Use plain identifiers whenever possible in the Coq printer.

This patch also fully qualifies some realized types and constructors to
avoid inadvertent shadowing.

drivers/coq-common.gen

@@ -19,31 +19,31 @@ theory BuiltIn
 
   prelude "Require Import BuiltIn."
 
-  syntax type int "Z"
-  syntax type real "R"
+  syntax type int "Numbers.BinNums.Z"
+  syntax type real "Reals.Rdefinitions.R"
   syntax predicate  (=)   "(%1 = %2)"
 end
 
 
 theory Unit
-  syntax type unit "unit"
+  syntax type unit "Init.Datatypes.unit"
 end
 
 theory Bool
 
-  syntax type bool   "bool"
+  syntax type bool "Init.Datatypes.bool"
 
-  syntax function True  "true"
-  syntax function False "false"
+  syntax function True  "Init.Datatypes.true"
+  syntax function False "Init.Datatypes.false"
 end
 
 theory bool.Bool
 
-  syntax function andb  "(Init.Datatypes.andb %1 %2)"
-  syntax function orb   "(Init.Datatypes.orb %1 %2)"
-  syntax function xorb  "(Init.Datatypes.xorb %1 %2)"
-  syntax function notb  "(Init.Datatypes.negb %1)"
-  syntax function implb "(Init.Datatypes.implb %1 %2)"
+  syntax function andb  "Init.Datatypes.andb"
+  syntax function orb   "Init.Datatypes.orb"
+  syntax function xorb  "Init.Datatypes.xorb"
+  syntax function notb  "Init.Datatypes.negb"
+  syntax function implb "Init.Datatypes.implb"
 
 end
 
@@ -87,7 +87,7 @@ end
 
 theory int.Abs
 
-  syntax function abs "(ZArith.BinInt.Z.abs %1)"
+  syntax function abs "ZArith.BinInt.Z.abs"
 
   remove prop Abs_pos
 
@@ -95,8 +95,8 @@ end
 
 theory int.MinMax
 
-  syntax function min "(ZArith.BinInt.Z.min %1 %2)"
-  syntax function max "(ZArith.BinInt.Z.max %1 %2)"
+  syntax function min "ZArith.BinInt.Z.min"
+  syntax function max "ZArith.BinInt.Z.max"
 
 end
 
@@ -106,8 +106,8 @@ end
 
 theory int.EuclideanDivision
 
-  syntax function div "(ZArith.BinInt.Z.div %1 %2)"
-  syntax function mod "(ZArith.BinInt.Z.modulo %1 %2)"
+  syntax function div "ZArith.BinInt.Z.div"
+  syntax function mod "ZArith.BinInt.Z.modulo"
 
   remove prop Div_mod
   remove prop Div_bound
@@ -124,8 +124,8 @@ theory int.ComputerDivision
      with the same convention as mainstream programming language
      such C, Java, OCaml *)
 
-  syntax function div "(ZArith.BinInt.Z.quot %1 %2)"
-  syntax function mod "(ZArith.BinInt.Z.rem %1 %2)"
+  syntax function div "ZArith.BinInt.Z.quot"
+  syntax function mod "ZArith.BinInt.Z.rem"
 
   remove prop Div_mod
   remove prop Div_bound
@@ -155,7 +155,7 @@ theory real.Real
   syntax function (-_) "(-%1)%R"
   syntax function (*)  "(%1 * %2)%R"
   syntax function (/)  "(%1 / %2)%R"
-  syntax function inv  "(Reals.Rdefinitions.Rinv %1)"
+  syntax function inv  "(/ %1)%R"
 
   syntax predicate (<=) "(%1 <= %2)%R"
   syntax predicate (<)  "(%1 < %2)%R"
@@ -207,7 +207,7 @@ theory real.Abs
 
   prelude "Require Reals.Rbasic_fun."
 
-  syntax function abs "(Reals.Rbasic_fun.Rabs %1)"
+  syntax function abs "Reals.Rbasic_fun.Rabs"
 
   remove prop Abs_le
   remove prop Abs_pos
@@ -216,14 +216,14 @@ end
 
 theory real.MinMax
 
-  syntax function min "(Reals.Rbasic_fun.Rmin %1 %2)"
-  syntax function max "(Reals.Rbasic_fun.Rmax %1 %2)"
+  syntax function min "Reals.Rbasic_fun.Rmin"
+  syntax function max "Reals.Rbasic_fun.Rmax"
 
 end
 
 theory real.FromInt
 
-  syntax function from_int "(BuiltIn.IZR %1)"
+  syntax function from_int "BuiltIn.IZR"
 
   remove prop Zero
   remove prop One
@@ -238,8 +238,8 @@ theory real.Square
 
   prelude "Require Reals.R_sqrt."
 
