diff --git a/src/core/inverse.ml b/src/core/inverse.ml
index 4ddd9217e..e5fd0a084 100644
--- a/src/core/inverse.ml
+++ b/src/core/inverse.ml
@@ -7,8 +7,8 @@ open Print
 open Lplib
 
 (** Logging function for unification. *)
-let log_inv = Logger.make 'v' "invr" "inverse"
-let log_inv = log_inv.pp
+let log = Logger.make 'v' "invr" "inverse"
+let log = log.pp
 
 (** [cache f s] is equivalent to [f s] but [f s] is computed only once unless
    the rules of [s] are changed. *)
@@ -23,10 +23,10 @@ let cache : (sym -> 'a) -> (sym -> 'a) = fun f ->
 (** [const_graph s] returns the list of pairs [(s0,s1)] such that [s]
    has a rule of the form [s (s0 ...) ↪ s1 ...]. *)
 let const_graph : sym -> (sym * sym) list = fun s ->
-  if Logger.log_enabled () then log_inv "check rules of %a" sym s;
+  if Logger.log_enabled () then log "check rules of %a" sym s;
   let add s0 s1 l =
     if Logger.log_enabled () then
-      log_inv (Color.yel "%a %a ↪ %a") sym s sym s0 sym s1;
+      log (Color.yel "%a %a ↪ %a") sym s sym s0 sym s1;
     (s0,s1)::l
   in
   let f l rule =
@@ -61,12 +61,12 @@ let inverse_const : sym -> sym -> sym = fun s s' ->
    a rule of the form [s (s0 _ _) ↪ Π x:s1 _, s2 r] with [b=true] iff [x]
    occurs in [r]. *)
 let prod_graph : sym -> (sym * sym * sym * bool) list = fun s ->
-  if Logger.log_enabled () then log_inv "check rules of %a" sym s;
+  if Logger.log_enabled () then log "check rules of %a" sym s;
   let add (s0,s1,s2,b) l =
     if Logger.log_enabled () then
-      if b then log_inv (Color.yel "%a (%a _ _) ↪ Π x:%a _, %a _[x]")
+      if b then log (Color.yel "%a (%a _ _) ↪ Π x:%a _, %a _[x]")
                   sym s sym s0 sym s1 sym s2
-      else log_inv (Color.yel "%a (%a _ _) ↪ %a _ → %a _")
+      else log (Color.yel "%a (%a _ _) ↪ %a _ → %a _")
              sym s sym s0 sym s1 sym s2;
     (s0,s1,s2,b)::l
   in
@@ -119,7 +119,7 @@ let inverse_prod : sym -> sym -> sym * sym * sym * bool = fun s s' ->
 (** [inverse s v] tries to compute a term [u] such that [s(u)] reduces to [v].
 @raise [Not_found] otherwise. *)
 let rec inverse : sym -> term -> term = fun s v ->
-  if Logger.log_enabled () then log_inv "compute %a⁻¹(%a)" sym s term v;
+  if Logger.log_enabled () then log "compute %a⁻¹(%a)" sym s term v;
   match get_args v with
   | Symb s', [t] when s' == s -> t
   | Symb s', ts -> add_args (mk_Symb (inverse_const s s')) ts
@@ -143,5 +143,5 @@ let rec inverse : sym -> term -> term = fun s v ->
 let inverse : sym -> term -> term = fun s v ->
   let t = inverse s v in let v' = mk_Appl(mk_Symb s,t) in
   if Eval.eq_modulo [] v' v then t
-  else (if Logger.log_enabled() then log_inv "%a ≢ %a@" term v' term v;
+  else (if Logger.log_enabled() then log "%a ≢ %a@" term v' term v;
         raise Not_found)
diff --git a/src/handle/command.ml b/src/handle/command.ml
index 25bb420bb..c4631c04b 100644
--- a/src/handle/command.ml
+++ b/src/handle/command.ml
@@ -416,7 +416,7 @@ let get_proof_data : compiler -> sig_state -> p_command -> cmd_output =
     (* Verify modifiers. *)
     let prop, expo, mstrat = handle_modifiers p_sym_mod in
     let opaq = List.exists Syntax.is_opaq p_sym_mod in
-    let pdata_prv = expo = Privat || (p_sym_def && opaq) in
+    let pdata_prv = opaq || expo = Privat in
     (match p_sym_def, opaq, prop, mstrat with
      | false, true, _, _ -> fatal pos "Symbol declarations cannot be opaque."
      | true, _, Const, _ -> fatal pos "Definitions cannot be constant."
@@ -515,9 +515,8 @@ let get_proof_data : compiler -> sig_state -> p_command -> cmd_output =
             wrn pe.pos "Proof admitted.";
             (* Keep the definition only if the symbol is not opaque. *)
             let d =
-              if pdata_prv then None
-              else
-                Option.map (fun m -> unfold (mk_Meta(m,[||]))) ps.proof_term
+              if opaq then None
+              else Option.map (fun m -> unfold (mk_Meta(m,[||]))) ps.proof_term
             in
             (* Add the symbol in the signature. *)
             fst (Sig_state.add_symbol
@@ -526,12 +525,10 @@ let get_proof_data : compiler -> sig_state -> p_command -> cmd_output =
             (* Check that the proof is indeed finished. *)
             if not (finished ps) then
               fatal pe.pos "The proof is not finished:@.%a" goals ps;
-            (* Keep the definition only if the symbol is not private and not
-               opaque. *)
+            (* Keep the definition only if the symbol is not opaque. *)
             let d =
-              if pdata_prv then None
-              else
-                Option.map (fun m -> unfold (mk_Meta(m,[||]))) ps.proof_term
+              if opaq then None
+              else Option.map (fun m -> unfold (mk_Meta(m,[||]))) ps.proof_term
             in
             (* Add the symbol in the signature. *)
             Console.out 2 (Color.red "symbol %a : %a") uid id term a;
diff --git a/tests/OK/1035.lp b/tests/OK/1035.lp
new file mode 100644
index 000000000..ba1a60078
--- /dev/null
+++ b/tests/OK/1035.lp
@@ -0,0 +1,18 @@
+symbol Set:TYPE;
+injective symbol τ:Set → TYPE;
+symbol ℕ:TYPE;
+symbol 0:ℕ;
+symbol 𝑰 [a]: ℕ → τ a;
+
+symbol code_S' : Set;
+symbol S' ≔ τ code_S';
+//print S';
+//debug +uv;
+symbol a':S' ≔ 𝑰 0;
+//debug -uv;
+
+private symbol code_S : Set;
+private symbol S ≔ τ code_S;
+//print S;
+//debug +uv;
+private symbol a: S ≔ 𝑰 0;