diff options
Diffstat (limited to 'backends/lean/Base/Arith/Base.lean')
| -rw-r--r-- | backends/lean/Base/Arith/Base.lean | 6 |
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 |