From 5e92ae6b361f9221f5c5f9a39ab4c28a36597a77 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Tue, 21 Nov 2023 11:40:59 +0100
Subject: Regenerate most of the test files

---
 tests/coq/array/Array.v                      |  32 ++++----
 tests/coq/array/Primitives.v                 |  88 +++++++++++---------
 tests/coq/betree/Primitives.v                |  88 +++++++++++---------
 tests/coq/hashmap/Hashmap_Funs.v             | 106 ++++++++++++------------
 tests/coq/hashmap/Primitives.v               |  88 +++++++++++---------
 tests/coq/hashmap_on_disk/HashmapMain_Funs.v | 116 +++++++++++++--------------
 tests/coq/hashmap_on_disk/Primitives.v       |  88 +++++++++++---------
 tests/coq/misc/Constants.v                   |   2 +-
 tests/coq/misc/External_Opaque.v             |   4 +-
 tests/coq/misc/Loops.v                       |  15 ++--
 tests/coq/misc/NoNestedBorrows.v             |   5 +-
 tests/coq/misc/Primitives.v                  |  88 +++++++++++---------
 tests/coq/traits/Primitives.v                |  88 +++++++++++---------
 13 files changed, 425 insertions(+), 383 deletions(-)

(limited to 'tests/coq')

diff --git a/tests/coq/array/Array.v b/tests/coq/array/Array.v
index 825f73e0..256ccd1c 100644
--- a/tests/coq/array/Array.v
+++ b/tests/coq/array/Array.v
@@ -101,7 +101,7 @@ Definition index_mut_slice_back
 Definition slice_subslice_shared_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
   core_slice_index_Slice_index u32 (core_ops_range_Range usize)
-    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
@@ -109,7 +109,7 @@ Definition slice_subslice_shared_
 Definition slice_subslice_mut_
   (x : slice u32) (y : usize) (z : usize) : result (slice u32) :=
   core_slice_index_Slice_index_mut u32 (core_ops_range_Range usize)
-    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
@@ -119,7 +119,7 @@ Definition slice_subslice_mut__back
   result (slice u32)
   :=
   core_slice_index_Slice_index_mut_back u32 (core_ops_range_Range usize)
-    (core_slice_index_Range_coresliceindexSliceIndexInst u32) x
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
 .
 
@@ -144,8 +144,8 @@ Definition array_to_slice_mut__back
 Definition array_subslice_shared_
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
-    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
-    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
@@ -153,8 +153,8 @@ Definition array_subslice_shared_
 Definition array_subslice_mut_
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index_mut u32 (core_ops_range_Range usize) 32%usize
-    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
-    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
@@ -164,8 +164,8 @@ Definition array_subslice_mut__back
   result (array u32 32%usize)
   :=
   core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 32%usize
-    (core_slice_index_Slice_coreopsindexIndexMutInst u32 (core_ops_range_Range
-    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |} ret
 .
 
@@ -309,9 +309,8 @@ Definition update_all : result unit :=
 Definition range_all : result unit :=
   s <-
     core_array_Array_index_mut u32 (core_ops_range_Range usize) 4%usize
-      (core_slice_index_Slice_coreopsindexIndexMutInst u32
-      (core_ops_range_Range usize)
-      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
       (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
       {|
         core_ops_range_Range_start := 1%usize;
@@ -320,9 +319,8 @@ Definition range_all : result unit :=
   s0 <- update_mut_slice s;
   _ <-
     core_array_Array_index_mut_back u32 (core_ops_range_Range usize) 4%usize
-      (core_slice_index_Slice_coreopsindexIndexMutInst u32
-      (core_ops_range_Range usize)
-      (core_slice_index_Range_coresliceindexSliceIndexInst u32))
+      (core_ops_index_IndexMutSliceTIInst u32 (core_ops_range_Range usize)
+      (core_slice_index_SliceIndexRangeUsizeSliceTInst u32))
       (mk_array u32 4%usize [ 0%u32; 0%u32; 0%u32; 0%u32 ])
       {|
         core_ops_range_Range_start := 1%usize;
@@ -430,8 +428,8 @@ Definition f2 (i : u32) : result unit :=
 Definition f4
   (x : array u32 32%usize) (y : usize) (z : usize) : result (slice u32) :=
   core_array_Array_index u32 (core_ops_range_Range usize) 32%usize
-    (core_slice_index_Slice_coreopsindexIndexInst u32 (core_ops_range_Range
-    usize) (core_slice_index_Range_coresliceindexSliceIndexInst u32)) x
+    (core_ops_index_IndexSliceTIInst u32 (core_ops_range_Range usize)
+    (core_slice_index_SliceIndexRangeUsizeSliceTInst u32)) x
     {| core_ops_range_Range_start := y; core_ops_range_Range_end_ := z |}
 .
 
diff --git a/tests/coq/array/Primitives.v b/tests/coq/array/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/array/Primitives.v
+++ b/tests/coq/array/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/betree/Primitives.v b/tests/coq/betree/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/betree/Primitives.v
+++ b/tests/coq/betree/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap/Hashmap_Funs.v b/tests/coq/hashmap/Hashmap_Funs.v
index 3ca52a9f..fbed86b5 100644
--- a/tests/coq/hashmap/Hashmap_Funs.v
+++ b/tests/coq/hashmap/Hashmap_Funs.v
@@ -14,7 +14,7 @@ Module Hashmap_Funs.
 Definition hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function *)
 Fixpoint hashMap_allocate_slots_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
   result (alloc_vec_Vec (List_t T))
@@ -31,7 +31,7 @@ Fixpoint hashMap_allocate_slots_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::allocate_slots]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::allocate_slots]: forward function *)
 Definition hashMap_allocate_slots
   (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (n0 : usize) :
   result (alloc_vec_Vec (List_t T))
@@ -39,7 +39,7 @@ Definition hashMap_allocate_slots
   hashMap_allocate_slots_loop T n slots n0
 .
 
