diff --git a/projects/lib/GmpAux.v b/projects/lib/GmpAux.v
index 640cbaa..8bdd8d1 100755
--- a/projects/lib/GmpAux.v
+++ b/projects/lib/GmpAux.v
@@ -25,13 +25,49 @@ Lemma Z_mod_add_carry: forall (a b m: Z),
    m > 0 -> 0 <= a < m -> 0 <= b < m ->
    (a + b) mod m < b ->
    a + b = (a + b) mod m + m.
-Proof. Admitted.
+Proof.
+  intros.
+  pose proof (Z_div_mod_eq_full (a + b) m).
+  assert (m <= a + b < 2 * m). {
+    assert (a + b >= m \/ b <= a + b < m). { lia. }
+    destruct H4.
+    + lia.
+    + assert ((a + b) mod m = a + b). { 
+        apply Z.mod_small.
+        lia.
+      }
+      lia.
+  }
+  assert ((a + b) / m = 1). {
+    pose proof (Zdiv_le_lower_bound (a + b) m 1 ltac:(lia) ltac:(lia)).
+    pose proof (Z.div_lt_upper_bound (a + b) m 2 ltac:(lia) ltac:(lia)).
+    lia.
+  }
+  rewrite H5 in H3.
+  nia.
+Qed.
 
 Lemma Z_mod_add_uncarry: forall (a b m: Z),
   m > 0 -> 0 <= a < m -> 0 <= b < m ->
   (a + b) mod m >= b ->
   a + b = (a + b) mod m.
-Proof. Admitted.
+Proof.
+  intros.
+  assert (b <= a + b < m). {
+    assert (a + b < m \/ m <= a + b < m + b). { lia. }
+    destruct H3.
+    + lia.
+    + assert ((a + b) / m = 1). { 
+        pose proof (Zdiv_le_lower_bound (a + b) m 1 ltac:(lia) ltac:(lia)).
+        pose proof (Z.div_lt_upper_bound (a + b) m 2 ltac:(lia) ltac:(lia)).
+        lia.
+      }
+      pose proof (Z_div_mod_eq_full (a + b) m).
+      rewrite H4 in H5.
+      lia.
+  }
+  rewrite Z.mod_small; lia.
+Qed.
 
 Lemma Z_mod_3add_carry10: forall (a b c m: Z),
   m > 0 -> 0 <= a < m -> 0 <= b < m -> 0 <= c < m ->
@@ -354,11 +390,6 @@ Proof.
   split; tauto.
 Qed.
 
-Lemma store_uint_array_rec_def2undef: forall x a b l,
-  store_uint_array_rec x a b l |--
-  store_undef_uint_array_rec x a b.
-Proof. Admitted.
-
 Lemma store_undef_uint_array_rec_divide: forall x l mid r,
   0 <= l <= r ->
   l <= mid <= r ->
@@ -387,4 +418,45 @@ Proof.
   rewrite H1.
   split; entailer!.
 Qed.
+
+Lemma store_uint_array_rec_def2undef: forall x a b l,
+  0 <= a <= b ->
+  store_uint_array_rec x a b l |--
+  store_undef_uint_array_rec x a b.
+Proof.
+  intros.
+  revert x a b H.
+  induction l; intros.
+  + unfold store_uint_array_rec.
+    simpl.
+    entailer!.
+    subst.
+    unfold store_undef_uint_array_rec.
+    assert (b - b = 0). { lia. }
+    rewrite H0; clear H0.
+    simpl.
+    entailer!.
+  + assert (a0 = b \/ a0 < b). { lia. }
+    destruct H0.
+    - unfold store_uint_array_rec.
+      simpl.
+      sep_apply store_array_rec_false; try lia.
+      entailer!.
+    - sep_apply store_uint_array_rec_cons; try lia.
+      pose proof (store_undef_uint_array_rec_divide x a0 (a0 + 1) b ltac:(lia) ltac:(lia)).
+      destruct H2 as [_ H2].
+      rewrite <-H2; clear H2.
+      specialize (IHl x (a0 + 1) b ltac:(lia)).
+      sep_apply IHl; entailer!.
+      assert ((x + a0 * sizeof ( UINT )) # UInt |-> a |-- 
+                store_uint_array_rec x a0 (a0 + 1) [a]). {
+        unfold store_uint_array_rec.
+        simpl.
+        entailer!.
+      }
+      sep_apply H2; clear H2.
+      sep_apply store_uint_array_single_to_undef.
+      entailer!.
+Qed.
+
 End Aux.
\ No newline at end of file
diff --git a/projects/lib/gmp_goal.v b/projects/lib/gmp_goal.v
index ce71dac..779f75b 100755
--- a/projects/lib/gmp_goal.v
+++ b/projects/lib/gmp_goal.v
@@ -6071,6 +6071,521 @@ forall (n: Z) (u: Z) ,
   **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr))
 .
 
