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array_repl
...
array_clea
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43a492aeed | ||
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a0914e68ed |
@@ -85,6 +85,8 @@ theorem ext' {as bs : Array α} (h : as.toList = bs.toList) : as = bs := by
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@[simp] theorem getElem_toList {a : Array α} {i : Nat} (h : i < a.size) : a.toList[i] = a[i] := rfl
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@[simp] theorem getElem?_toList {a : Array α} {i : Nat} : a.toList[i]? = a[i]? := rfl
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/-- `a ∈ as` is a predicate which asserts that `a` is in the array `as`. -/
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-- NB: This is defined as a structure rather than a plain def so that a lemma
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-- like `sizeOf_lt_of_mem` will not apply with no actual arrays around.
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@@ -29,7 +29,7 @@ that we need to write lemmas about `List.toArray`.
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-/
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namespace Array
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theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? = some a[i] :=
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@[simp] theorem getElem?_eq_getElem {a : Array α} {i : Nat} (h : i < a.size) : a[i]? = some a[i] :=
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getElem?_pos ..
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@[simp] theorem getElem?_eq_none_iff {a : Array α} : a[i]? = none ↔ a.size ≤ i := by
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@@ -91,6 +91,9 @@ theorem toArray_inj {a b : List α} (h : a.toArray = b.toArray) : a = b := by
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@[simp] theorem back?_toArray (l : List α) : l.toArray.back? = l.getLast? := by
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simp [back?, List.getLast?_eq_getElem?]
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@[simp] theorem set_toArray (l : List α) (i : Nat) (a : α) (h : i < l.length) :
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(l.toArray.set i a) = (l.set i a).toArray := rfl
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@[simp] theorem forIn'_loop_toArray [Monad m] (l : List α) (f : (a : α) → a ∈ l.toArray → β → m (ForInStep β)) (i : Nat)
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(h : i ≤ l.length) (b : β) :
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Array.forIn'.loop l.toArray f i h b =
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@@ -526,38 +529,50 @@ theorem exists_push_of_size_eq_add_one {xs : Array α} (h : xs.size = n + 1) :
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/-! ## L[i] and L[i]? -/
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@[deprecated List.getElem_toArray (since := "2024-11-29")]
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theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
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theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
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-- getElem?_eq_none_iff is above.
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@[simp] theorem none_eq_getElem?_iff {a : Array α} {i : Nat} : none = a[i]? ↔ a.size ≤ i := by
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simp [eq_comm (a := none)]
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theorem getElem?_eq {a : Array α} {i : Nat} :
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a[i]? = if h : i < a.size then some a[i] else none := by
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split
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· simp_all [getElem?_eq_getElem]
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· simp_all
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theorem getElem?_eq_some_iff {a : Array α} : a[i]? = some b ↔ ∃ h : i < a.size, a[i] = b := by
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simp [getElem?_eq]
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simp [getElem?_def]
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theorem getElem?_eq_none {a : Array α} (h : a.size ≤ i) : a[i]? = none := by
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simp [getElem?_eq_none_iff, h]
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-- getElem?_eq_getElem is above.
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theorem some_eq_getElem?_iff {a : Array α} : some b = a[i]? ↔ ∃ h : i < a.size, a[i] = b := by
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rw [eq_comm, getElem?_eq_some_iff]
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theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
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rw [getElem?_eq]
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split <;> simp_all
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-- getElem?_eq_some_iff is above.
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@[simp] theorem some_getElem_eq_getElem?_iff (a : Array α) (i : Nat) (h : i < a.size) :
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(some a[i] = a[i]?) ↔ True := by
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simp [h]
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@[simp] theorem getElem?_eq_some_getElem_iff (a : Array α) (i : Nat) (h : i < a.size) :
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(a[i]? = some a[i]) ↔ True := by
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simp [h]
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theorem getElem_eq_iff {a : Array α} {n : Nat} {h : n < a.size} : a[n] = x ↔ a[n]? = some x := by
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simp only [getElem?_eq_some_iff]
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exact ⟨fun w => ⟨h, w⟩, fun h => h.2⟩
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theorem getElem_eq_getElem?_get (a : Array α) (i : Nat) (h : i < a.size) :
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a[i] = a[i]?.get (by simp [getElem?_eq_getElem, h]) := by
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simp [getElem_eq_iff]
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@[simp] theorem getElem?_empty {n : Nat} : (#[] : Array α)[n]? = none := rfl
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theorem getElem_push_lt (a : Array α) (x : α) (i : Nat) (h : i < a.size) :
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have : i < (a.push x).size := by simp [*, Nat.lt_succ_of_le, Nat.le_of_lt]
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(a.push x)[i] = a[i] := by
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simp only [push, getElem_eq_getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