-(** [hashmap::HashMap::{0}::new_with_capacity]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::new_with_capacity]: forward function *)
 Definition hashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -58,12 +58,12 @@ Definition hashMap_new_with_capacity
     |}
 .
 
-(** [hashmap::HashMap::{0}::new]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::new]: forward function *)
 Definition hashMap_new (T : Type) (n : nat) : result (HashMap_t T) :=
   hashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashMap_clear_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (List_t T)) (i : usize) :
@@ -78,14 +78,14 @@ Fixpoint hashMap_clear_loop
       i1 <- usize_add i 1%usize;
       slots0 <-
         alloc_vec_Vec_index_mut_back (List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
-          slots i List_Nil;
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i
+          List_Nil;
       hashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
-(** [hashmap::HashMap::{0}::clear]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_clear
   (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
@@ -99,12 +99,12 @@ Definition hashMap_clear
     |}
 .
 
-(** [hashmap::HashMap::{0}::len]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::len]: forward function *)
 Definition hashMap_len (T : Type) (self : HashMap_t T) : result usize :=
   Return self.(hashMap_num_entries)
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function *)
 Fixpoint hashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
@@ -122,7 +122,7 @@ Fixpoint hashMap_insert_in_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: forward function *)
 Definition hashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result bool
@@ -130,7 +130,7 @@ Definition hashMap_insert_in_list
   hashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0 *)
 Fixpoint hashMap_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
@@ -150,7 +150,7 @@ Fixpoint hashMap_insert_in_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::insert_in_list]: backward function 0 *)
 Definition hashMap_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : List_t T) :
   result (List_t T)
@@ -158,7 +158,7 @@ Definition hashMap_insert_in_list_back
   hashMap_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_insert_no_resize
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
@@ -169,7 +169,7 @@ Definition hashMap_insert_no_resize
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   inserted <- hashMap_insert_in_list T n key value l;
   if inserted
@@ -178,7 +178,7 @@ Definition hashMap_insert_no_resize
     l0 <- hashMap_insert_in_list_back T n key value l;
     v <-
       alloc_vec_Vec_index_mut_back (List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
         self.(hashMap_slots) hash_mod l0;
     Return
       {|
@@ -191,7 +191,7 @@ Definition hashMap_insert_no_resize
     l0 <- hashMap_insert_in_list_back T n key value l;
     v <-
       alloc_vec_Vec_index_mut_back (List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
         self.(hashMap_slots) hash_mod l0;
     Return
       {|
@@ -202,7 +202,7 @@ Definition hashMap_insert_no_resize
       |})
 .
 
-(** [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashMap_move_elements_from_list_loop
   (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
@@ -220,7 +220,7 @@ Fixpoint hashMap_move_elements_from_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_move_elements_from_list
   (T : Type) (n : nat) (ntable : HashMap_t T) (ls : List_t T) :
@@ -229,7 +229,7 @@ Definition hashMap_move_elements_from_list
   hashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : HashMap_t T)
@@ -244,22 +244,20 @@ Fixpoint hashMap_move_elements_loop
     then (
       l <-
         alloc_vec_Vec_index_mut (List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
-          slots i;
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i;
       let ls := core_mem_replace (List_t T) l List_Nil in
       ntable0 <- hashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
       let l0 := core_mem_replace_back (List_t T) l List_Nil in
       slots0 <-
         alloc_vec_Vec_index_mut_back (List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
-          slots i l0;
+          (core_slice_index_SliceIndexUsizeSliceTInst (List_t T)) slots i l0;
       hashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_move_elements
   (T : Type) (n : nat) (ntable : HashMap_t T)
@@ -269,7 +267,7 @@ Definition hashMap_move_elements
   hashMap_move_elements_loop T n ntable slots i
 .
 
-(** [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_try_resize
   (T : Type) (n : nat) (self : HashMap_t T) : result (HashMap_t T) :=
@@ -301,7 +299,7 @@ Definition hashMap_try_resize
       |}
 .
 