+(*----- Function mpz_swap -----*)
+
+Definition mpz_swap_return_wit_1_1 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+|--
+  (store_Z u_pre m )
+  **  (store_Z v_pre n )
+.
+
+Definition mpz_swap_return_wit_1_2 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+|--
+  (store_Z u_pre m )
+  **  (store_Z v_pre n )
+.
+
+Definition mpz_swap_return_wit_1_3 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+|--
+  (store_Z u_pre m )
+  **  (store_Z v_pre n )
+.
+
+Definition mpz_swap_return_wit_1_4 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+|--
+  (store_Z u_pre m )
+  **  (store_Z v_pre n )
+.
+
+Definition mpz_swap_partial_solve_wit_1 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) ,
+  (store_Z u_pre n )
+  **  (store_Z v_pre m )
+|--
+  (store_Z u_pre n )
+  **  (store_Z v_pre m )
+.
+
+Definition mpz_swap_partial_solve_wit_2 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) ,
+  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  (store_Z v_pre m )
+|--
+  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  (store_Z v_pre m )
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_3 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) ,
+  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  (store_Z v_pre m )
+|--
+  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  (store_Z v_pre m )
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_4 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_5 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_6 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_7 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+.
+
+Definition mpz_swap_partial_solve_wit_8 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+.
+
+Definition mpz_swap_partial_solve_wit_9 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+.
+
+Definition mpz_swap_partial_solve_wit_10 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+.
+
+Definition mpz_swap_partial_solve_wit_11 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+.
+
+Definition mpz_swap_partial_solve_wit_12 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+.
+
+Definition mpz_swap_partial_solve_wit_13 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  (mpd_store_Z_compact ptr1 n size1 cap1 )
+.
+
+Definition mpz_swap_partial_solve_wit_14 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+|--
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+.
+
+Definition mpz_swap_partial_solve_wit_15 := 
+forall (v_pre: Z) (u_pre: Z) (m: Z) (n: Z) (ptr1: Z) (cap1: Z) (size1: Z) (ptr2: Z) (cap2: Z) (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+|--
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |] 
+  &&  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1)
+  **  ((&((u_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v_pre)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+.
+
+Definition mpz_swap_which_implies_wit_1 := 
+forall (n: Z) (u: Z) ,
+  (store_Z u n )
+|--
+  (EX (ptr1: Z)  (cap1: Z)  (size1: Z) ,
+  [| (size1 >= 0) |] 
+  &&  [| (n >= 0) |]
+  &&  (mpd_store_Z_compact ptr1 n size1 cap1 )
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1))
+  ||
+  (EX (ptr1: Z)  (cap1: Z)  (size1: Z) ,
+  [| (size1 < 0) |] 
+  &&  [| (n < 0) |]
+  &&  (mpd_store_Z_compact ptr1 (-n) (-size1) cap1 )
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size1)
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap1)
+  **  ((&((u)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr1))
+.
+
+Definition mpz_swap_which_implies_wit_2 := 
+forall (m: Z) (v: Z) ,
+  (store_Z v m )
+|--
+  (EX (ptr2: Z)  (cap2: Z)  (size2: Z) ,
+  [| (size2 >= 0) |] 
+  &&  [| (m >= 0) |]
+  &&  (mpd_store_Z_compact ptr2 m size2 cap2 )
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2))
+  ||
+  (EX (ptr2: Z)  (cap2: Z)  (size2: Z) ,
+  [| (size2 < 0) |] 
+  &&  [| (m < 0) |]
+  &&  (mpd_store_Z_compact ptr2 (-m) (-size2) cap2 )
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_size")) # Int  |-> size2)
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_alloc")) # Int  |-> cap2)
+  **  ((&((v)  # "__mpz_struct" ->ₛ "_mp_d")) # Ptr  |-> ptr2))
+.
+
 Module Type VC_Correct.
 