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simp only [push, ← getElem_toList, List.concat_eq_append, List.getElem_append_left, h]
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@[simp] theorem getElem_push_eq (a : Array α) (x : α) : (a.push x)[a.size] = x := by
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simp only [push, getElem_eq_getElem_toList, List.concat_eq_append]
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rw [List.getElem_append_right] <;> simp [getElem_eq_getElem_toList, Nat.zero_lt_one]
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simp only [push, ← getElem_toList, List.concat_eq_append]
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rw [List.getElem_append_right] <;> simp [← getElem_toList, Nat.zero_lt_one]
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theorem getElem_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size) :
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(a.push x)[i] = if h : i < a.size then a[i] else x := by
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@@ -566,9 +581,12 @@ theorem getElem_push (a : Array α) (x : α) (i : Nat) (h : i < (a.push x).size)
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· simp at h
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simp [getElem_push_lt, Nat.le_antisymm (Nat.le_of_lt_succ h) (Nat.ge_of_not_lt h')]
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@[deprecated getElem_push (since := "2024-10-21")] abbrev get_push := @getElem_push
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@[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
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@[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
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theorem getElem?_push {a : Array α} {x} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
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simp [getElem?_def, getElem_push]
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(repeat' split) <;> first | rfl | omega
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@[simp] theorem getElem?_push_size {a : Array α} {x} : (a.push x)[a.size]? = some x := by
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simp [getElem?_push]
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@[simp] theorem mem_push {a : Array α} {x y : α} : x ∈ a.push y ↔ x ∈ a ∨ x = y := by
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simp [mem_def]
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@@ -755,12 +773,14 @@ theorem get!_eq_getD [Inhabited α] (a : Array α) : a.get! n = a.getD n default
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@[simp] theorem getElem_set_eq (a : Array α) (i : Nat) (h : i < a.size) (v : α) {j : Nat}
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(eq : i = j) (p : j < (a.set i v).size) :
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(a.set i v)[j]'p = v := by
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simp [set, getElem_eq_getElem_toList, ←eq]
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cases a
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simp
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simp [set, ← getElem_toList, ←eq]
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@[simp] theorem getElem_set_ne (a : Array α) (i : Nat) (h' : i < a.size) (v : α) {j : Nat}
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(pj : j < (a.set i v).size) (h : i ≠ j) :
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(a.set i v)[j]'pj = a[j]'(size_set a i v _ ▸ pj) := by
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simp only [set, getElem_eq_getElem_toList, List.getElem_set_ne h]
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simp only [set, ← getElem_toList, List.getElem_set_ne h]
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theorem getElem_set (a : Array α) (i : Nat) (h' : i < a.size) (v : α) (j : Nat)
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(h : j < (a.set i v).size) :
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@@ -882,7 +902,7 @@ theorem ofFn_succ (f : Fin (n+1) → α) :
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theorem mkArray_eq_toArray_replicate (n : Nat) (v : α) : mkArray n v = (List.replicate n v).toArray := rfl
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@[simp] theorem getElem_mkArray (n : Nat) (v : α) (h : i < (mkArray n v).size) :
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(mkArray n v)[i] = v := by simp [Array.getElem_eq_getElem_toList]
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(mkArray n v)[i] = v := by simp [← getElem_toList]
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theorem getElem?_mkArray (n : Nat) (v : α) (i : Nat) :
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(mkArray n v)[i]? = if i < n then some v else none := by
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@@ -927,10 +947,10 @@ theorem getElem?_size_le (a : Array α) (i : Nat) (h : a.size ≤ i) : a[i]? = n
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@[deprecated getElem?_size_le (since := "2024-10-21")] abbrev get?_len_le := @getElem?_size_le
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theorem getElem_mem_toList (a : Array α) (h : i < a.size) : a[i] ∈ a.toList := by
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simp only [getElem_eq_getElem_toList, List.getElem_mem]
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simp only [← getElem_toList, List.getElem_mem]
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theorem get?_eq_get?_toList (a : Array α) (i : Nat) : a.get? i = a.toList.get? i := by
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simp [getElem?_eq_getElem?_toList]
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simp [← getElem?_toList]
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theorem get!_eq_get? [Inhabited α] (a : Array α) : a.get! n = (a.get? n).getD default := by
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simp only [get!_eq_getElem?, get?_eq_getElem?]
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@@ -939,7 +959,7 @@ theorem back!_eq_back? [Inhabited α] (a : Array α) : a.back! = a.back?.getD de
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simp only [back!, get!_eq_getElem?, get?_eq_getElem?, back?]
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@[simp] theorem back?_push (a : Array α) : (a.push x).back? = some x := by
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simp [back?, getElem?_eq_getElem?_toList]
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simp [back?, ← getElem?_toList]
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@[simp] theorem back!_push [Inhabited α] (a : Array α) : (a.push x).back! = x := by
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simp [back!_eq_back?]