-(** [hashmap::HashMap::{0}::insert]: merged forward/backward function
+(** [hashmap::{hashmap::HashMap<T>}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashMap_insert
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (value : T) :
@@ -314,7 +312,7 @@ Definition hashMap_insert
   else Return self0
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function *)
 Fixpoint hashMap_contains_key_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   match n with
@@ -330,13 +328,13 @@ Fixpoint hashMap_contains_key_in_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::contains_key_in_list]: forward function *)
 Definition hashMap_contains_key_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result bool :=
   hashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::contains_key]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::contains_key]: forward function *)
 Definition hashMap_contains_key
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result bool :=
   hash <- hash_key key;
@@ -344,12 +342,12 @@ Definition hashMap_contains_key
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   hashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: loop 0: forward function *)
 Fixpoint hashMap_get_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   match n with
@@ -365,13 +363,13 @@ Fixpoint hashMap_get_in_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::get_in_list]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get_in_list]: forward function *)
 Definition hashMap_get_in_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result T :=
   hashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::get]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get]: forward function *)
 Definition hashMap_get
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
   hash <- hash_key key;
@@ -379,12 +377,12 @@ Definition hashMap_get
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   hashMap_get_in_list T n key l
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function *)
 Fixpoint hashMap_get_mut_in_list_loop
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   match n with
@@ -400,13 +398,13 @@ Fixpoint hashMap_get_mut_in_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: forward function *)
 Definition hashMap_get_mut_in_list
   (T : Type) (n : nat) (ls : List_t T) (key : usize) : result T :=
   hashMap_get_mut_in_list_loop T n ls key
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0 *)
 Fixpoint hashMap_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
@@ -426,7 +424,7 @@ Fixpoint hashMap_get_mut_in_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut_in_list]: backward function 0 *)
 Definition hashMap_get_mut_in_list_back
   (T : Type) (n : nat) (ls : List_t T) (key : usize) (ret : T) :
   result (List_t T)
@@ -434,7 +432,7 @@ Definition hashMap_get_mut_in_list_back
   hashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap::HashMap::{0}::get_mut]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: forward function *)
 Definition hashMap_get_mut
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) : result T :=
   hash <- hash_key key;
@@ -442,12 +440,12 @@ Definition hashMap_get_mut
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   hashMap_get_mut_in_list T n l key
 .
 
-(** [hashmap::HashMap::{0}::get_mut]: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::get_mut]: backward function 0 *)
 Definition hashMap_get_mut_back
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) (ret : T) :
   result (HashMap_t T)
@@ -457,12 +455,12 @@ Definition hashMap_get_mut_back
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   l0 <- hashMap_get_mut_in_list_back T n l key ret;
   v <-
     alloc_vec_Vec_index_mut_back (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod l0;
   Return
     {|
@@ -473,7 +471,7 @@ Definition hashMap_get_mut_back
     |}
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function *)
 Fixpoint hashMap_remove_from_list_loop
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   match n with
@@ -495,13 +493,13 @@ Fixpoint hashMap_remove_from_list_loop
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: forward function *)
 Definition hashMap_remove_from_list
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (option T) :=
   hashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1 *)
 Fixpoint hashMap_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   match n with
@@ -525,13 +523,13 @@ Fixpoint hashMap_remove_from_list_loop_back
   end
 .
 
-(** [hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
+(** [hashmap::{hashmap::HashMap<T>}::remove_from_list]: backward function 1 *)
 Definition hashMap_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : List_t T) : result (List_t T) :=
   hashMap_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap::HashMap::{0}::remove]: forward function *)
+(** [hashmap::{hashmap::HashMap<T>}::remove]: forward function *)
 Definition hashMap_remove
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
   result (option T)
@@ -541,7 +539,7 @@ Definition hashMap_remove
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   x <- hashMap_remove_from_list T n key l;
   match x with
@@ -551,7 +549,7 @@ Definition hashMap_remove
   end
 .
 