 Axiom proof_of_gmp_abs_safety_wit_1 : gmp_abs_safety_wit_1.
@@ -6249,5 +6764,26 @@ Axiom proof_of_mpz_sgn_partial_solve_wit_1 : mpz_sgn_partial_solve_wit_1.
 Axiom proof_of_mpz_sgn_partial_solve_wit_2 : mpz_sgn_partial_solve_wit_2.
 Axiom proof_of_mpz_sgn_partial_solve_wit_3 : mpz_sgn_partial_solve_wit_3.
 Axiom proof_of_mpz_sgn_which_implies_wit_1 : mpz_sgn_which_implies_wit_1.
+Axiom proof_of_mpz_swap_return_wit_1_1 : mpz_swap_return_wit_1_1.
+Axiom proof_of_mpz_swap_return_wit_1_2 : mpz_swap_return_wit_1_2.
+Axiom proof_of_mpz_swap_return_wit_1_3 : mpz_swap_return_wit_1_3.
+Axiom proof_of_mpz_swap_return_wit_1_4 : mpz_swap_return_wit_1_4.
+Axiom proof_of_mpz_swap_partial_solve_wit_1 : mpz_swap_partial_solve_wit_1.
+Axiom proof_of_mpz_swap_partial_solve_wit_2 : mpz_swap_partial_solve_wit_2.
+Axiom proof_of_mpz_swap_partial_solve_wit_3 : mpz_swap_partial_solve_wit_3.
+Axiom proof_of_mpz_swap_partial_solve_wit_4 : mpz_swap_partial_solve_wit_4.
+Axiom proof_of_mpz_swap_partial_solve_wit_5 : mpz_swap_partial_solve_wit_5.
+Axiom proof_of_mpz_swap_partial_solve_wit_6 : mpz_swap_partial_solve_wit_6.
+Axiom proof_of_mpz_swap_partial_solve_wit_7 : mpz_swap_partial_solve_wit_7.
+Axiom proof_of_mpz_swap_partial_solve_wit_8 : mpz_swap_partial_solve_wit_8.
+Axiom proof_of_mpz_swap_partial_solve_wit_9 : mpz_swap_partial_solve_wit_9.
+Axiom proof_of_mpz_swap_partial_solve_wit_10 : mpz_swap_partial_solve_wit_10.
+Axiom proof_of_mpz_swap_partial_solve_wit_11 : mpz_swap_partial_solve_wit_11.
+Axiom proof_of_mpz_swap_partial_solve_wit_12 : mpz_swap_partial_solve_wit_12.
+Axiom proof_of_mpz_swap_partial_solve_wit_13 : mpz_swap_partial_solve_wit_13.
+Axiom proof_of_mpz_swap_partial_solve_wit_14 : mpz_swap_partial_solve_wit_14.
+Axiom proof_of_mpz_swap_partial_solve_wit_15 : mpz_swap_partial_solve_wit_15.
+Axiom proof_of_mpz_swap_which_implies_wit_1 : mpz_swap_which_implies_wit_1.
+Axiom proof_of_mpz_swap_which_implies_wit_2 : mpz_swap_which_implies_wit_2.
 
 End VC_Correct.
diff --git a/projects/lib/gmp_proof_auto.v b/projects/lib/gmp_proof_auto.v
index 91ba3d5..7cbae94 100755
--- a/projects/lib/gmp_proof_auto.v
+++ b/projects/lib/gmp_proof_auto.v
@@ -339,3 +339,48 @@ Proof. Admitted.
 Lemma proof_of_mpz_sgn_partial_solve_wit_3 : mpz_sgn_partial_solve_wit_3.
 Proof. Admitted. 
 
