3 files changed, 34 insertions, 0 deletions
diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
index 9c11ed45..8ada4171 100644
--- a/backends/lean/Base/Arith/Base.lean
+++ b/backends/lean/Base/Arith/Base.lean
@@ -57,4 +57,16 @@ theorem int_pos_ind (p : Int → Prop) :
 -- TODO: there is probably something more general to do
 theorem nat_zero_eq_int_zero : (0 : Nat) = (0 : Int) := by simp
 
+-- This is mostly used in termination proofs
+theorem to_int_to_nat_lt (x y : ℤ) (h0 : 0 ≤ x) (h1 : x < y) :
+  ↑(x.toNat) < y := by
+  simp [*]
+
+-- This is mostly used in termination proofs
+theorem to_int_sub_to_nat_lt (x y : ℤ) (x' : ℕ)
+  (h0 : ↑x' ≤ x) (h1 : x - ↑x' < y) :
+  ↑(x.toNat - x') < y := by
+  have : 0 ≤ x := by linarith
+  simp [Int.toNat_sub_of_le, *]
+
 end Arith
diff --git a/backends/lean/Base/Arith/Int.lean b/backends/lean/Base/Arith/Int.lean
index 3359ecdb..2959e245 100644
--- a/backends/lean/Base/Arith/Int.lean
+++ b/backends/lean/Base/Arith/Int.lean
@@ -270,6 +270,17 @@ elab "int_tac" args:(" split_goal"?): tactic =>
   let split := args.raw.getArgs.size > 0
   intTac split (do pure ())
 
+-- For termination proofs
+syntax "int_decr_tac" : tactic
+macro_rules
+  | `(tactic| int_decr_tac) =>
+    `(tactic|
+      simp_wf;
+      -- TODO: don't use a macro (namespace problems)
+      (first | apply Arith.to_int_to_nat_lt
+             | apply Arith.to_int_sub_to_nat_lt) <;>
+      simp_all <;> int_tac)
+
 example (x : Int) (h0: 0 ≤ x) (h1: x ≠ 0) : 0 < x := by
   int_tac_preprocess
   linarith
diff --git a/backends/lean/Base/Arith/Scalar.lean b/backends/lean/Base/Arith/Scalar.lean
index 47751c8a..66c31129 100644
--- a/backends/lean/Base/Arith/Scalar.lean
+++ b/backends/lean/Base/Arith/Scalar.lean
@@ -36,6 +36,17 @@ def scalarTac (splitGoalConjs : Bool) : Tactic.TacticM Unit := do
 elab "scalar_tac" : tactic =>
   scalarTac false
 
+-- For termination proofs
+syntax "scalar_decr_tac" : tactic
+macro_rules
+  | `(tactic| scalar_decr_tac) =>
+    `(tactic|
+      simp_wf;
+      -- TODO: don't use a macro (namespace problems)
+      (first | apply Arith.to_int_to_nat_lt
+             | apply Arith.to_int_sub_to_nat_lt) <;>
+      simp_all <;> scalar_tac)
+
 instance (ty : ScalarTy) : HasIntProp (Scalar ty) where
   -- prop_ty is inferred
   prop := λ x => And.intro x.hmin x.hmax