-(** [hashmap::HashMap::{0}::remove]: backward function 0 *)
+(** [hashmap::{hashmap::HashMap<T>}::remove]: backward function 0 *)
 Definition hashMap_remove_back
   (T : Type) (n : nat) (self : HashMap_t T) (key : usize) :
   result (HashMap_t T)
@@ -561,7 +559,7 @@ Definition hashMap_remove_back
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
       self.(hashMap_slots) hash_mod;
   x <- hashMap_remove_from_list T n key l;
   match x with
@@ -569,7 +567,7 @@ Definition hashMap_remove_back
     l0 <- hashMap_remove_from_list_back T n key l;
     v <-
       alloc_vec_Vec_index_mut_back (List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
         self.(hashMap_slots) hash_mod l0;
     Return
       {|
@@ -583,7 +581,7 @@ Definition hashMap_remove_back
     l0 <- hashMap_remove_from_list_back T n key l;
     v <-
       alloc_vec_Vec_index_mut_back (List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (List_t T))
+        (core_slice_index_SliceIndexUsizeSliceTInst (List_t T))
         self.(hashMap_slots) hash_mod l0;
     Return
       {|
diff --git a/tests/coq/hashmap/Primitives.v b/tests/coq/hashmap/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/hashmap/Primitives.v
+++ b/tests/coq/hashmap/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
index eac78186..6f3848e6 100644
--- a/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
+++ b/tests/coq/hashmap_on_disk/HashmapMain_Funs.v
@@ -16,7 +16,7 @@ Module HashmapMain_Funs.
 Definition hashmap_hash_key (k : usize) : result usize :=
   Return k.
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_allocate_slots_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
   :
@@ -34,7 +34,7 @@ Fixpoint hashmap_HashMap_allocate_slots_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::allocate_slots]: forward function *)
 Definition hashmap_HashMap_allocate_slots
   (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (n0 : usize)
   :
@@ -43,7 +43,7 @@ Definition hashmap_HashMap_allocate_slots
   hashmap_HashMap_allocate_slots_loop T n slots n0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new_with_capacity]: forward function *)
 Definition hashmap_HashMap_new_with_capacity
   (T : Type) (n : nat) (capacity : usize) (max_load_dividend : usize)
   (max_load_divisor : usize) :
@@ -62,13 +62,13 @@ Definition hashmap_HashMap_new_with_capacity
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::new]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::new]: forward function *)
 Definition hashmap_HashMap_new
   (T : Type) (n : nat) : result (hashmap_HashMap_t T) :=
   hashmap_HashMap_new_with_capacity T n 32%usize 4%usize 5%usize
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_HashMap_clear_loop
   (T : Type) (n : nat) (slots : alloc_vec_Vec (hashmap_List_t T)) (i : usize) :
@@ -83,14 +83,14 @@ Fixpoint hashmap_HashMap_clear_loop
       i1 <- usize_add i 1%usize;
       slots0 <-
         alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-          T)) slots i Hashmap_List_Nil;
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i Hashmap_List_Nil;
       hashmap_HashMap_clear_loop T n0 slots0 i1)
     else Return slots
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::clear]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_clear
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
@@ -106,13 +106,13 @@ Definition hashmap_HashMap_clear
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::len]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::len]: forward function *)
 Definition hashmap_HashMap_len
   (T : Type) (self : hashmap_HashMap_t T) : result usize :=
   Return self.(hashmap_HashMap_num_entries)
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_insert_in_list_loop
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
@@ -130,7 +130,7 @@ Fixpoint hashmap_HashMap_insert_in_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: forward function *)
 Definition hashmap_HashMap_insert_in_list
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result bool
@@ -138,7 +138,7 @@ Definition hashmap_HashMap_insert_in_list
   hashmap_HashMap_insert_in_list_loop T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: loop 0: backward function 0 *)
 Fixpoint hashmap_HashMap_insert_in_list_loop_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result (hashmap_List_t T)
@@ -159,7 +159,7 @@ Fixpoint hashmap_HashMap_insert_in_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_in_list]: backward function 0 *)
 Definition hashmap_HashMap_insert_in_list_back
   (T : Type) (n : nat) (key : usize) (value : T) (ls : hashmap_List_t T) :
   result (hashmap_List_t T)
@@ -167,7 +167,7 @@ Definition hashmap_HashMap_insert_in_list_back
   hashmap_HashMap_insert_in_list_loop_back T n key value ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert_no_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_insert_no_resize
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
@@ -178,7 +178,7 @@ Definition hashmap_HashMap_insert_no_resize
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   inserted <- hashmap_HashMap_insert_in_list T n key value l;
   if inserted
@@ -187,8 +187,8 @@ Definition hashmap_HashMap_insert_no_resize
     l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
       alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-        T)) self.(hashmap_HashMap_slots) hash_mod l0;
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
         hashmap_HashMap_num_entries := i0;
@@ -201,8 +201,8 @@ Definition hashmap_HashMap_insert_no_resize
     l0 <- hashmap_HashMap_insert_in_list_back T n key value l;
     v <-
       alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-        T)) self.(hashmap_HashMap_slots) hash_mod l0;
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
@@ -213,7 +213,7 @@ Definition hashmap_HashMap_insert_no_resize
       |})
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_HashMap_move_elements_from_list_loop
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
@@ -231,7 +231,7 @@ Fixpoint hashmap_HashMap_move_elements_from_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements_from_list]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_move_elements_from_list
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T) (ls : hashmap_List_t T) :
@@ -240,7 +240,7 @@ Definition hashmap_HashMap_move_elements_from_list
   hashmap_HashMap_move_elements_from_list_loop T n ntable ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: loop 0: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Fixpoint hashmap_HashMap_move_elements_loop
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
@@ -255,22 +255,22 @@ Fixpoint hashmap_HashMap_move_elements_loop
     then (
       l <-
         alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-          T)) slots i;
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i;
       let ls := core_mem_replace (hashmap_List_t T) l Hashmap_List_Nil in
       ntable0 <- hashmap_HashMap_move_elements_from_list T n0 ntable ls;
       i1 <- usize_add i 1%usize;
       let l0 := core_mem_replace_back (hashmap_List_t T) l Hashmap_List_Nil in
       slots0 <-
         alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-          T)) slots i l0;
+          (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T)) slots
+          i l0;
       hashmap_HashMap_move_elements_loop T n0 ntable0 slots0 i1)
     else Return (ntable, slots)
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::move_elements]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_move_elements
   (T : Type) (n : nat) (ntable : hashmap_HashMap_t T)
@@ -280,7 +280,7 @@ Definition hashmap_HashMap_move_elements
   hashmap_HashMap_move_elements_loop T n ntable slots i
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::try_resize]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_try_resize
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) :
@@ -317,7 +317,7 @@ Definition hashmap_HashMap_try_resize
       |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::insert]: merged forward/backward function
     (there is a single backward function, and the forward function returns ()) *)
 Definition hashmap_HashMap_insert
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (value : T) :
@@ -330,7 +330,7 @@ Definition hashmap_HashMap_insert
   else Return self0
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_contains_key_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
   match n with
@@ -346,13 +346,13 @@ Fixpoint hashmap_HashMap_contains_key_in_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key_in_list]: forward function *)
 Definition hashmap_HashMap_contains_key_in_list
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result bool :=
   hashmap_HashMap_contains_key_in_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::contains_key]: forward function *)
 Definition hashmap_HashMap_contains_key
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result bool
@@ -362,12 +362,12 @@ Definition hashmap_HashMap_contains_key
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   hashmap_HashMap_contains_key_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_get_in_list_loop
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
   match n with
@@ -383,13 +383,13 @@ Fixpoint hashmap_HashMap_get_in_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_in_list]: forward function *)
 Definition hashmap_HashMap_get_in_list
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) : result T :=
   hashmap_HashMap_get_in_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get]: forward function *)
 Definition hashmap_HashMap_get
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
   hash <- hashmap_hash_key key;
@@ -397,12 +397,12 @@ Definition hashmap_HashMap_get
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   hashmap_HashMap_get_in_list T n key l
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_get_mut_in_list_loop
   (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
   match n with
@@ -418,13 +418,13 @@ Fixpoint hashmap_HashMap_get_mut_in_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: forward function *)
 Definition hashmap_HashMap_get_mut_in_list
   (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) : result T :=
   hashmap_HashMap_get_mut_in_list_loop T n ls key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: loop 0: backward function 0 *)
 Fixpoint hashmap_HashMap_get_mut_in_list_loop_back
   (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
   result (hashmap_List_t T)
@@ -444,7 +444,7 @@ Fixpoint hashmap_HashMap_get_mut_in_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut_in_list]: backward function 0 *)
 Definition hashmap_HashMap_get_mut_in_list_back
   (T : Type) (n : nat) (ls : hashmap_List_t T) (key : usize) (ret : T) :
   result (hashmap_List_t T)
@@ -452,7 +452,7 @@ Definition hashmap_HashMap_get_mut_in_list_back
   hashmap_HashMap_get_mut_in_list_loop_back T n ls key ret
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: forward function *)
 Definition hashmap_HashMap_get_mut
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) : result T :=
   hash <- hashmap_hash_key key;
@@ -460,12 +460,12 @@ Definition hashmap_HashMap_get_mut
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   hashmap_HashMap_get_mut_in_list T n l key
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::get_mut]: backward function 0 *)
 Definition hashmap_HashMap_get_mut_back
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) (ret : T) :
   result (hashmap_HashMap_t T)
@@ -475,12 +475,12 @@ Definition hashmap_HashMap_get_mut_back
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   l0 <- hashmap_HashMap_get_mut_in_list_back T n l key ret;
   v <-
     alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod l0;
   Return
     {|
@@ -491,7 +491,7 @@ Definition hashmap_HashMap_get_mut_back
     |}
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: forward function *)
 Fixpoint hashmap_HashMap_remove_from_list_loop
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
@@ -516,7 +516,7 @@ Fixpoint hashmap_HashMap_remove_from_list_loop
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: forward function *)
 Definition hashmap_HashMap_remove_from_list
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (option T)
@@ -524,7 +524,7 @@ Definition hashmap_HashMap_remove_from_list
   hashmap_HashMap_remove_from_list_loop T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: loop 0: backward function 1 *)
 Fixpoint hashmap_HashMap_remove_from_list_loop_back
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (hashmap_List_t T)
@@ -551,7 +551,7 @@ Fixpoint hashmap_HashMap_remove_from_list_loop_back
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove_from_list]: backward function 1 *)
 Definition hashmap_HashMap_remove_from_list_back
   (T : Type) (n : nat) (key : usize) (ls : hashmap_List_t T) :
   result (hashmap_List_t T)
@@ -559,7 +559,7 @@ Definition hashmap_HashMap_remove_from_list_back
   hashmap_HashMap_remove_from_list_loop_back T n key ls
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove]: forward function *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: forward function *)
 Definition hashmap_HashMap_remove
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result (option T)
@@ -569,7 +569,7 @@ Definition hashmap_HashMap_remove
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
@@ -579,7 +579,7 @@ Definition hashmap_HashMap_remove
   end
 .
 