+Lemma proof_of_mpz_swap_partial_solve_wit_1 : mpz_swap_partial_solve_wit_1.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_2 : mpz_swap_partial_solve_wit_2.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_3 : mpz_swap_partial_solve_wit_3.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_4 : mpz_swap_partial_solve_wit_4.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_5 : mpz_swap_partial_solve_wit_5.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_6 : mpz_swap_partial_solve_wit_6.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_7 : mpz_swap_partial_solve_wit_7.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_8 : mpz_swap_partial_solve_wit_8.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_9 : mpz_swap_partial_solve_wit_9.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_10 : mpz_swap_partial_solve_wit_10.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_11 : mpz_swap_partial_solve_wit_11.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_12 : mpz_swap_partial_solve_wit_12.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_13 : mpz_swap_partial_solve_wit_13.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_14 : mpz_swap_partial_solve_wit_14.
+Proof. Admitted. 
+
+Lemma proof_of_mpz_swap_partial_solve_wit_15 : mpz_swap_partial_solve_wit_15.
+Proof. Admitted. 
+
diff --git a/projects/lib/gmp_proof_manual.v b/projects/lib/gmp_proof_manual.v
index 5c88acf..c9c2d2d 100755
--- a/projects/lib/gmp_proof_manual.v
+++ b/projects/lib/gmp_proof_manual.v
@@ -692,7 +692,7 @@ Proof.
   entailer!.
   rewrite H20.
   entailer!.
-  apply store_uint_array_rec_def2undef.
+  apply store_uint_array_rec_def2undef; try lia.
   assert (Zlength l' = n_pre) by lia.
   rewrite <- H7.
   tauto.
@@ -1261,7 +1261,7 @@ Proof.
   entailer!.
   rewrite H10.
   entailer!.
-  apply store_uint_array_rec_def2undef.
+  apply store_uint_array_rec_def2undef; try lia.
   rewrite <- H29.
   assert (val_a_prefix = val_a). {
     rewrite <-H18 in H7.
@@ -1722,3 +1722,74 @@ Proof.
     Exists ptr cap size.
     entailer!.
 Qed.
+
+Lemma proof_of_mpz_swap_return_wit_1_1 : mpz_swap_return_wit_1_1.
+Proof.
+  pre_process.
+  unfold store_Z.
+  Exists ptr2 cap2 size2.
+  Exists ptr1 cap1 size1.
+  Right; Right.
+  entailer!.
+Qed.
+
+Lemma proof_of_mpz_swap_return_wit_1_2 : mpz_swap_return_wit_1_2.
+Proof.
+  pre_process.
+  subst.
+  unfold store_Z.
+  Exists ptr2 cap2 size2.
+  Exists ptr1 cap1 size1.
+  Right; Left.
+  entailer!.
+Qed.
+
+Lemma proof_of_mpz_swap_return_wit_1_3 : mpz_swap_return_wit_1_3.
+Proof.
+  pre_process.
+  unfold store_Z.
+  Exists ptr2 cap2 size2.
+  Exists ptr1 cap1 size1.
+  Left; Right.
+  entailer!.
+Qed.
+
+Lemma proof_of_mpz_swap_return_wit_1_4 : mpz_swap_return_wit_1_4.
+Proof.
+  pre_process.
+  unfold store_Z.
+  Exists ptr2 cap2 size2.
+  Exists ptr1 cap1 size1.
+  Left; Left.
+  entailer!.
+Qed.
+
+Lemma proof_of_mpz_swap_which_implies_wit_1 : mpz_swap_which_implies_wit_1.
+Proof.
+  pre_process.
+  unfold store_Z.
+  Intros ptr cap size.
+  rewrite orp_sepcon_left.
+  Split.
+  + Right.
+    Exists ptr cap size.
+    entailer!.
+  + Left.
+    Exists ptr cap size.
+    entailer!.
+Qed.
+
+Lemma proof_of_mpz_swap_which_implies_wit_2 : mpz_swap_which_implies_wit_2.
+Proof.
+  pre_process.
+  unfold store_Z.
+  Intros ptr cap size.
+  rewrite orp_sepcon_left.
+  Split.
+  + Right.
+    Exists ptr cap size.
+    entailer!.
+  + Left.
+    Exists ptr cap size.
+    entailer!.
+Qed.
\ No newline at end of file
diff --git a/projects/mini-gmp.c b/projects/mini-gmp.c
index fa44022..5ba45f6 100755
--- a/projects/mini-gmp.c
+++ b/projects/mini-gmp.c
@@ -569,13 +569,44 @@ mpz_sgn (const mpz_t u)
   return gmp_cmp (u->_mp_size, 0);
 }
 