-  syntax function sqr  "(Reals.RIneq.Rsqr %1)"
-  syntax function sqrt "(Reals.R_sqrt.sqrt %1)"  (* and not Rsqrt *)
+  syntax function sqr  "Reals.RIneq.Rsqr"
+  syntax function sqrt "Reals.R_sqrt.sqrt"  (* and not Rsqrt *)
 
   remove prop Sqrt_positive
   remove prop Sqrt_square
@@ -252,8 +252,8 @@ theory real.ExpLog
   prelude "Require Reals.Rtrigo_def."
   prelude "Require Reals.Rpower."
 
-  syntax function exp "(Reals.Rtrigo_def.exp %1)"
-  syntax function log "(Reals.Rpower.ln %1)"
+  syntax function exp "Reals.Rtrigo_def.exp"
+  syntax function log "Reals.Rpower.ln"
 
   remove prop Exp_zero
   remove prop Exp_sum
@@ -268,7 +268,7 @@ theory real.PowerInt
 
   prelude "Require Reals.Rfunctions."
 
-  syntax function power "(Reals.Rfunctions.powerRZ %1 %2)"
+  syntax function power "Reals.Rfunctions.powerRZ"
 
   remove prop Power_0 (* already as powerRZ_O *)
   (* remove prop Power_s *)
@@ -280,7 +280,7 @@ end
 
 theory real.PowerReal
 
-  syntax function pow "(Reals.Rpower.Rpower %1 %2)"
+  syntax function pow "Reals.Rpower.Rpower"
 
 end
 
@@ -290,14 +290,14 @@ theory real.Trigonometry
   prelude "Require Reals.Rtrigo1."
   prelude "Require Reals.Ratan."
 
-  syntax function cos "(Reals.Rtrigo_def.cos %1)"
-  syntax function sin "(Reals.Rtrigo_def.sin %1)"
+  syntax function cos "Reals.Rtrigo_def.cos"
+  syntax function sin "Reals.Rtrigo_def.sin"
 
   syntax function pi "Reals.Rtrigo1.PI"
 
-  syntax function tan "(Reals.Rtrigo1.tan %1)"
+  syntax function tan "Reals.Rtrigo1.tan"
 
-  syntax function atan "(Reals.Ratan.atan %1)"
+  syntax function atan "Reals.Ratan.atan"
 
   remove prop Pythagorean_identity
   remove prop Cos_le_one
@@ -313,41 +313,41 @@ end
 
 theory list.List
 
-  syntax type list "(list %1)"
+  syntax type list "Init.Datatypes.list"
   syntax function Nil "Init.Datatypes.nil"
-  syntax function Cons "(Init.Datatypes.cons %1 %2)"
+  syntax function Cons "Init.Datatypes.cons"
 
 end
 
 theory list.Append
 
-  syntax function (++) "(Init.Datatypes.app %1 %2)"
+  syntax function (++) "Init.Datatypes.app"
 
 end
 
 theory list.Reverse
 
-  syntax function reverse "(Lists.List.rev %1)"
+  syntax function reverse "Lists.List.rev"
 
 end
 
 theory list.RevAppend
 
-  syntax function rev_append "(Lists.List.rev_append %1 %2)"
+  syntax function rev_append "Lists.List.rev_append"
 
 end
 
 theory list.Combine
 
-  syntax function combine "(Lists.List.combine %1 %2)"
+  syntax function combine "Lists.List.combine"
 
 end
 
 theory option.Option
 
-  syntax type option "(option %1)"
+  syntax type option "Init.Datatypes.option"
   syntax function None "Init.Datatypes.None"
-  syntax function Some "(Init.Datatypes.Some %1)"
+  syntax function Some "Init.Datatypes.Some"
 
 end
 

lib/coq/bool/Bool.v

@@ -16,11 +16,12 @@ Require BuiltIn.
 