-(** [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 *)
+(** [hashmap_main::hashmap::{hashmap_main::hashmap::HashMap<T>}::remove]: backward function 0 *)
 Definition hashmap_HashMap_remove_back
   (T : Type) (n : nat) (self : hashmap_HashMap_t T) (key : usize) :
   result (hashmap_HashMap_t T)
@@ -589,7 +589,7 @@ Definition hashmap_HashMap_remove_back
   hash_mod <- usize_rem hash i;
   l <-
     alloc_vec_Vec_index_mut (hashmap_List_t T) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t T))
+      (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
       self.(hashmap_HashMap_slots) hash_mod;
   x <- hashmap_HashMap_remove_from_list T n key l;
   match x with
@@ -597,8 +597,8 @@ Definition hashmap_HashMap_remove_back
     l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
       alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-        T)) self.(hashmap_HashMap_slots) hash_mod l0;
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
         hashmap_HashMap_num_entries := self.(hashmap_HashMap_num_entries);
@@ -612,8 +612,8 @@ Definition hashmap_HashMap_remove_back
     l0 <- hashmap_HashMap_remove_from_list_back T n key l;
     v <-
       alloc_vec_Vec_index_mut_back (hashmap_List_t T) usize
-        (core_slice_index_usize_coresliceindexSliceIndexInst (hashmap_List_t
-        T)) self.(hashmap_HashMap_slots) hash_mod l0;
+        (core_slice_index_SliceIndexUsizeSliceTInst (hashmap_List_t T))
+        self.(hashmap_HashMap_slots) hash_mod l0;
     Return
       {|
         hashmap_HashMap_num_entries := i0;
diff --git a/tests/coq/hashmap_on_disk/Primitives.v b/tests/coq/hashmap_on_disk/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/hashmap_on_disk/Primitives.v
+++ b/tests/coq/hashmap_on_disk/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/misc/Constants.v b/tests/coq/misc/Constants.v
index 03653f69..1f2ab812 100644
--- a/tests/coq/misc/Constants.v
+++ b/tests/coq/misc/Constants.v
@@ -68,7 +68,7 @@ Record Wrap_t (T : Type) := mkWrap_t { wrap_value : T; }.
 Arguments mkWrap_t { _ }.
 Arguments wrap_value { _ }.
 
