Update the standard libraries

5 files changed, 85 insertions, 78 deletions

diff --git a/backends/coq/Primitives.v b/backends/coq/Primitives.v
index 85e38f01..846a5e4b 100644
--- a/backends/coq/Primitives.v
+++ b/backends/coq/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).
@@ -683,22 +683,14 @@ 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;
@@ -711,16 +703,24 @@ Definition core_slice_index_Range_coresliceindexSliceIndexInst (T : Type) :
 |}.
 
 (* Trait implementation: [core::slice::index::[T]] *)
-Definition core_slice_index_Slice_coreopsindexIndexMutInst (T Idx : Type)
+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_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/backends/fstar/Primitives.fst b/backends/fstar/Primitives.fst
index 3297803c..19c4e7a3 100644
--- a/backends/fstar/Primitives.fst
+++ b/backends/fstar/Primitives.fst
@@ -351,14 +351,14 @@ let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
 let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
 
 // Trait instance
-let alloc_boxed_Box_coreOpsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
   target = self;
   deref = alloc_boxed_Box_deref self;
 }
 
 // Trait instance
-let alloc_boxed_Box_coreOpsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
-  derefInst = alloc_boxed_Box_coreOpsDerefInst self;
+let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+  derefInst = alloc_boxed_Box_coreopsDerefInst self;
   deref_mut = alloc_boxed_Box_deref_mut self;
   deref_mut_back = alloc_boxed_Box_deref_mut_back self;
 }
@@ -559,22 +559,14 @@ let core_array_Array_index_mut_back
   (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
   admit () // TODO
 
-// Trait implementation: [core::slice::index::[T]]
-let core_slice_index_Slice_coreopsindexIndexInst (t idx : Type0)
-  (inst : core_slice_index_SliceIndex idx (slice t)) :
-  core_ops_index_Index (slice t) idx = {
-  output = inst.output;
-  index = core_slice_index_Slice_index t idx inst;
-}
-
 // Trait implementation: [core::slice::index::private_slice_index::Range]
-let core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
   : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
 
 // Trait implementation: [core::slice::index::Range]
-let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
   core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
-  sealedInst = core_slice_index_private_slice_index_Range_coresliceindexprivate_slice_indexSealedInst;
+  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
   output = slice t;
   get = core_slice_index_Range_get t;
   get_mut = core_slice_index_Range_get_mut t;
@@ -587,16 +579,24 @@ let core_slice_index_Range_coresliceindexSliceIndexInst (t : Type0) :
 }
 
 // Trait implementation: [core::slice::index::[T]]
-let core_slice_index_Slice_coreopsindexIndexMutInst (t idx : Type0)
+let core_ops_index_IndexSliceTIInst (t idx : Type0)
+  (inst : core_slice_index_SliceIndex idx (slice t)) :
+  core_ops_index_Index (slice t) idx = {
+  output = inst.output;
+  index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
   (inst : core_slice_index_SliceIndex idx (slice t)) :
   core_ops_index_IndexMut (slice t) idx = {
-  indexInst = core_slice_index_Slice_coreopsindexIndexInst t idx inst;
+  indexInst = core_ops_index_IndexSliceTIInst t idx inst;
   index_mut = core_slice_index_Slice_index_mut t idx inst;
   index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
 }
 
 // Trait implementation: [core::array::[T; N]]
-let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
+let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize)
   (inst : core_ops_index_Index (slice t) idx) :
   core_ops_index_Index (array t n) idx = {
   output = inst.output;
@@ -604,10 +604,10 @@ let core_array_Array_coreopsindexIndexInst (t idx : Type0) (n : usize)
 }
 
 // Trait implementation: [core::array::[T; N]]
-let core_array_Array_coreopsindexIndexMutInst (t idx : Type0) (n : usize)
+let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
   (inst : core_ops_index_IndexMut (slice t) idx) :
   core_ops_index_IndexMut (array t n) idx = {
-  indexInst = core_array_Array_coreopsindexIndexInst t idx n inst.indexInst;
+  indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
   index_mut = core_array_Array_index_mut t idx n inst;
   index_mut_back = core_array_Array_index_mut_back t idx n inst;
 }
@@ -651,13 +651,13 @@ let core_slice_index_usize_index_mut_back
   admit () // TODO
 