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@@ -959,21 +979,6 @@ theorem getElem?_push_eq (a : Array α) (x : α) : (a.push x)[a.size]? = some x
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@[deprecated getElem?_push_eq (since := "2024-10-21")] abbrev get?_push_eq := @getElem?_push_eq
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theorem getElem?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some x else a[i]? := by
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match Nat.lt_trichotomy i a.size with
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| Or.inl g =>
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have h1 : i < a.size + 1 := by omega
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have h2 : i ≠ a.size := by omega
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simp [getElem?_def, size_push, g, h1, h2, getElem_push_lt]
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| Or.inr (Or.inl heq) =>
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simp [heq, getElem?_pos, getElem_push_eq]
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| Or.inr (Or.inr g) =>
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simp only [getElem?_def, size_push]
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have h1 : ¬ (i < a.size) := by omega
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have h2 : ¬ (i < a.size + 1) := by omega
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have h3 : i ≠ a.size := by omega
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simp [h1, h2, h3]
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@[deprecated getElem?_push (since := "2024-10-21")] abbrev get?_push := @getElem?_push
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@[simp] theorem getElem?_size {a : Array α} : a[a.size]? = none := by
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@@ -985,7 +990,7 @@ theorem getElem?_push {a : Array α} : (a.push x)[i]? = if i = a.size then some
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theorem get_set_eq (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
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(a.set i v h)[i]'(by simp [h]) = v := by
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simp only [set, getElem_eq_getElem_toList, List.getElem_set_self]
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simp only [set, ← getElem_toList, List.getElem_set_self]
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theorem get?_set_eq (a : Array α) (i : Nat) (v : α) (h : i < a.size) :
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(a.set i v)[i]? = v := by simp [getElem?_pos, h]
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@@ -1004,7 +1009,7 @@ theorem get_set (a : Array α) (i : Nat) (hi : i < a.size) (j : Nat) (hj : j < a
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@[simp] theorem get_set_ne (a : Array α) (i : Nat) (hi : i < a.size) {j : Nat} (v : α) (hj : j < a.size)
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(h : i ≠ j) : (a.set i v)[j]'(by simp [*]) = a[j] := by
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simp only [set, getElem_eq_getElem_toList, List.getElem_set_ne h]
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simp only [set, ← getElem_toList, List.getElem_set_ne h]
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theorem set_set (a : Array α) (i : Nat) (h) (v v' : α) :
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(a.set i v h).set i v' (by simp [h]) = a.set i v' := by simp [set, List.set_set]
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@@ -1090,23 +1095,23 @@ theorem size_eq_length_toList (as : Array α) : as.size = as.toList.length := rf
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@[simp]
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theorem getElem_range {n : Nat} {x : Nat} (h : x < (Array.range n).size) : (Array.range n)[x] = x := by
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simp [getElem_eq_getElem_toList]
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simp [← getElem_toList]
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@[simp] theorem toList_reverse (a : Array α) : a.reverse.toList = a.toList.reverse := by
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let rec go (as : Array α) (i j hj)
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(h : i + j + 1 = a.size) (h₂ : as.size = a.size)
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(H : ∀ k, as.toList[k]? = if i ≤ k ∧ k ≤ j then a.toList[k]? else a.toList.reverse[k]?)
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(k : Nat) : (reverse.loop as i ⟨j, hj⟩).toList[k]? = a.toList.reverse[k]? := by
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rw [reverse.loop]; dsimp; split <;> rename_i h₁
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rw [reverse.loop]; dsimp only; split <;> rename_i h₁
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· match j with | j+1 => ?_
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simp only [Nat.add_sub_cancel]
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rw [(go · (i+1) j)]
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· rwa [Nat.add_right_comm i]
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· simp [size_swap, h₂]
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· intro k
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rw [← getElem?_eq_getElem?_toList, getElem?_swap]
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simp only [H, getElem_eq_getElem_toList, ← List.getElem?_eq_getElem, Nat.le_of_lt h₁,
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getElem?_eq_getElem?_toList]
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rw [getElem?_toList, getElem?_swap]
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simp only [H, ← getElem_toList, ← List.getElem?_eq_getElem, Nat.le_of_lt h₁,
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← getElem?_toList]
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split <;> rename_i h₂
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· simp only [← h₂, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, and_false]
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exact (List.getElem?_reverse' (j+1) i (Eq.trans (by simp_arith) h)).symm
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@@ -1533,7 +1538,7 @@ theorem getElem_append {as bs : Array α} (h : i < (as ++ bs).size) :
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theorem getElem_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt : i < as.size) :
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(as ++ bs)[i] = as[i] := by
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simp only [getElem_eq_getElem_toList]
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simp only [← getElem_toList]
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have h' : i < (as.toList ++ bs.toList).length := by rwa [← length_toList, toList_append] at h
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conv => rhs; rw [← List.getElem_append_left (bs := bs.toList) (h' := h')]
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apply List.get_of_eq; rw [toList_append]
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@@ -1541,7 +1546,7 @@ theorem getElem_append_left {as bs : Array α} {h : i < (as ++ bs).size} (hlt :
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theorem getElem_append_right {as bs : Array α} {h : i < (as ++ bs).size} (hle : as.size ≤ i)
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(hlt : i - as.size < bs.size := Nat.sub_lt_left_of_lt_add hle (size_append .. ▸ h)) :
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(as ++ bs)[i] = bs[i - as.size] := by
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simp only [getElem_eq_getElem_toList]
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simp only [← getElem_toList]
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have h' : i < (as.toList ++ bs.toList).length := by rwa [← length_toList, toList_append] at h
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conv => rhs; rw [← List.getElem_append_right (h₁ := hle) (h₂ := h')]
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apply List.get_of_eq; rw [toList_append]
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@@ -1853,9 +1858,9 @@ theorem all_toList {p : α → Bool} (as : Array α) : as.toList.all p = as.all
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rw [Bool.eq_iff_iff, all_eq_true, List.all_eq_true]; simp only [List.mem_iff_getElem]
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constructor
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· intro w i
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exact w as[i] ⟨i, i.2, (getElem_eq_getElem_toList i.2).symm⟩
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exact w as[i] ⟨i, i.2, getElem_toList i.2⟩
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· rintro w x ⟨r, h, rfl⟩
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rw [← getElem_eq_getElem_toList]
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rw [getElem_toList]
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exact w ⟨r, h⟩
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theorem all_eq_true_iff_forall_mem {l : Array α} : l.all p ↔ ∀ x, x ∈ l → p x := by
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@@ -2018,11 +2023,6 @@ Our goal is to have `simp` "pull `List.toArray` outwards" as much as possible.