 (* Why3 goal *)
 Lemma andb_def :
-  forall (x:bool) (y:bool),
-  ((Init.Datatypes.andb x y) = match x with
-                               | true => y
-                               | false => false
-                               end).
+  forall (x:Init.Datatypes.bool) (y:Init.Datatypes.bool),
+  ((Init.Datatypes.andb x y) =
+   match x with
+   | Init.Datatypes.true => y
+   | Init.Datatypes.false => Init.Datatypes.false
+   end).
 Proof.
 intros x y.
 apply refl_equal.
@@ -28,11 +29,12 @@ Qed.
 
 (* Why3 goal *)
 Lemma orb_def :
-  forall (x:bool) (y:bool),
-  ((Init.Datatypes.orb x y) = match x with
-                              | false => y
-                              | true => true
-                              end).
+  forall (x:Init.Datatypes.bool) (y:Init.Datatypes.bool),
+  ((Init.Datatypes.orb x y) =
+   match x with
+   | Init.Datatypes.false => y
+   | Init.Datatypes.true => Init.Datatypes.true
+   end).
 Proof.
 intros x y.
 apply refl_equal.
@@ -40,11 +42,12 @@ Qed.
 
 (* Why3 goal *)
 Lemma notb_def :
-  forall (x:bool),
-  ((Init.Datatypes.negb x) = match x with
-                             | false => true
-                             | true => false
-                             end).
+  forall (x:Init.Datatypes.bool),
+  ((Init.Datatypes.negb x) =
+   match x with
+   | Init.Datatypes.false => Init.Datatypes.true
+   | Init.Datatypes.true => Init.Datatypes.false
+   end).
 Proof.
 intros x.
 apply refl_equal.
@@ -52,11 +55,11 @@ Qed.
 
 (* Why3 goal *)
 Lemma xorb_def :
-  forall (x:bool) (y:bool),
+  forall (x:Init.Datatypes.bool) (y:Init.Datatypes.bool),
   ((Init.Datatypes.xorb x y) =
    match x with
-   | false => y
-   | true => (Init.Datatypes.negb y)
+   | Init.Datatypes.false => y
+   | Init.Datatypes.true => Init.Datatypes.negb y
    end).
 Proof.
 intros x y.
@@ -65,11 +68,12 @@ Qed.
 
 (* Why3 goal *)
 Lemma implb_def :
-  forall (x:bool) (y:bool),
-  ((Init.Datatypes.implb x y) = match x with
-                                | false => true
-                                | true => y
-                                end).
+  forall (x:Init.Datatypes.bool) (y:Init.Datatypes.bool),
+  ((Init.Datatypes.implb x y) =
+   match x with
+   | Init.Datatypes.false => Init.Datatypes.true
+   | Init.Datatypes.true => y
+   end).
 Proof.
 now intros [|] [|].
 Qed.

lib/coq/bv/BV_Gen.v

@@ -27,7 +27,7 @@ Local Parameter last_bit : nat.
 Definition size_nat: nat := S last_bit.
 
 (* Why3 goal *)
-Definition size : Z.
+Definition size : Numbers.BinNums.Z.
   exact (Z.of_nat size_nat).
 Defined.
 
@@ -189,7 +189,7 @@ Qed.
 (* end of nth helpers *)
 
 (* Why3 goal *)
-Definition nth : t -> Z -> bool.
+Definition nth : t -> Numbers.BinNums.Z -> Init.Datatypes.bool.
   exact nth_aux.
 Defined.
 
@@ -213,7 +213,8 @@ Qed.
 
 (* Why3 goal *)
 Lemma nth_out_of_bound :
-  forall (x:t) (n:Z), (n < 0%Z)%Z \/ (size <= n)%Z -> ((nth x n) = false).
+  forall (x:t) (n:Numbers.BinNums.Z), (n < 0%Z)%Z \/ (size <= n)%Z ->
+  ((nth x n) = Init.Datatypes.false).
 intros.
 unfold nth.
 rewrite nth_aux_out_of_bound; auto with zarith.
@@ -236,7 +237,8 @@ Lemma Nth_zeros_aux : forall {l} (n:Z), ((@nth_aux l zeros_aux n) = false).
 Qed.
 
 (* Why3 goal *)
-Lemma Nth_zeros : forall (n:Z), ((nth zeros n) = false).
+Lemma Nth_zeros :
+  forall (n:Numbers.BinNums.Z), ((nth zeros n) = Init.Datatypes.false).
 intros n; apply Nth_zeros_aux.
 Qed.
 
@@ -260,7 +262,8 @@ Defined.
 
