Improve the Lean backend

2 files changed, 18 insertions, 0 deletions

diff --git a/backends/lean/Base/Primitives/Base.lean b/backends/lean/Base/Primitives/Base.lean
index 3d70c84a..9dbaf133 100644
--- a/backends/lean/Base/Primitives/Base.lean
+++ b/backends/lean/Base/Primitives/Base.lean
@@ -116,6 +116,13 @@ def Result.attach {α: Type} (o : Result α): Result { x : α // o = ret x } :=
 @[simp] theorem bind_tc_div (f : α → Result β) :
   (do let y ← div; f y) = div := by simp [Bind.bind, bind]
 
+@[simp] theorem bind_assoc_eq {a b c : Type u}
+  (e : Result a) (g :  a → Result b) (h : b → Result c) :
+  (Bind.bind (Bind.bind e g) h) =
+  (Bind.bind e (λ x => Bind.bind (g x) h)) := by
+  simp [Bind.bind]
+  cases e <;> simp
+
 ----------
 -- MISC --
 ----------
diff --git a/backends/lean/Base/Primitives/Scalar.lean b/backends/lean/Base/Primitives/Scalar.lean
index a8eda6d5..2c34774b 100644
--- a/backends/lean/Base/Primitives/Scalar.lean
+++ b/backends/lean/Base/Primitives/Scalar.lean
@@ -1038,6 +1038,17 @@ instance {ty} : LT (Scalar ty) where
 
 instance {ty} : LE (Scalar ty) where le a b := LE.le a.val b.val
 
+theorem Scalar.lt_equiv {ty : ScalarTy} (x y : Scalar ty) :
+  x < y ↔ x.val < y.val := by simp [LT.lt]
+
+theorem Scalar.le_equiv {ty : ScalarTy} (x y : Scalar ty) :
+  x ≤ y ↔ x.val ≤ y.val := by simp [LE.le]
+
+-- Not marking this one with @[simp] on purpose
+theorem Scalar.eq_equiv {ty : ScalarTy} (x y : Scalar ty) :
+  x = y ↔ x.val = y.val := by
+  cases x; cases y; simp_all
+
 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 ..