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apply ext'
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simp
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@[simp] theorem set_toArray (l : List α) (i : Fin l.toArray.size) (a : α) :
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l.toArray.set i a = (l.set i a).toArray := by
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apply ext'
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simp
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@[simp] theorem uset_toArray (l : List α) (i : USize) (a : α) (h : i.toNat < l.toArray.size) :
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l.toArray.uset i a h = (l.set i.toNat a).toArray := by
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apply ext'
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@@ -2355,15 +2355,6 @@ end Array
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namespace List
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@[deprecated toArray_toList (since := "2024-09-09")]
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abbrev toArray_data := @toArray_toList
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@[deprecated "Use the reverse direction of `List.push_toArray`." (since := "2024-09-27")]
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theorem toArray_concat {as : List α} {x : α} :
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(as ++ [x]).toArray = as.toArray.push x := by
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apply ext'
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simp
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@[deprecated back!_toArray (since := "2024-10-31")] abbrev back_toArray := @back!_toArray
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@[deprecated setIfInBounds_toArray (since := "2024-11-24")] abbrev setD_toArray := @setIfInBounds_toArray
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@@ -2372,141 +2363,29 @@ end List
|
||||
|
||||
namespace Array
|
||||
|
||||
@[deprecated getElem_eq_getElem_toList (since := "2024-09-25")]
|
||||
abbrev getElem_eq_toList_getElem := @getElem_eq_getElem_toList
|
||||
|
||||
@[deprecated getElem_eq_toList_getElem (since := "2024-09-09")]
|
||||
abbrev getElem_eq_data_getElem := @getElem_eq_getElem_toList
|
||||
|
||||
@[deprecated getElem_eq_toList_getElem (since := "2024-06-12")]
|
||||
theorem getElem_eq_toList_get (a : Array α) (h : i < a.size) : a[i] = a.toList.get ⟨i, h⟩ := by
|
||||
simp
|
||||
|
||||
@[deprecated toArray_toList (since := "2024-09-09")]
|
||||
abbrev toArray_data := @toArray_toList
|
||||
|
||||
@[deprecated length_toList (since := "2024-09-09")]
|
||||
abbrev data_length := @length_toList
|
||||
|
||||
@[deprecated toList_map (since := "2024-09-09")]
|
||||
abbrev map_data := @toList_map
|
||||
|
||||
@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
|
||||
abbrev foldl_toList_eq_bind := @foldl_toList_eq_flatMap
|
||||
|
||||
@[deprecated foldl_toList_eq_flatMap (since := "2024-10-16")]
|
||||
abbrev foldl_data_eq_bind := @foldl_toList_eq_flatMap
|
||||
|
||||
@[deprecated foldl_toList_eq_map (since := "2024-09-09")]
|
||||
abbrev foldl_data_eq_map := @foldl_toList_eq_map
|
||||
|
||||
@[deprecated toList_mkArray (since := "2024-09-09")]
|
||||
abbrev mkArray_data := @toList_mkArray
|
||||
|
||||
@[deprecated mem_toList (since := "2024-09-09")]
|
||||
abbrev mem_data := @mem_toList
|
||||
|
||||
@[deprecated getElem_mem (since := "2024-10-17")]
|
||||
abbrev getElem?_mem := @getElem_mem
|
||||
|
||||
@[deprecated getElem_fin_eq_getElem_toList (since := "2024-10-17")]
|
||||
abbrev getElem_fin_eq_toList_get := @getElem_fin_eq_getElem_toList
|
||||
|
||||
@[deprecated getElem_fin_eq_getElem_toList (since := "2024-09-09")]
|
||||
abbrev getElem_fin_eq_data_get := @getElem_fin_eq_getElem_toList
|
||||
|
||||
@[deprecated getElem_mem_toList (since := "2024-09-09")]
|
||||
abbrev getElem_mem_data := @getElem_mem_toList
|
||||
|
||||
@[deprecated getElem?_eq_getElem?_toList (since := "2024-10-17")]
|
||||
abbrev getElem?_eq_toList_getElem? := @getElem?_eq_getElem?_toList
|
||||
|
||||
@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-30")]
|
||||
theorem getElem?_eq_toList_get? (a : Array α) (i : Nat) : a[i]? = a.toList.get? i := by
|
||||
by_cases i < a.size <;> simp_all [getElem?_pos, getElem?_neg, List.get?_eq_get, eq_comm]
|
||||
|
||||
set_option linter.deprecated false in
|
||||
@[deprecated getElem?_eq_toList_getElem? (since := "2024-09-09")]
|
||||
abbrev getElem?_eq_data_get? := @getElem?_eq_toList_get?
