diff options
Diffstat (limited to 'backends/lean/Base/IList')
| -rw-r--r-- | backends/lean/Base/IList/IList.lean | 25 |
1 files changed, 14 insertions, 11 deletions
diff --git a/backends/lean/Base/IList/IList.lean b/backends/lean/Base/IList/IList.lean index e90d1e0d..51457c20 100644 --- a/backends/lean/Base/IList/IList.lean +++ b/backends/lean/Base/IList/IList.lean @@ -66,13 +66,15 @@ theorem indexOpt_eq_index [Inhabited α] (ls : List α) (i : Int) : i < ls.len → ls.indexOpt i = some (ls.index i) := match ls with - | [] => by simp; intros; linarith + | [] => by simp | hd :: tl => if h: i = 0 then by simp [*] - else + else by have hi := indexOpt_eq_index tl (i - 1) - by simp [*]; intros; apply hi <;> int_tac + simp [*]; intros + -- TODO: there seems to be syntax errors if we don't put the parentheses below?? + apply hi <;> (int_tac) -- Remark: the list is unchanged if the index is not in bounds (in particular -- if it is < 0) @@ -83,7 +85,7 @@ def update (ls : List α) (i : Int) (y : α) : List α := -- Remark: the whole list is dropped if the index is not in bounds (in particular -- if it is < 0) -def idrop (i : Int) (ls : List α) : List α := +def idrop {α : Type u} (i : Int) (ls : List α) : List α := match ls with | [] => [] | x :: tl => if i = 0 then x :: tl else idrop (i - 1) tl @@ -117,7 +119,7 @@ variable {α : Type u} def ireplicate {α : Type u} (i : ℤ) (x : α) : List α := if i ≤ 0 then [] else x :: ireplicate (i - 1) x -termination_by ireplicate i x => i.toNat +termination_by i.toNat decreasing_by int_decr_tac @[simp] theorem update_nil : update ([] : List α) i y = [] := by simp [update] @@ -137,7 +139,7 @@ decreasing_by int_decr_tac @[simp] theorem ireplicate_zero : ireplicate 0 x = [] := by rw [ireplicate]; simp @[simp] theorem ireplicate_nzero_cons (hne : 0 < i) : ireplicate i x = x :: ireplicate (i - 1) x := by - rw [ireplicate]; simp [*]; intro; linarith + rw [ireplicate]; simp [*] @[simp] theorem slice_nzero_cons (i j : Int) (x : α) (tl : List α) (hne : i ≠ 0) : slice i j ((x :: tl) : List α) = slice (i - 1) (j - 1) tl := @@ -148,11 +150,12 @@ theorem slice_nzero_cons (i j : Int) (x : α) (tl : List α) (hne : i ≠ 0) : s have : i = 1 := by int_tac simp [*, slice] else - have := slice_nzero_cons (i - 1) (j - 1) hd tl h + have hi := slice_nzero_cons (i - 1) (j - 1) hd tl h by conv => lhs; simp [slice, *] - conv at this => lhs; simp [slice, *] - simp [*, slice] + conv at hi => lhs; simp [slice, *] + simp [slice] + simp [*] @[simp] theorem ireplicate_replicate {α : Type u} (l : ℤ) (x : α) (h : 0 ≤ l) : @@ -166,7 +169,7 @@ theorem ireplicate_replicate {α : Type u} (l : ℤ) (x : α) (h : 0 ≤ l) : have hl : l.toNat = .succ (l.toNat - 1) := by cases hl: l.toNat <;> simp_all conv => rhs; rw[hl] -termination_by ireplicate_replicate l x h => l.toNat +termination_by l.toNat decreasing_by int_decr_tac @[simp] @@ -178,7 +181,7 @@ theorem ireplicate_len {α : Type u} (l : ℤ) (x : α) (h : 0 ≤ l) : have : 0 < l := by int_tac have hr := ireplicate_len (l - 1) x (by int_tac) simp [*] -termination_by ireplicate_len l x h => l.toNat +termination_by l.toNat decreasing_by int_decr_tac theorem len_eq_length (ls : List α) : ls.len = ls.length := by |