From 0a8211041814b5eafac0b9e2dbcd956957a322b5 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Tue, 18 Jul 2023 18:02:03 +0200
Subject: Move an arithmetic lemma

---
 backends/lean/Base/Arith/Base.lean | 6 ++++++
 1 file changed, 6 insertions(+)

(limited to 'backends/lean/Base/Arith')

diff --git a/backends/lean/Base/Arith/Base.lean b/backends/lean/Base/Arith/Base.lean
index a6e59b74..e008f7b9 100644
--- a/backends/lean/Base/Arith/Base.lean
+++ b/backends/lean/Base/Arith/Base.lean
@@ -28,6 +28,12 @@ theorem ne_is_lt_or_gt {x y : Int} (hne : x ≠ y) : x < y ∨ x > y := by
   | .inl _ => left; linarith
   | .inr _ => right; linarith
 
+-- TODO: move?
+theorem add_one_le_iff_le_ne (n m : Nat) (h1 : m ≤ n) (h2 : m ≠ n) : m + 1 ≤ n := by
+  -- Damn, those proofs on natural numbers are hard - I wish Omega was in mathlib4...
+  simp [Nat.add_one_le_iff]
+  simp [Nat.lt_iff_le_and_ne]
+  simp_all
 
 /- Induction over positive integers -/
 -- TODO: move
-- 
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