diff options
| author | Son Ho | 2023-09-18 19:56:27 +0200 |
|---|---|---|
| committer | Son Ho | 2023-09-18 19:56:27 +0200 |
| commit | 0eb62047b052cb4fbf842525170dd916679e8b7e (patch) | |
| tree | da155463273c10c9a66338d0cd2e96101d211f59 /backends/lean/Base/IList | |
| parent | 28f4ea9ffe02d4204bb60273b6a77db7ed48781b (diff) | |
Simplify some lemmas and prove that the scalars and Vec are inhabited
Diffstat (limited to 'backends/lean/Base/IList')
| -rw-r--r-- | backends/lean/Base/IList/IList.lean | 16 |
1 files changed, 7 insertions, 9 deletions
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean index a940da25..214a6582 100644 --- a/backends/lean/Base/IList/IList.lean +++ b/backends/lean/Base/IList/IList.lean @@ -375,12 +375,11 @@ theorem index_itake_append_end [Inhabited α] (i j : Int) (l0 l1 : List α) simp_all @[simp] -theorem index_ne +theorem index_update_ne {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (j: ℤ) (x: α) : - 0 ≤ i → i < l.len → 0 ≤ j → j < l.len → j ≠ i → - (l.update i x).index j = l.index j + j ≠ i → (l.update i x).index j = l.index j := - λ _ _ _ _ _ => match l with + λ _ => match l with | [] => by simp at * | hd :: tl => if h: i = 0 then @@ -391,12 +390,11 @@ theorem index_ne by simp [*] else by - simp [*] - simp at * - apply index_ne <;> scalar_tac + simp_all + apply index_update_ne; scalar_tac @[simp] -theorem index_eq +theorem index_update_eq {α : Type u} [Inhabited α] (l: List α) (i: ℤ) (x: α) : 0 ≤ i → i < l.len → (l.update i x).index i = x @@ -411,7 +409,7 @@ theorem index_eq by simp [*] simp at * - apply index_eq <;> scalar_tac + apply index_update_eq <;> scalar_tac theorem update_map_eq {α : Type u} {β : Type v} (ls : List α) (i : Int) (x : α) (f : α → β) : (ls.update i x).map f = (ls.map f).update i (f x) := |