List.map_length; eauto.
 }
 omega.
-Qed.
\ No newline at end of file
+Qed.
+
diff --git a/lib/coq/set/Fset.v b/lib/coq/set/Fset.v
index 32e9742c0659285c586efac5951a33b7a5a74a84..ab29510f4c50f6f891b25343b6a5c8b178fdd086 100644
--- a/lib/coq/set/Fset.v
+++ b/lib/coq/set/Fset.v
@@ -4,8 +4,6 @@ Require Import BuiltIn.
 Require BuiltIn.
 Require HighOrd.
 Require int.Int.
-Require set.Cardinal.
-Require set.Set.
 
 (* Why3 goal *)
 Definition fset : forall (a:Type), Type.
@@ -19,6 +17,8 @@ Defined.
 Definition mem {a:Type} {a_WT:WhyType a} : a -> fset a -> Prop.
 Proof.
 intros. destruct X0 as (f, P).
+(* TODO remove this *)
+Require set.Set.
 apply (set.Set.mem X f).
 Defined.
 
@@ -34,7 +34,8 @@ Proof.
 intros s1 s2 h1.
 unfold infix_eqeq in h1. unfold mem in h1.
 destruct s1, s2.
-assert (x = x0). eapply set.Set.extensionality. intro. eauto.
+assert (x = x0).
+eapply set.Set.extensionality. intro. eauto.
 subst.
 assert (e = e0).
 (* TODO maybe provable on such property ? *)
@@ -71,7 +72,10 @@ Definition is_empty {a:Type} {a_WT:WhyType a} (s:fset a) : Prop :=
 (* Why3 goal *)
 Definition empty {a:Type} {a_WT:WhyType a} : fset a.
 Proof.
-exists (fun x => false). apply Cardinal.is_finite_empty. unfold set.Set.is_empty.
+exists (fun x => false). 
+(* TODO remove this *)
+Require Cardinal.
+apply Cardinal.is_finite_empty. unfold set.Set.is_empty.
 unfold set.Set.mem. intuition.
 Defined.
 
diff --git a/lib/coq/set/FsetInt.v b/lib/coq/set/FsetInt.v
index 3daf6246497958798a63b16075b6b9ae05094d45..7d770c02a113af41e008da282f16b5cc976b5a4e 100644
--- a/lib/coq/set/FsetInt.v
+++ b/lib/coq/set/FsetInt.v
@@ -196,7 +196,6 @@ unfold interval, Fset.mem, set.Set.mem.
 destruct Z_le_dec; try destruct Z_lt_dec; intuition; try inversion H.
 Qed.
 
-
 Lemma interval_is_finite: forall l r, 
   Cardinal.is_finite (fun x : int => 
     if Z_le_dec l x then if Z_lt_dec x r then true