 (* Why3 goal *)
 Lemma Nth_ones :
-  forall (n:Z), (0%Z <= n)%Z /\ (n < size)%Z -> ((nth ones n) = true).
+  forall (n:Numbers.BinNums.Z), (0%Z <= n)%Z /\ (n < size)%Z ->
+  ((nth ones n) = Init.Datatypes.true).
   intros; apply nth_const; easy.
 Qed.
 
@@ -271,7 +274,7 @@ Defined.
 
 (* Why3 goal *)
 Lemma Nth_bw_and :
-  forall (v1:t) (v2:t) (n:Z), (0%Z <= n)%Z /\ (n < size)%Z ->
+  forall (v1:t) (v2:t) (n:Numbers.BinNums.Z), (0%Z <= n)%Z /\ (n < size)%Z ->
   ((nth (bw_and v1 v2) n) = (Init.Datatypes.andb (nth v1 n) (nth v2 n))).
   symmetry.
   apply nth_aux_map2 with (f := fun x y => x && y); easy.
@@ -284,7 +287,7 @@ Defined.
 
 (* Why3 goal *)
 Lemma Nth_bw_or :
-  forall (v1:t) (v2:t) (n:Z), (0%Z <= n)%Z /\ (n < size)%Z ->
+  forall (v1:t) (v2:t) (n:Numbers.BinNums.Z), (0%Z <= n)%Z /\ (n < size)%Z ->
   ((nth (bw_or v1 v2) n) = (Init.Datatypes.orb (nth v1 n) (nth v2 n))).
   symmetry.
   apply nth_aux_map2; easy.
@@ -297,7 +300,7 @@ Defined.
 
 (* Why3 goal *)
 Lemma Nth_bw_xor :
-  forall (v1:t) (v2:t) (n:Z), (0%Z <= n)%Z /\ (n < size)%Z ->
+  forall (v1:t) (v2:t) (n:Numbers.BinNums.Z), (0%Z <= n)%Z /\ (n < size)%Z ->
   ((nth (bw_xor v1 v2) n) = (Init.Datatypes.xorb (nth v1 n) (nth v2 n))).
   symmetry.
   apply nth_aux_map2; easy.
@@ -310,14 +313,14 @@ Defined.
 
 (* Why3 goal *)
 Lemma Nth_bw_not :
-  forall (v:t) (n:Z), (0%Z <= n)%Z /\ (n < size)%Z ->
+  forall (v:t) (n:Numbers.BinNums.Z), (0%Z <= n)%Z /\ (n < size)%Z ->
   ((nth (bw_not v) n) = (Init.Datatypes.negb (nth v n))).
   symmetry.
   apply nth_aux_map; easy.
 Qed.
 
 (* Why3 goal *)
-Definition lsr : t -> Z -> t.
+Definition lsr : t -> Numbers.BinNums.Z -> t.
   exact (fun v m => BshiftRl_iter last_bit v (Z.to_nat m)).
 Defined.
 
@@ -339,8 +342,9 @@ Qed.
 
 (* Why3 goal *)
 Lemma Lsr_nth_low :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= s)%Z -> (0%Z <= n)%Z ->
-  ((n + s)%Z < size)%Z -> ((nth (lsr b s) n) = (nth b (n + s)%Z)).
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z), (0%Z <= s)%Z ->
+  (0%Z <= n)%Z -> ((n + s)%Z < size)%Z ->
+  ((nth (lsr b s) n) = (nth b (n + s)%Z)).
 intros b n s h1 h2 h3.
 rewrite <-Z2Nat.id with (n := s) at 2; auto.
 apply bshiftRl_iter_nth; omega.
@@ -348,8 +352,9 @@ Qed.
 
 (* Why3 goal *)
 Lemma Lsr_nth_high :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= s)%Z -> (0%Z <= n)%Z ->
-  (size <= (n + s)%Z)%Z -> ((nth (lsr b s) n) = false).
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z), (0%Z <= s)%Z ->
+  (0%Z <= n)%Z -> (size <= (n + s)%Z)%Z ->
+  ((nth (lsr b s) n) = Init.Datatypes.false).
   intros b n s h1 h2 h3.
   unfold nth,lsr.
   cut (nth_aux b (n + Z.of_nat (Z.to_nat s)) = false).
@@ -366,7 +371,7 @@ auto.
 Qed.
 
