diff --git a/easycrypt.project b/easycrypt.project
index 727e5f7819..eb800b8bb8 100644
--- a/easycrypt.project
+++ b/easycrypt.project
@@ -1,3 +1,3 @@
 [general]
-provers = CVC5@1.0
-provers = Z3@4.12
+provers = CVC5@1.1
+provers = Z3@4.16
diff --git a/examples/cramer-shoup/cramer_shoup.ec b/examples/cramer-shoup/cramer_shoup.ec
index f852e4bcbb..b66255ee1d 100644
--- a/examples/cramer-shoup/cramer_shoup.ec
+++ b/examples/cramer-shoup/cramer_shoup.ec
@@ -868,8 +868,10 @@ section Security_Aux.
     (forall (x : 'a), mu1 dt x <= r) => mu dt (mem l) <= n%r * r.
   proof.
     move=> Hsize Hmu1;apply (ler_trans ((size l)%r * r)).
-    + by apply mu_mem_le_mu1.
-    apply ler_wpmul2r; 1: smt (mu_bounded).
+    + by apply: mu_mem_le_mu1.
+    apply: ler_wpmul2r.
+    + apply: (ler_trans (mu1 dt witness)); 1:exact: ge0_mu.
+      exact: Hmu1.
     by apply le_fromint.
   qed.
 
diff --git a/examples/ehoare/adversary.ec b/examples/ehoare/adversary.ec
index 6117ad1639..270ed0f29f 100644
--- a/examples/ehoare/adversary.ec
+++ b/examples/ehoare/adversary.ec
@@ -14,7 +14,11 @@ axiom dr_mu_test : 0%r < p.
 op eps : real.
 axiom dr_mu1 : forall (x:r), mu1 dr x <= eps.
 
-lemma eps_ge0: 0%r <= eps. by smt(dr_mu1 mu_bounded). qed.
+lemma eps_ge0: 0%r <= eps.
+apply: (ler_trans (mu1 dr witness)).
++ exact: ge0_mu.
+exact: dr_mu1.
+qed.
 
 module type Oracle = { 
   proc o () : unit 
diff --git a/theories/algebra/Bigalg.ec b/theories/algebra/Bigalg.ec
index c6cacc944d..fee55788ac 100644
--- a/theories/algebra/Bigalg.ec
+++ b/theories/algebra/Bigalg.ec
@@ -324,7 +324,7 @@ elim: s => // x s IHs F_ge0; rewrite BMul.big_cons.
 have {IHs} IHs := IHs _; first by smt().
 case: (P x) => [Px F_big_gt0 a a_x_s Pa| nPx /IHs]; 2:smt().
 rewrite pmulr_gt0 in F_big_gt0; 1, 3:smt().
-apply: prodr_ge0_seq; smt().
+by apply: prodr_ge0_seq; smt().
 qed.
 
 lemma ler_prod_seq (P : 'a -> bool) (F1 F2 : 'a -> t) s:
diff --git a/theories/algebra/DynMatrix.eca b/theories/algebra/DynMatrix.eca
index 3f813c4ec9..ba04eb0044 100644
--- a/theories/algebra/DynMatrix.eca
+++ b/theories/algebra/DynMatrix.eca
@@ -1939,7 +1939,11 @@ qed.
 lemma supp_dmatrix_full m d r c : 
   0 <= r => 0 <= c =>
   is_full d => m \in dmatrix d r c <=> size m = (r,c).
-proof. smt(supp_dmatrix). qed.
+proof.
+move=> ge0_r ge0_c d_fu.
+rewrite supp_dmatrix //; split=> //.
+by move=> -> /= i j _; rewrite d_fu.
+qed.
 
 lemma dvector_rnd_funi (d : R distr) (v1 v2 : vector) l :
   is_funiform d => size v1 = size v2 => 
diff --git a/theories/datatypes/List.ec b/theories/datatypes/List.ec
index 47e026db5f..7bfc7fbaef 100644
--- a/theories/datatypes/List.ec
+++ b/theories/datatypes/List.ec
@@ -858,7 +858,10 @@ proof. by rewrite /= lezNgt; case: (0 < n). qed.
 
 lemma size_drop n (s : 'a list):
   0 <= n => size (drop n s) = max 0 (size s - n).
-proof. by elim: s n => //= /#. qed.
+proof.
+elim: s n => //= [/#|x xs ih n ge0_n].
+smt(size_ge0).
+qed.
 
 lemma drop_cat n (s1 s2 : 'a list):
   drop n (s1 ++ s2) =
diff --git a/theories/distributions/Distr.ec b/theories/distributions/Distr.ec
index c7f35b146e..8746e2c991 100644
--- a/theories/distributions/Distr.ec
+++ b/theories/distributions/Distr.ec
@@ -650,7 +650,8 @@ qed.
 
 lemma distr_0Vmem (d : 'a distr) : d = dnull \/ exists x, x \in d.
 proof.
-have := pred_0Vmem (support d); smt(support_eq0 supportP).
+have:= pred_0Vmem (support d); case: (exists x, x \in d)=> //=.
+by rewrite negb_exists=> /support_eq0.
 qed.
 
 lemma pmax_dnull ['a] : p_max dnull<:'a> = 0%r.