|
||||
@[deprecated "Use reverse direction of `getElem?_toList`" (since := "2024-10-17")]
|
||||
abbrev getElem?_eq_toList_getElem? := @getElem?_toList
|
||||
|
||||
@[deprecated get?_eq_get?_toList (since := "2024-10-17")]
|
||||
abbrev get?_eq_toList_get? := @get?_eq_get?_toList
|
||||
|
||||
@[deprecated get?_eq_toList_get? (since := "2024-09-09")]
|
||||
abbrev get?_eq_data_get? := @get?_eq_get?_toList
|
||||
|
||||
@[deprecated toList_set (since := "2024-09-09")]
|
||||
abbrev data_set := @toList_set
|
||||
|
||||
@[deprecated toList_swap (since := "2024-09-09")]
|
||||
abbrev data_swap := @toList_swap
|
||||
|
||||
@[deprecated getElem?_swap (since := "2024-10-17")] abbrev get?_swap := @getElem?_swap
|
||||
|
||||
@[deprecated toList_pop (since := "2024-09-09")] abbrev data_pop := @toList_pop
|
||||
|
||||
@[deprecated size_eq_length_toList (since := "2024-09-09")]
|
||||
abbrev size_eq_length_data := @size_eq_length_toList
|
||||
|
||||
@[deprecated toList_range (since := "2024-09-09")]
|
||||
abbrev data_range := @toList_range
|
||||
|
||||
@[deprecated toList_reverse (since := "2024-09-30")]
|
||||
abbrev reverse_toList := @toList_reverse
|
||||
|
||||
@[deprecated mapM_eq_mapM_toList (since := "2024-09-09")]
|
||||
abbrev mapM_eq_mapM_data := @mapM_eq_mapM_toList
|
||||
|
||||
@[deprecated getElem_modify (since := "2024-08-08")]
|
||||
theorem get_modify {arr : Array α} {x i} (h : i < (arr.modify x f).size) :
|
||||
(arr.modify x f).get i h =
|
||||
if x = i then f (arr.get i (by simpa using h)) else arr.get i (by simpa using h) := by
|
||||
simp [getElem_modify h]
|
||||
|
||||
@[deprecated toList_filter (since := "2024-09-09")]
|
||||
abbrev filter_data := @toList_filter
|
||||
|
||||
@[deprecated toList_filterMap (since := "2024-09-09")]
|
||||
abbrev filterMap_data := @toList_filterMap
|
||||
|
||||
@[deprecated toList_empty (since := "2024-09-09")]
|
||||
abbrev empty_data := @toList_empty
|
||||
|
||||
@[deprecated getElem_append_left (since := "2024-09-30")]
|
||||
abbrev get_append_left := @getElem_append_left
|
||||
|
||||
@[deprecated getElem_append_right (since := "2024-09-30")]
|
||||
abbrev get_append_right := @getElem_append_right
|
||||
|
||||
@[deprecated "Use the reverse direction of `Array.any_toList`" (since := "2024-09-30")]
|
||||
abbrev any_def := @any_toList
|
||||
|
||||
@[deprecated "Use the reverse direction of `Array.all_toList`" (since := "2024-09-30")]
|
||||
abbrev all_def := @all_toList
|
||||
|
||||
@[deprecated getElem_extract_loop_lt_aux (since := "2024-09-30")]
|
||||
abbrev get_extract_loop_lt_aux := @getElem_extract_loop_lt_aux
|
||||
@[deprecated getElem_extract_loop_lt (since := "2024-09-30")]
|
||||
abbrev get_extract_loop_lt := @getElem_extract_loop_lt
|
||||
@[deprecated getElem_extract_loop_ge_aux (since := "2024-09-30")]
|
||||
abbrev get_extract_loop_ge_aux := @getElem_extract_loop_ge_aux
|
||||
@[deprecated getElem_extract_loop_ge (since := "2024-09-30")]
|
||||
abbrev get_extract_loop_ge := @getElem_extract_loop_ge
|
||||
@[deprecated getElem_extract_aux (since := "2024-09-30")]
|
||||
abbrev get_extract_aux := @getElem_extract_aux
|
||||
@[deprecated getElem_extract (since := "2024-09-30")]
|
||||
abbrev get_extract := @getElem_extract
|
||||
|
||||
@[deprecated getElem_swap_right (since := "2024-09-30")]
|
||||
abbrev get_swap_right := @getElem_swap_right
|
||||
@[deprecated getElem_swap_left (since := "2024-09-30")]
|
||||
abbrev get_swap_left := @getElem_swap_left
|
||||
@[deprecated getElem_swap_of_ne (since := "2024-09-30")]
|
||||
abbrev get_swap_of_ne := @getElem_swap_of_ne
|
||||
@[deprecated getElem_swap (since := "2024-09-30")]
|
||||
abbrev get_swap := @getElem_swap
|
||||
@[deprecated getElem_swap' (since := "2024-09-30")]
|
||||
abbrev get_swap' := @getElem_swap'
|
||||
@[deprecated getElem_push (since := "2024-10-21")] abbrev get_push := @getElem_push
|
||||
@[deprecated getElem_push_lt (since := "2024-10-21")] abbrev get_push_lt := @getElem_push_lt
|
||||
@[deprecated getElem_push_eq (since := "2024-10-21")] abbrev get_push_eq := @getElem_push_eq
|
||||
|
||||
@[deprecated back!_eq_back? (since := "2024-10-31")] abbrev back_eq_back? := @back!_eq_back?