-/*void
+void
 mpz_swap (mpz_t u, mpz_t v)
+/*@
+  With
+    n m
+  Require
+    store_Z(u, n) * store_Z(v, m)
+  Ensure
+    store_Z(u@pre, m) * store_Z(v@pre, n)
+*/
 {
-  int_swap (u->_mp_alloc, v->_mp_alloc);
-  mp_ptr_swap(u->_mp_d, v->_mp_d);
-  int_swap (u->_mp_size, v->_mp_size);
-}*/
+  /*@
+    store_Z(u, n)
+    which implies
+    exists ptr1 cap1 size1,
+      (size1 < 0 && n < 0 && mpd_store_Z_compact(ptr1, -n, -size1, cap1) ||
+        size1 >= 0 && n >= 0 && mpd_store_Z_compact(ptr1, n, size1, cap1)) &&
+      u->_mp_size == size1 && 
+      u->_mp_alloc == cap1 && 
+      u->_mp_d == ptr1
+  */
+  /*@
+    store_Z(v, m)
+    which implies
+    exists ptr2 cap2 size2,
+      (size2 < 0 && m < 0 && mpd_store_Z_compact(ptr2, -m, -size2, cap2) ||
+        size2 >= 0 && m >= 0 && mpd_store_Z_compact(ptr2, m, size2, cap2)) &&
+      v->_mp_size == size2 && 
+      v->_mp_alloc == cap2 && 
+      v->_mp_d == ptr2
+  */
+  /*@
+    Given ptr1 cap1 size1 ptr2 cap2 size2
+  */
+  int_swap (&u->_mp_alloc, &v->_mp_alloc);
+  mp_ptr_swap(&u->_mp_d, &v->_mp_d);
+  int_swap (&u->_mp_size, &v->_mp_size);
+}
 
 /* MPZ addition and subtraction */
 
diff --git a/projects/mini-gmp.h b/projects/mini-gmp.h
index 84f2deb..72670bb 100755
--- a/projects/mini-gmp.h
+++ b/projects/mini-gmp.h
@@ -30,18 +30,38 @@ typedef const __mpz_struct *mpz_srcptr;
 /* BEGIN Given Functions */
 
 /* Swap functions. */
-void int_swap(int x, int y)
+void int_swap(int *x, int *y)
 /*@
+  With
+    px py
   Require
-    emp
+    *x == px && *y == py
   Ensure
-    x == y@pre && y == x@pre
+    *x@pre == py && *y@pre == px
 */
 ;
 
-void mp_ptr_swap(unsigned int *x, unsigned int *y);
+void mp_ptr_swap(unsigned int **x, unsigned int **y)
+/*@
+  With
+    px py
+  Require
+    *x == px && *y == py
+  Ensure
+    *x@pre == py && *y@pre == px
+*/
+;
 
-void mpz_srcptr_swap(mpz_srcptr x, mpz_srcptr y);
+void mpz_srcptr_swap(mpz_srcptr *x, mpz_srcptr *y)
+/*@
+  With
+    px py
+  Require
+    *x == px && *y == py
+  Ensure
+    *x@pre == py && *y@pre == px
+*/
+;
 
 /* Memory allocation functions. */
 static unsigned int *
@@ -96,7 +116,7 @@ void mpz_clear (mpz_t r);
 int mpz_sgn (const mpz_t u);
 
 void mpz_neg (mpz_t, const mpz_t);
-void mpz_swap (mpz_t, mpz_t);
+void mpz_swap (mpz_t u, mpz_t v);
 
 void mpz_add (mpz_t, const mpz_t, const mpz_t);
 void mpz_sub (mpz_t, const mpz_t, const mpz_t);