-(** [constants::Wrap::{0}::new]: forward function *)
+(** [constants::{constants::Wrap<T>}::new]: forward function *)
 Definition wrap_new (T : Type) (value : T) : result (Wrap_t T) :=
   Return {| wrap_value := value |}
 .
diff --git a/tests/coq/misc/External_Opaque.v b/tests/coq/misc/External_Opaque.v
index 80be37e7..10c05583 100644
--- a/tests/coq/misc/External_Opaque.v
+++ b/tests/coq/misc/External_Opaque.v
@@ -25,12 +25,12 @@ Axiom core_mem_swap_back1 :
   forall(T : Type), T -> T -> state -> state -> result (state * T)
 .
 
-(** [core::num::nonzero::NonZeroU32::{14}::new]: forward function *)
+(** [core::num::nonzero::{core::num::nonzero::NonZeroU32#14}::new]: forward function *)
 Axiom core_num_nonzero_NonZeroU32_new
   : u32 -> state -> result (state * (option core_num_nonzero_NonZeroU32_t))
 .
 
-(** [core::option::Option::{0}::unwrap]: forward function *)
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function *)
 Axiom core_option_Option_unwrap :
   forall(T : Type), option T -> state -> result (state * T)
 .
diff --git a/tests/coq/misc/Loops.v b/tests/coq/misc/Loops.v
index 1c0eab17..e5ff6c8e 100644
--- a/tests/coq/misc/Loops.v
+++ b/tests/coq/misc/Loops.v
@@ -77,7 +77,7 @@ Fixpoint clear_loop
       i1 <- usize_add i 1%usize;
       v0 <-
         alloc_vec_Vec_index_mut_back u32 usize
-          (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0%u32;
+          (core_slice_index_SliceIndexUsizeSliceTInst u32) v i 0%u32;
       clear_loop n0 v0 i1)
     else Return v
   end
@@ -209,8 +209,7 @@ Definition get_elem_mut
   :=
   l <-
     alloc_vec_Vec_index_mut (List_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
-      slots 0%usize;
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
   get_elem_mut_loop n x l
 .
 
@@ -240,12 +239,11 @@ Definition get_elem_mut_back
   :=
   l <-
     alloc_vec_Vec_index_mut (List_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
-      slots 0%usize;
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
   l0 <- get_elem_mut_loop_back n x l ret;
   alloc_vec_Vec_index_mut_back (List_t usize) usize
-    (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize)) slots
-    0%usize l0
+    (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize
+    l0
 .
 
 (** [loops::get_elem_shared]: loop 0: forward function *)
@@ -269,8 +267,7 @@ Definition get_elem_shared
   :=
   l <-
     alloc_vec_Vec_index (List_t usize) usize
-      (core_slice_index_usize_coresliceindexSliceIndexInst (List_t usize))
-      slots 0%usize;
+      (core_slice_index_SliceIndexUsizeSliceTInst (List_t usize)) slots 0%usize;
   get_elem_shared_loop n x l
 .
 
diff --git a/tests/coq/misc/NoNestedBorrows.v b/tests/coq/misc/NoNestedBorrows.v
index c7af496f..376e722c 100644
--- a/tests/coq/misc/NoNestedBorrows.v
+++ b/tests/coq/misc/NoNestedBorrows.v
@@ -151,8 +151,9 @@ Check (test_list1 )%return.
 