|
||||
@[deprecated back!_push (since := "2024-10-31")] abbrev back_push := @back!_push
|
||||
@@ -2520,4 +2399,20 @@ abbrev eq_push_pop_back_of_size_ne_zero := @eq_push_pop_back!_of_size_ne_zero
|
||||
@[deprecated getD_get?_setIfInBounds (since := "2024-11-24")] abbrev getD_setD := @getD_get?_setIfInBounds
|
||||
@[deprecated getElem_setIfInBounds (since := "2024-11-24")] abbrev getElem_setD := @getElem_setIfInBounds
|
||||
|
||||
@[deprecated List.getElem_toArray (since := "2024-11-29")]
|
||||
theorem getElem_mk {xs : List α} {i : Nat} (h : i < xs.length) : (Array.mk xs)[i] = xs[i] := rfl
|
||||
|
||||
@[deprecated Array.getElem_toList (since := "2024-12-08")]
|
||||
theorem getElem_eq_getElem_toList {a : Array α} (h : i < a.size) : a[i] = a.toList[i] := rfl
|
||||
|
||||
@[deprecated Array.getElem?_toList (since := "2024-12-08")]
|
||||
theorem getElem?_eq_getElem?_toList (a : Array α) (i : Nat) : a[i]? = a.toList[i]? := by
|
||||
rw [getElem?_def]
|
||||
split <;> simp_all
|
||||
|
||||
@[deprecated LawfulGetElem.getElem?_def (since := "2024-12-08")]
|
||||
theorem getElem?_eq {a : Array α} {i : Nat} :
|
||||
a[i]? = if h : i < a.size then some a[i] else none := by
|
||||
rw [getElem?_def]
|
||||
|
||||
end Array
|
||||
|
||||
@@ -12,7 +12,7 @@ namespace Array
|
||||
theorem exists_of_uset (self : Array α) (i d h) :
|
||||
∃ l₁ l₂, self.toList = l₁ ++ self[i] :: l₂ ∧ List.length l₁ = i.toNat ∧
|
||||
(self.uset i d h).toList = l₁ ++ d :: l₂ := by
|
||||
simpa only [ugetElem_eq_getElem, getElem_eq_getElem_toList, uset, toList_set] using
|
||||
simpa only [ugetElem_eq_getElem, ← getElem_toList, uset, toList_set] using
|
||||
List.exists_of_set _
|
||||
|
||||
end Array
|
||||
|
||||
@@ -220,15 +220,6 @@ We simplify `l[n]!` to `(l[n]?).getD default`.
|
||||
|
||||
/-! ### getElem? and getElem -/
|
||||
|
||||
@[simp] theorem getElem?_eq_getElem {l : List α} {n} (h : n < l.length) : l[n]? = some l[n] := by
|
||||
simp only [getElem?_def, h, ↓reduceDIte]
|
||||
|
||||
theorem getElem?_eq_some_iff {l : List α} : l[n]? = some a ↔ ∃ h : n < l.length, l[n] = a := by
|
||||
simp only [← get?_eq_getElem?, get?_eq_some_iff, get_eq_getElem]
|
||||
|
||||
theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? ↔ ∃ h : n < l.length, l[n] = a := by
|
||||
rw [eq_comm, getElem?_eq_some_iff]
|
||||
|
||||
@[simp] theorem getElem?_eq_none_iff : l[n]? = none ↔ length l ≤ n := by
|
||||
simp only [← get?_eq_getElem?, get?_eq_none_iff]
|
||||
|
||||
@@ -237,11 +228,20 @@ theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? ↔ ∃ h : n < l.le
|
||||
|
||||
theorem getElem?_eq_none (h : length l ≤ n) : l[n]? = none := getElem?_eq_none_iff.mpr h
|
||||
|
||||
@[simp] theorem some_getElem_eq_getElem?_iff {α} (xs : List α) (i : Nat) (h : i < xs.length) :
|
||||
@[simp] theorem getElem?_eq_getElem {l : List α} {n} (h : n < l.length) : l[n]? = some l[n] :=
|
||||
getElem?_pos ..