 (* Why3 goal *)
-Definition asr : t -> Z -> t.
+Definition asr : t -> Numbers.BinNums.Z -> t.
   exact (fun v m => BshiftRa_iter last_bit v (Z.to_nat m)).
 Defined.
 
@@ -443,8 +448,9 @@ Qed.
 
 (* Why3 goal *)
 Lemma Asr_nth_low :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= s)%Z -> (0%Z <= n)%Z /\ (n < size)%Z ->
-  ((n + s)%Z < size)%Z -> ((nth (asr b s) n) = (nth b (n + s)%Z)).
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z), (0%Z <= s)%Z ->
+  (0%Z <= n)%Z /\ (n < size)%Z -> ((n + s)%Z < size)%Z ->
+  ((nth (asr b s) n) = (nth b (n + s)%Z)).
   unfold nth, lsr.
   intros.
   assert ((n + s)%Z = (n + Z.of_nat (Z.to_nat s))%Z).
@@ -489,8 +495,9 @@ Qed.
 
 (* Why3 goal *)
 Lemma Asr_nth_high :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= s)%Z -> (0%Z <= n)%Z /\ (n < size)%Z ->
-  (size <= (n + s)%Z)%Z -> ((nth (asr b s) n) = (nth b (size - 1%Z)%Z)).
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z), (0%Z <= s)%Z ->
+  (0%Z <= n)%Z /\ (n < size)%Z -> (size <= (n + s)%Z)%Z ->
+  ((nth (asr b s) n) = (nth b (size - 1%Z)%Z)).
   unfold nth, asr.
   intros.
   apply BhiftRa_iter_nth_high.
@@ -504,7 +511,7 @@ auto.
 Qed.
 
 (* Why3 goal *)
-Definition lsl : t -> Z -> t.
+Definition lsl : t -> Numbers.BinNums.Z -> t.
   exact (fun v m => BshiftL_iter last_bit v (Z.to_nat m)).
 Defined.
 
@@ -526,7 +533,8 @@ Qed.
 
 (* Why3 goal *)
 Lemma Lsl_nth_high :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= s)%Z /\ (s <= n)%Z /\ (n < size)%Z ->
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z),
+  (0%Z <= s)%Z /\ (s <= n)%Z /\ (n < size)%Z ->
   ((nth (lsl b s) n) = (nth b (n - s)%Z)).
   intros.
   unfold lsl, nth.
@@ -556,8 +564,8 @@ Qed.
 
 (* Why3 goal *)
 Lemma Lsl_nth_low :
-  forall (b:t) (n:Z) (s:Z), (0%Z <= n)%Z /\ (n < s)%Z ->
-  ((nth (lsl b s) n) = false).
+  forall (b:t) (n:Numbers.BinNums.Z) (s:Numbers.BinNums.Z),
+  (0%Z <= n)%Z /\ (n < s)%Z -> ((nth (lsl b s) n) = Init.Datatypes.false).
   intros.
   apply Lsl_nth_low_aux.
   rewrite Z2Nat.id; omega.
@@ -1091,13 +1099,14 @@ Lemma bvec_to_nat_shiftout_mod1 : forall {l} v, Z.of_nat (bvec_to_nat l (Vector.
 Qed.
 
 (* Why3 goal *)
-Definition rotate_right : t -> Z -> t.
+Definition rotate_right : t -> Numbers.BinNums.Z -> t.
   exact (fun b p => rotate_right_aux b (Z.to_nat p)).
 Defined.
 
 (* Why3 goal *)
 Lemma Nth_rotate_right :
-  forall (v:t) (n:Z) (i:Z), (0%Z <= i)%Z /\ (i < size)%Z -> (0%Z <= n)%Z ->
+  forall (v:t) (n:Numbers.BinNums.Z) (i:Numbers.BinNums.Z),
+  (0%Z <= i)%Z /\ (i < size)%Z -> (0%Z <= n)%Z ->
   ((nth (rotate_right v n) i) =
    (nth v (int.EuclideanDivision.mod1 (i + n)%Z size))).
   intros v n i h1 h2.
@@ -1115,13 +1124,14 @@ Lemma Nth_rotate_right :
 Qed.
 
 (* Why3 goal *)
-Definition rotate_left : t -> Z -> t.
+Definition rotate_left : t -> Numbers.BinNums.Z -> t.
   exact (fun b p => rotate_left_aux b (Z.to_nat p)).
 Defined.
 