 // Trait implementation: [core::slice::index::private_slice_index::usize]
-let core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst
+let core_slice_index_private_slice_index_SealedUsizeInst
   : core_slice_index_private_slice_index_Sealed usize = ()
 
 // Trait implementation: [core::slice::index::usize]
-let core_slice_index_usize_coresliceindexSliceIndexInst (t : Type0) :
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
   core_slice_index_SliceIndex usize (slice t) = {
-  sealedInst = core_slice_index_private_slice_index_usize_coresliceindexprivate_slice_indexSealedInst;
+  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
   output = t;
   get = core_slice_index_usize_get t;
   get_mut = core_slice_index_usize_get_mut t;
@@ -706,24 +706,24 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
 
 let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
   Lemma (
-    alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+    alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
       alloc_vec_Vec_index_usize v i)
-  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
   =
   admit()
 
 let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
   Lemma (
-    alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i ==
+    alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
       alloc_vec_Vec_index_usize v i)
-  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i)]
+  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
   =
   admit()
 
 let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
   Lemma (
-    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)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)]
+  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
   =
   admit()
diff --git a/backends/lean/Base/Primitives/Alloc.lean b/backends/lean/Base/Primitives/Alloc.lean
index 34590499..6c89c6bb 100644
--- a/backends/lean/Base/Primitives/Alloc.lean
+++ b/backends/lean/Base/Primitives/Alloc.lean
@@ -16,16 +16,16 @@ def deref_mut (T : Type) (x : T) : Result T := ret x
 def deref_mut_back (T : Type) (_ : T) (x : T) : Result T := ret x
 
 /-- Trait instance -/
-def coreOpsDerefInst (Self : Type) :
+def coreopsDerefInst (Self : Type) :
   core.ops.deref.Deref Self := {
   Target := Self
   deref := deref Self
 }
 
 /-- Trait instance -/
-def coreOpsDerefMutInst (Self : Type) :
+def coreopsDerefMutInst (Self : Type) :
   core.ops.deref.DerefMut Self := {
-  derefInst := coreOpsDerefInst Self
+  derefInst := coreopsDerefInst Self
   deref_mut := deref_mut Self
   deref_mut_back := deref_mut_back Self
 }
diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean
index cfc9a6b2..8bb9a855 100644
--- a/backends/lean/Base/Primitives/ArraySlice.lean
+++ b/backends/lean/Base/Primitives/ArraySlice.lean
@@ -439,23 +439,14 @@ def core.array.Array.index_mut_back
   (a : Array T N) (i : I) (x : inst.indexInst.Output) : Result (Array T N) :=
   sorry -- TODO
 
-/- Trait implementation: [core::slice::index::[T]] -/
-def core.slice.index.Slice.coreopsindexIndexInst (T I : Type)
-  (inst : core.slice.index.SliceIndex I (Slice T)) :
-  core.ops.index.Index (Slice T) I := {
-  Output := inst.Output
-  index := core.slice.index.Slice.index T I inst
-}
-
 /- Trait implementation: [core::slice::index::private_slice_index::Range] -/
-def core.slice.index.private_slice_index.Range.coresliceindexprivate_slice_indexSealedInst
+def core.slice.index.private_slice_index.SealedRangeUsizeInst
   : core.slice.index.private_slice_index.Sealed (Range Usize) := {}
 
 /- Trait implementation: [core::slice::index::Range] -/
-def core.slice.index.Range.coresliceindexSliceIndexInst (T : Type) :
+def core.slice.index.SliceIndexRangeUsizeSliceTInst (T : Type) :
   core.slice.index.SliceIndex (Range Usize) (Slice T) := {
-  sealedInst :=
-    core.slice.index.private_slice_index.Range.coresliceindexprivate_slice_indexSealedInst
+  sealedInst := core.slice.index.private_slice_index.SealedRangeUsizeInst
   Output := Slice T
   get := core.slice.index.Range.get T
   get_mut := core.slice.index.Range.get_mut T
@@ -468,16 +459,24 @@ def core.slice.index.Range.coresliceindexSliceIndexInst (T : Type) :
 }
 