|
||||
|
||||
theorem getElem?_eq_some_iff {l : List α} : l[n]? = some a ↔ ∃ h : n < l.length, l[n] = a := by
|
||||
simp only [← get?_eq_getElem?, get?_eq_some_iff, get_eq_getElem]
|
||||
|
||||
theorem some_eq_getElem?_iff {l : List α} : some a = l[n]? ↔ ∃ h : n < l.length, l[n] = a := by
|
||||
rw [eq_comm, getElem?_eq_some_iff]
|
||||
|
||||
@[simp] theorem some_getElem_eq_getElem?_iff (xs : List α) (i : Nat) (h : i < xs.length) :
|
||||
(some xs[i] = xs[i]?) ↔ True := by
|
||||
simp [h]
|
||||
|
||||
@[simp] theorem getElem?_eq_some_getElem_iff {α} (xs : List α) (i : Nat) (h : i < xs.length) :
|
||||
@[simp] theorem getElem?_eq_some_getElem_iff (xs : List α) (i : Nat) (h : i < xs.length) :
|
||||
(xs[i]? = some xs[i]) ↔ True := by
|
||||
simp [h]
|
||||
|
||||
@@ -253,6 +253,12 @@ theorem getElem_eq_getElem?_get (l : List α) (i : Nat) (h : i < l.length) :
|
||||
l[i] = l[i]?.get (by simp [getElem?_eq_getElem, h]) := by
|
||||
simp [getElem_eq_iff]
|
||||
|
||||
theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
|
||||
simp
|
||||
|
||||
theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
|
||||
simp
|
||||
|
||||
@[simp] theorem getElem?_nil {n : Nat} : ([] : List α)[n]? = none := rfl
|
||||
|
||||
theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
|
||||
@@ -264,6 +270,13 @@ theorem getElem?_cons_zero {l : List α} : (a::l)[0]? = some a := by simp
|
||||
theorem getElem?_cons : (a :: l)[i]? = if i = 0 then some a else l[i-1]? := by
|
||||
cases i <;> simp
|
||||
|
||||
@[simp] theorem getElem_singleton (a : α) (h : i < 1) : [a][i] = a :=
|
||||
match i, h with
|
||||
| 0, _ => rfl
|
||||
|
||||
theorem getElem?_singleton (a : α) (i : Nat) : [a][i]? = if i = 0 then some a else none := by
|
||||
simp [getElem?_cons]
|
||||
|
||||
/--
|
||||
If one has `l[i]` in an expression and `h : l = l'`,
|
||||
`rw [h]` will give a "motive it not type correct" error, as it cannot rewrite the
|
||||
@@ -273,10 +286,6 @@ such a rewrite, with `rw [getElem_of_eq h]`.
|
||||
theorem getElem_of_eq {l l' : List α} (h : l = l') {i : Nat} (w : i < l.length) :
|
||||
l[i] = l'[i]'(h ▸ w) := by cases h; rfl
|
||||
|
||||
@[simp] theorem getElem_singleton (a : α) (h : i < 1) : [a][i] = a :=
|
||||
match i, h with
|
||||
| 0, _ => rfl
|
||||
|
||||
theorem getElem_zero {l : List α} (h : 0 < l.length) : l[0] = l.head (length_pos.mp h) :=
|
||||
match l, h with
|
||||
| _ :: _, _ => rfl
|
||||
@@ -300,12 +309,6 @@ theorem ext_getElem {l₁ l₂ : List α} (hl : length l₁ = length l₂)
|
||||
theorem getElem?_concat_length (l : List α) (a : α) : (l ++ [a])[l.length]? = some a := by
|
||||
simp
|
||||
|
||||
theorem isSome_getElem? {l : List α} {n : Nat} : l[n]?.isSome ↔ n < l.length := by
|
||||
simp
|
||||
|
||||
theorem isNone_getElem? {l : List α} {n : Nat} : l[n]?.isNone ↔ l.length ≤ n := by
|
||||
simp
|
||||
|
||||
/-! ### mem -/
|
||||
|
||||
@[simp] theorem not_mem_nil (a : α) : ¬ a ∈ [] := nofun
|
||||
|
||||
@@ -237,15 +237,15 @@ theorem getElem?_mapIdx_go : ∀ {l : List α} {arr : Array β} {i : Nat},
|
||||
if h : i < arr.size then some arr[i] else Option.map (f i) l[i - arr.size]?