 (** [no_nested_borrows::test_box1]: forward function *)
 Definition test_box1 : result unit :=
-  let b := 1%i32 in
-  let x := b in
+  let b := 0%i32 in
+  b0 <- alloc_boxed_Box_deref_mut_back i32 b 1%i32;
+  x <- alloc_boxed_Box_deref i32 b0;
   if negb (x s= 1%i32) then Fail_ Failure else Return tt
 .
 
diff --git a/tests/coq/misc/Primitives.v b/tests/coq/misc/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/misc/Primitives.v
+++ b/tests/coq/misc/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
diff --git a/tests/coq/traits/Primitives.v b/tests/coq/traits/Primitives.v
index 85e38f01..83f860b6 100644
--- a/tests/coq/traits/Primitives.v
+++ b/tests/coq/traits/Primitives.v
@@ -467,14 +467,14 @@ Definition alloc_boxed_Box_deref_mut (T : Type) (x : T) : result T := Return x.
 Definition alloc_boxed_Box_deref_mut_back (T : Type) (_ : T) (x : T) : result T := Return x.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
+Definition alloc_boxed_Box_coreopsDerefInst (Self : Type) : core_ops_deref_Deref Self := {|
   core_ops_deref_Deref_target := Self;
   core_ops_deref_Deref_deref := alloc_boxed_Box_deref Self;
 |}.
 
 (* Trait instance *)
-Definition alloc_boxed_Box_coreOpsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
-  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreOpsDerefInst Self;
+Definition alloc_boxed_Box_coreopsDerefMutInst (Self : Type) : core_ops_deref_DerefMut Self := {|
+  core_ops_deref_DerefMut_derefInst := alloc_boxed_Box_coreopsDerefInst Self;
   core_ops_deref_DerefMut_deref_mut := alloc_boxed_Box_deref_mut Self;
   core_ops_deref_DerefMut_deref_mut_back := alloc_boxed_Box_deref_mut_back Self;
 |}.
@@ -576,7 +576,7 @@ Definition alloc_vec_Vec_insert (T: Type) (v: alloc_vec_Vec T) (i: usize) (x: T)
     else Fail_ Failure).
 
 (* Helper *)
-Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result T.
+Axiom alloc_vec_Vec_index_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize), result T.
 
 (* Helper *)
 Axiom alloc_vec_Vec_update_usize : forall {T : Type} (v : alloc_vec_Vec T) (i : usize) (x : T), result (alloc_vec_Vec T).
@@ -620,18 +620,18 @@ Definition core_slice_index_Slice_index
   end.
 
 (* [core::slice::index::Range:::get]: forward function *)
-Axiom core_slice_index_Range_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
+Axiom core_slice_index_RangeUsize_get : forall (T : Type) (i : core_ops_range_Range usize) (s : slice T), result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: forward function *)
-Axiom core_slice_index_Range_get_mut :
+Axiom core_slice_index_RangeUsize_get_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (option (slice T)).
 
 (* [core::slice::index::Range::get_mut]: backward function 0 *)
-Axiom core_slice_index_Range_get_mut_back :
+Axiom core_slice_index_RangeUsize_get_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> option (slice T) -> result (slice T).
 
 (* [core::slice::index::Range::get_unchecked]: forward function *)
-Definition core_slice_index_Range_get_unchecked
+Definition core_slice_index_RangeUsize_get_unchecked
   (T : Type) :
   core_ops_range_Range usize -> const_raw_ptr (slice T) -> result (const_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -639,7 +639,7 @@ Definition core_slice_index_Range_get_unchecked
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::get_unchecked_mut]: forward function *)
-Definition core_slice_index_Range_get_unchecked_mut
+Definition core_slice_index_RangeUsize_get_unchecked_mut
   (T : Type) :
   core_ops_range_Range usize -> mut_raw_ptr (slice T) -> result (mut_raw_ptr (slice T)) :=
   (* Don't know what the model should be - for now we always fail to make
@@ -647,15 +647,15 @@ Definition core_slice_index_Range_get_unchecked_mut
   fun _ _ => Fail_ Failure.
 
 (* [core::slice::index::Range::index]: forward function *)
-Axiom core_slice_index_Range_index :
+Axiom core_slice_index_RangeUsize_index :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: forward function *)
-Axiom core_slice_index_Range_index_mut :
+Axiom core_slice_index_RangeUsize_index_mut :
   forall (T : Type), core_ops_range_Range usize -> slice T -> result (slice T).
 
 (* [core::slice::index::Range::index_mut]: backward function 0 *)
-Axiom core_slice_index_Range_index_mut_back :
+Axiom core_slice_index_RangeUsize_index_mut_back :
   forall (T : Type), core_ops_range_Range usize -> slice T -> slice T -> result (slice T).
 
 (* [core::slice::index::[T]::index_mut]: forward function *)
@@ -683,44 +683,44 @@ Axiom core_array_Array_index_mut_back :
   forall (T Idx : Type) (N : usize) (inst : core_ops_index_IndexMut (slice T) Idx)
   (a : array T N) (i : Idx) (x : inst.(core_ops_index_IndexMut_indexInst).(core_ops_index_Index_Output)), result (array T N).
 
-(* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexInst (T Idx : Type)
-  (inst : core_slice_index_SliceIndex Idx (slice T)) :
-  core_ops_index_Index (slice T) Idx := {|
-  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
-  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
-|}.
-
 (* Trait implementation: [core::slice::index::private_slice_index::Range] *)
-Definition core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) := tt.
 
