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author | Son Ho | 2023-12-05 17:34:13 +0100 |
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committer | Son Ho | 2023-12-05 17:34:13 +0100 |
commit | 726db4911add81a853aafcec3936b457aaeff5b4 (patch) | |
tree | 2663915767c3558203990ed14f8d5604b7fd21d1 /backends/lean/Base/Arith/Base.lean | |
parent | 92887b89e35607e99bae2f19e4c5b2f162683d02 (diff) | |
parent | 4795e5f823bc89504855d8eb946b111d9314f4d5 (diff) |
Merge branch 'main' into son_fixes2
Diffstat (limited to '')
-rw-r--r-- | backends/lean/Base/Arith/Base.lean | 12 |
1 files changed, 12 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 |