4 files changed, 16 insertions, 8 deletions
diff --git a/backends/lean/Base/Primitives/ArraySlice.lean b/backends/lean/Base/Primitives/ArraySlice.lean
index ef658e1b..91ca7284 100644
--- a/backends/lean/Base/Primitives/ArraySlice.lean
+++ b/backends/lean/Base/Primitives/ArraySlice.lean
@@ -2,7 +2,6 @@
 import Lean
 import Lean.Meta.Tactic.Simp
 import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
 import Mathlib.Tactic.Linarith
 import Base.IList
 import Base.Primitives.Scalar
@@ -269,7 +268,7 @@ def Array.update_subslice (α : Type u) (n : Usize) (a : Array α n) (r : Range
       . scalar_tac
       . scalar_tac
     let na := s_beg.append (s.val.append s_end)
-    have : na.len = a.val.len := by simp [*]
+    have : na.len = a.val.len := by simp [na, *]
     ok ⟨ na, by simp_all [← List.len_eq_length]; scalar_tac ⟩
   else
     fail panic
@@ -343,7 +342,7 @@ def Slice.update_subslice (α : Type u) (s : Slice α) (r : Range Usize) (ss : S
       . scalar_tac
       . scalar_tac
     let ns := s_beg.append (ss.val.append s_end)
-    have : ns.len = s.val.len := by simp [*]
+    have : ns.len = s.val.len := by simp [ns, *]
     ok ⟨ ns, by simp_all [← List.len_eq_length]; scalar_tac ⟩
   else
     fail panic
diff --git a/backends/lean/Base/Primitives/Range.lean b/backends/lean/Base/Primitives/Range.lean
index a268bcba..416cd201 100644
--- a/backends/lean/Base/Primitives/Range.lean
+++ b/backends/lean/Base/Primitives/Range.lean
@@ -2,7 +2,6 @@
 import Lean
 import Lean.Meta.Tactic.Simp
 import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
 import Mathlib.Tactic.Linarith
 import Base.IList
 import Base.Primitives.Scalar
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index c298ba92..98d695a4 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -265,6 +265,14 @@ theorem Scalar.cMax_suffices ty (h : x ≤ Scalar.cMax ty) : x ≤ Scalar.max ty
   have := Scalar.cMax_bound ty
   linarith
 
+/-- The scalar type.
+
+    We could use a subtype, but it using a custom structure type allows us
+    to have more control over the coercions and the simplifications (we tried
+    using a subtype and it caused issues especially as we had to make the Scalar
+    type non-reducible, so that we could have more control, but leading to
+    some natural equalities not being obvious to the simplifier anymore).
+ -/
 structure Scalar (ty : ScalarTy) where
   val : Int
   hmin : Scalar.min ty ≤ val
@@ -274,6 +282,9 @@ deriving Repr
 instance (ty : ScalarTy) : CoeOut (Scalar ty) Int where
   coe := λ v => v.val
 
+/- Activate the ↑ notation -/
+attribute [coe] Scalar.val
+
 theorem Scalar.bound_suffices (ty : ScalarTy) (x : Int) :
   Scalar.cMin ty ≤ x ∧ x ≤ Scalar.cMax ty ->
   Scalar.min ty ≤ x ∧ x ≤ Scalar.max ty
@@ -1117,19 +1128,19 @@ theorem Scalar.eq_equiv {ty : ScalarTy} (x y : Scalar ty) :
 
 -- This is sometimes useful when rewriting the goal with the local assumptions
 @[simp] theorem Scalar.eq_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x = y → (↑x : Int) = ↑y := (eq_equiv x y).mp
+  (↑x : Int) = ↑y → x = y := (eq_equiv x y).mpr
 
 theorem Scalar.lt_equiv {ty : ScalarTy} (x y : Scalar ty) :
   x < y ↔ (↑x : Int) < ↑y := by simp [LT.lt]
 
 @[simp] theorem Scalar.lt_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x < y → (↑x : Int) < ↑y := (lt_equiv x y).mp
+  (↑x : Int) < (↑y) → x < y := (lt_equiv x y).mpr
 
 theorem Scalar.le_equiv {ty : ScalarTy} (x y : Scalar ty) :
   x ≤ y ↔ (↑x : Int) ≤ ↑y := by simp [LE.le]
 
 @[simp] theorem Scalar.le_imp {ty : ScalarTy} (x y : Scalar ty) :
-  x ≤ y → (↑x : Int) ≤ ↑y := (le_equiv x y).mp
+  (↑x : Int) ≤ ↑y → x ≤ y := (le_equiv x y).mpr
 
 instance Scalar.decLt {ty} (a b : Scalar ty) : Decidable (LT.lt a b) := Int.decLt ..
 instance Scalar.decLe {ty} (a b : Scalar ty) : Decidable (LE.le a b) := Int.decLe ..
diff --git a/backends/lean/Base/Primitives/Vec.lean b/backends/lean/Base/Primitives/Vec.lean
index dbe5c8dd..8e2d65a8 100644
--- a/backends/lean/Base/Primitives/Vec.lean
+++ b/backends/lean/Base/Primitives/Vec.lean
@@ -2,7 +2,6 @@
 import Lean
 import Lean.Meta.Tactic.Simp
 import Init.Data.List.Basic
-import Mathlib.Tactic.RunCmd
 import Mathlib.Tactic.Linarith
 import Base.IList
 import Base.Primitives.Scalar