 (* Trait implementation: [core::slice::index::Range] *)
-Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexRangeUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedRangeUsizeInst;
   core_slice_index_SliceIndex_Output := slice T;
-  core_slice_index_SliceIndex_get := core_slice_index_Range_get T;
-  core_slice_index_SliceIndex_get_mut := core_slice_index_Range_get_mut T;
-  core_slice_index_SliceIndex_get_mut_back := core_slice_index_Range_get_mut_back T;
-  core_slice_index_SliceIndex_get_unchecked := core_slice_index_Range_get_unchecked T;
-  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_Range_get_unchecked_mut T;
-  core_slice_index_SliceIndex_index := core_slice_index_Range_index T;
-  core_slice_index_SliceIndex_index_mut := core_slice_index_Range_index_mut T;
-  core_slice_index_SliceIndex_index_mut_back := core_slice_index_Range_index_mut_back T;
+  core_slice_index_SliceIndex_get := core_slice_index_RangeUsize_get T;
+  core_slice_index_SliceIndex_get_mut := core_slice_index_RangeUsize_get_mut T;
+  core_slice_index_SliceIndex_get_mut_back := core_slice_index_RangeUsize_get_mut_back T;
+  core_slice_index_SliceIndex_get_unchecked := core_slice_index_RangeUsize_get_unchecked T;
+  core_slice_index_SliceIndex_get_unchecked_mut := core_slice_index_RangeUsize_get_unchecked_mut T;
+  core_slice_index_SliceIndex_index := core_slice_index_RangeUsize_index T;
+  core_slice_index_SliceIndex_index_mut := core_slice_index_RangeUsize_index_mut T;
+  core_slice_index_SliceIndex_index_mut_back := core_slice_index_RangeUsize_index_mut_back T;
+|}.
+
+(* Trait implementation: [core::slice::index::[T]] *)
+Definition core_ops_index_IndexSliceTIInst (T Idx : Type)
+  (inst : core_slice_index_SliceIndex Idx (slice T)) :
+  core_ops_index_Index (slice T) Idx := {|
+  core_ops_index_Index_Output := inst.(core_slice_index_SliceIndex_Output);
+  core_ops_index_Index_index := core_slice_index_Slice_index T Idx inst;
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+Definition core_ops_index_IndexMutSliceTIInst (T Idx : Type)
   (inst : core_slice_index_SliceIndex Idx (slice T)) :
   core_ops_index_IndexMut (slice T) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_slice_index_Slice_coreopsindexIndexInst T Idx inst;
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexSliceTIInst T Idx inst;
   core_ops_index_IndexMut_index_mut := core_slice_index_Slice_index_mut T Idx inst;
   core_ops_index_IndexMut_index_mut_back := core_slice_index_Slice_index_mut_back T Idx inst;
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_Index (slice T) Idx) :
   core_ops_index_Index (array T N) Idx := {|
   core_ops_index_Index_Output := inst.(core_ops_index_Index_Output);
@@ -728,10 +728,10 @@ Definition core_array_Array_coreopsindexIndexInst (T Idx : Type) (N : usize)
 |}.
 
 (* Trait implementation: [core::array::[T; N]] *)
-Definition core_array_Array_coreopsindexIndexMutInst (T Idx : Type) (N : usize)
+Definition core_ops_index_IndexMutArrayInst (T Idx : Type) (N : usize)
   (inst : core_ops_index_IndexMut (slice T) Idx) :
   core_ops_index_IndexMut (array T N) Idx := {|
-  core_ops_index_IndexMut_indexInst := core_array_Array_coreopsindexIndexInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
+  core_ops_index_IndexMut_indexInst := core_ops_index_IndexArrayInst T Idx N inst.(core_ops_index_IndexMut_indexInst);
   core_ops_index_IndexMut_index_mut := core_array_Array_index_mut T Idx N inst;
   core_ops_index_IndexMut_index_mut_back := core_array_Array_index_mut_back T Idx N inst;
 |}.
@@ -765,13 +765,13 @@ Axiom core_slice_index_usize_index_mut_back :
   forall (T : Type), usize -> slice T -> T -> result (slice T).
 
 (* Trait implementation: [core::slice::index::private_slice_index::usize] *)
-Definition core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+Definition core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize := tt.
 
 (* Trait implementation: [core::slice::index::usize] *)
-Definition core_slice_index_usize_coresliceindexSliceIndexInst (T : Type) :
+Definition core_slice_index_SliceIndexUsizeSliceTInst (T : Type) :
   core_slice_index_SliceIndex usize (slice T) := {|
-  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  core_slice_index_SliceIndex_sealedInst := core_slice_index_private_slice_index_SealedUsizeInst;
   core_slice_index_SliceIndex_Output := T;
   core_slice_index_SliceIndex_get := core_slice_index_usize_get T;
   core_slice_index_SliceIndex_get_mut := core_slice_index_usize_get_mut T;
@@ -815,8 +815,16 @@ Definition alloc_vec_Vec_coreopsindexIndexMutInst (T Idx : Type)
 
 (*** Theorems *)
 
+Axiom alloc_vec_Vec_index_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
+Axiom alloc_vec_Vec_index_mut_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
+  alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i =
+    alloc_vec_Vec_index_usize v i.
+
 Axiom alloc_vec_Vec_index_mut_back_eq : forall {a : Type} (v : alloc_vec_Vec a) (i : usize) (x : a),
-  alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x =
+  alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x =
     alloc_vec_Vec_update_usize v i x.
 
 End Primitives.
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