 /- Trait implementation: [core::slice::index::[T]] -/
-def core.slice.index.Slice.coreopsindexIndexMutInst (T I : Type)
+def core.ops.index.IndexSliceTIInst (T I : Type)
+  (inst : core.slice.index.SliceIndex I (Slice T)) :
+  core.ops.index.Index (Slice T) I := {
+  Output := inst.Output
+  index := core.slice.index.Slice.index T I inst
+}
+
+/- Trait implementation: [core::slice::index::[T]] -/
+def core.ops.index.IndexMutSliceTIInst (T I : Type)
   (inst : core.slice.index.SliceIndex I (Slice T)) :
   core.ops.index.IndexMut (Slice T) I := {
-  indexInst := core.slice.index.Slice.coreopsindexIndexInst T I inst
+  indexInst := core.ops.index.IndexSliceTIInst T I inst
   index_mut := core.slice.index.Slice.index_mut T I inst
   index_mut_back := core.slice.index.Slice.index_mut_back T I inst
 }
 
 /- Trait implementation: [core::array::[T; N]] -/
-def core.array.Array.coreopsindexIndexInst (T I : Type) (N : Usize)
+def core.ops.index.IndexArrayIInst (T I : Type) (N : Usize)
   (inst : core.ops.index.Index (Slice T) I) :
   core.ops.index.Index (Array T N) I := {
   Output := inst.Output
@@ -485,10 +484,10 @@ def core.array.Array.coreopsindexIndexInst (T I : Type) (N : Usize)
 }
 
 /- Trait implementation: [core::array::[T; N]] -/
-def core.array.Array.coreopsindexIndexMutInst (T I : Type) (N : Usize)
+def core.ops.index.IndexMutArrayIInst (T I : Type) (N : Usize)
   (inst : core.ops.index.IndexMut (Slice T) I) :
   core.ops.index.IndexMut (Array T N) I := {
-  indexInst := core.array.Array.coreopsindexIndexInst T I N inst.indexInst
+  indexInst := core.ops.index.IndexArrayIInst T I N inst.indexInst
   index_mut := core.array.Array.index_mut T I N inst
   index_mut_back := core.array.Array.index_mut_back T I N inst
 }
@@ -532,13 +531,13 @@ def core.slice.index.Usize.index_mut_back
   sorry -- TODO
 
 /- Trait implementation: [core::slice::index::private_slice_index::usize] -/
-def core.slice.index.private_slice_index.usize.coresliceindexprivate_slice_indexSealedInst
+def core.slice.index.private_slice_index.SealedUsizeInst
   : core.slice.index.private_slice_index.Sealed Usize := {}
 
 /- Trait implementation: [core::slice::index::usize] -/
-def core.slice.index.usize.coresliceindexSliceIndexInst (T : Type) :
+def core.slice.index.SliceIndexUsizeSliceTInst (T : Type) :
   core.slice.index.SliceIndex Usize (Slice T) := {
-  sealedInst := core.slice.index.private_slice_index.usize.coresliceindexprivate_slice_indexSealedInst
+  sealedInst := core.slice.index.private_slice_index.SealedUsizeInst
   Output := T
   get := core.slice.index.Usize.get T
   get_mut := core.slice.index.Usize.get_mut T
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index bbed6082..e600a151 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -153,19 +153,19 @@ def Vec.coreopsindexIndexMutInst (T I : Type)
 
 @[simp]
 theorem Vec.index_slice_index {α : Type} (v : Vec α) (i : Usize) :
-  Vec.index α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i =
+  Vec.index α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i =
   Vec.index_usize v i :=
   sorry
 
 @[simp]
 theorem Vec.index_mut_slice_index {α : Type} (v : Vec α) (i : Usize) :
-  Vec.index_mut α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i =
+  Vec.index_mut α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i =
   Vec.index_usize v i :=
   sorry
 
 @[simp]
 theorem Vec.index_mut_back_slice_index {α : Type} (v : Vec α) (i : Usize) (x : α) :
-  Vec.index_mut_back α Usize (core.slice.index.usize.coresliceindexSliceIndexInst α) v i x =
+  Vec.index_mut_back α Usize (core.slice.index.SliceIndexUsizeSliceTInst α) v i x =
   Vec.update_usize v i x :=
   sorry