 (* Why3 goal *)
 Lemma Nth_rotate_left :
-  forall (v:t) (n:Z) (i:Z), (0%Z <= i)%Z /\ (i < size)%Z -> (0%Z <= n)%Z ->
+  forall (v:t) (n:Numbers.BinNums.Z) (i:Numbers.BinNums.Z),
+  (0%Z <= i)%Z /\ (i < size)%Z -> (0%Z <= n)%Z ->
   ((nth (rotate_left v n) i) =
    (nth v (int.EuclideanDivision.mod1 (i - n)%Z size))).
   intros v n i h1 h2.
@@ -1139,12 +1149,12 @@ Lemma Nth_rotate_left :
 Qed.
 
 (* Why3 goal *)
-Definition two_power_size : Z.
+Definition two_power_size : Numbers.BinNums.Z.
   exact (Pow2int.pow2 size)%Z.
 Defined.
 
 (* Why3 goal *)
-Definition max_int : Z.
+Definition max_int : Numbers.BinNums.Z.
   exact (Pow2int.pow2 size - 1)%Z.
 Defined.
 
@@ -1164,7 +1174,7 @@ Definition is_signed_positive : t -> Prop.
 Defined.
 
 (* Why3 goal *)
-Definition to_uint : t -> Z.
+Definition to_uint : t -> Numbers.BinNums.Z.
   exact (fun x => Z.of_nat (bvec_to_nat size_nat x)).
 Defined.
 
@@ -1173,12 +1183,12 @@ Lemma max_int_S : (two_power_size = max_int + 1)%Z.
 Qed.
 
 (* Why3 goal *)
-Definition of_int : Z -> t.
+Definition of_int : Numbers.BinNums.Z -> t.
   exact (fun x => nat_to_bvec size_nat (Z.to_nat x)).
 Defined.
 
 (* Why3 goal *)
-Definition to_int : t -> Z.
+Definition to_int : t -> Numbers.BinNums.Z.
   exact (twos_complement size_nat).
 Defined.
 
@@ -1223,7 +1233,8 @@ Lemma to_int_extensionality :
 Qed.
 
 (* Why3 assumption *)
-Definition uint_in_range (i:Z) : Prop := (0%Z <= i)%Z /\ (i <= max_int)%Z.
+Definition uint_in_range (i:Numbers.BinNums.Z) : Prop :=
+  (0%Z <= i)%Z /\ (i <= max_int)%Z.
 
 (* Why3 goal *)
 Lemma to_uint_bounds :
@@ -1332,7 +1343,7 @@ Qed.
 
 (* Why3 goal *)
 Lemma to_uint_of_int :
-  forall (i:Z), (0%Z <= i)%Z /\ (i < two_power_size)%Z ->
+  forall (i:Numbers.BinNums.Z), (0%Z <= i)%Z /\ (i < two_power_size)%Z ->
   ((to_uint (of_int i)) = i).
   intros i h1; destruct h1.
   unfold to_uint, of_int.
@@ -1674,7 +1685,7 @@ trivial.
 Qed.
 
 (* Why3 goal *)
-Definition nth_bv : t -> t -> bool.
+Definition nth_bv : t -> t -> Init.Datatypes.bool.
   exact (fun v w => nth v (to_uint w)).
 Defined.
 
@@ -1706,7 +1717,8 @@ Qed.
 (* Why3 goal *)
 Lemma nth_bv_def :
   forall (x:t) (i:t),
-  ((nth_bv x i) = true) <-> ~ ((bw_and (lsr_bv x i) one) = zeros).
+  ((nth_bv x i) = Init.Datatypes.true) <->
+  ~ ((bw_and (lsr_bv x i) one) = zeros).
   intros; unfold nth_bv.
   case (Z_lt_ge_dec (to_uint i) size); intro.
   rewrite <-(Zplus_0_l (to_uint i)).
@@ -1745,7 +1757,8 @@ Qed.
 
 (* Why3 goal *)
 Lemma Nth_bv_is_nth2 :
-  forall (x:t) (i:Z), (0%Z <= i)%Z /\ (i < two_power_size)%Z ->
+  forall (x:t) (i:Numbers.BinNums.Z),
+  (0%Z <= i)%Z /\ (i < two_power_size)%Z ->
   ((nth_bv x (of_int i)) = (nth x i)).
   intros x i h1.
   rewrite <-Nth_bv_is_nth.
@@ -1770,8 +1783,10 @@ Lemma eq_sub_bv_def :
 Qed.