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authorSon Ho2023-07-18 18:02:03 +0200
committerSon Ho2023-07-18 18:02:03 +0200
commit0a8211041814b5eafac0b9e2dbcd956957a322b5 (patch)
treec823a5a3668201ddcc0caded7933dea0061a059a /backends/lean/Base/Arith
parent0f430c055c3a531ceab83635adc5df92f0015c6e (diff)
Move an arithmetic lemma
Diffstat (limited to 'backends/lean/Base/Arith')
-rw-r--r--backends/lean/Base/Arith/Base.lean6
1 files changed, 6 insertions, 0 deletions
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