|
||||
| [], arr, i => by
|
||||
simp only [mapIdx.go, Array.toListImpl_eq, getElem?_def, Array.length_toList,
|
||||
Array.getElem_eq_getElem_toList, length_nil, Nat.not_lt_zero, ↓reduceDIte, Option.map_none']
|
||||
← Array.getElem_toList, length_nil, Nat.not_lt_zero, ↓reduceDIte, Option.map_none']
|
||||
| a :: l, arr, i => by
|
||||
rw [mapIdx.go, getElem?_mapIdx_go]
|
||||
simp only [Array.size_push]
|
||||
split <;> split
|
||||
· simp only [Option.some.injEq]
|
||||
rw [Array.getElem_eq_getElem_toList]
|
||||
rw [← Array.getElem_toList]
|
||||
simp only [Array.push_toList]
|
||||
rw [getElem_append_left, Array.getElem_eq_getElem_toList]
|
||||
rw [getElem_append_left, ← Array.getElem_toList]
|
||||
· have : i = arr.size := by omega
|
||||
simp_all
|
||||
· omega
|
||||
|
||||
@@ -118,12 +118,16 @@ instance (priority := low) [GetElem coll idx elem valid] [∀ xs i, Decidable (v
|
||||
GetElem? coll idx elem valid where
|
||||
getElem? xs i := decidableGetElem? xs i
|
||||
|
||||
theorem getElem_congr_coll [GetElem coll idx elem valid] {c d : coll} {i : idx} {h : valid c i}
|
||||
(h' : c = d) : c[i] = d[i]'(h' ▸ h) := by
|
||||
cases h'; rfl
|
||||
theorem getElem_congr [GetElem coll idx elem valid] {c d : coll} (h : c = d)
|
||||
{i j : idx} (h' : i = j) (w : valid c i) : c[i] = d[j]'(h' ▸ h ▸ w) := by
|
||||
cases h; cases h'; rfl
|
||||
|
||||
theorem getElem_congr [GetElem coll idx elem valid] {c : coll} {i j : idx} {h : valid c i}
|
||||
(h' : i = j) : c[i] = c[j]'(h' ▸ h) := by
|
||||
theorem getElem_congr_coll [GetElem coll idx elem valid] {c d : coll} {i : idx} {w : valid c i}
|
||||
(h : c = d) : c[i] = d[i]'(h ▸ w) := by
|
||||
cases h; rfl
|
||||
|
||||
theorem getElem_congr_idx [GetElem coll idx elem valid] {c : coll} {i j : idx} {w : valid c i}
|
||||
(h' : i = j) : c[i] = c[j]'(h' ▸ w) := by
|
||||
cases h'; rfl
|
||||
|
||||
class LawfulGetElem (cont : Type u) (idx : Type v) (elem : outParam (Type w))
|
||||
@@ -216,13 +220,9 @@ instance : GetElem (List α) Nat α fun as i => i < as.length where
|
||||
@[simp] theorem getElem_cons_zero (a : α) (as : List α) (h : 0 < (a :: as).length) : getElem (a :: as) 0 h = a := by
|
||||
rfl
|
||||
|
||||
@[deprecated getElem_cons_zero (since := "2024-06-12")] abbrev cons_getElem_zero := @getElem_cons_zero
|
||||
|
||||
@[simp] theorem getElem_cons_succ (a : α) (as : List α) (i : Nat) (h : i + 1 < (a :: as).length) : getElem (a :: as) (i+1) h = getElem as i (Nat.lt_of_succ_lt_succ h) := by
|
||||
rfl
|
||||
|
||||
@[deprecated getElem_cons_succ (since := "2024-06-12")] abbrev cons_getElem_succ := @getElem_cons_succ
|
||||
|
||||
@[simp] theorem getElem_mem : ∀ {l : List α} {n} (h : n < l.length), l[n]'h ∈ l
|
||||
| _ :: _, 0, _ => .head ..
|
||||
| _ :: l, _+1, _ => .tail _ (getElem_mem (l := l) ..)
|
||||
|
||||
@@ -216,7 +216,7 @@ theorem expand.go_eq [BEq α] [Hashable α] [PartialEquivBEq α] (source : Array
|
||||
refine ih.trans ?_
|
||||
simp only [Array.get_eq_getElem, AssocList.foldl_eq, Array.toList_set]
|
||||
rw [List.drop_eq_getElem_cons hi, List.flatMap_cons, List.foldl_append,
|
||||
List.drop_set_of_lt _ _ (by omega), Array.getElem_eq_getElem_toList]
|
||||
List.drop_set_of_lt _ _ (by omega), Array.getElem_toList]
|
||||
· next i source target hi =>
|
||||
rw [expand.go_neg hi, List.drop_eq_nil_of_le, flatMap_nil, foldl_nil]
|
||||
rwa [Array.size_eq_length_toList, Nat.not_lt] at hi
|
||||
|
||||
@@ -297,7 +297,7 @@ theorem ofArray_eq (arr : Array (Literal (PosFin n)))
|
||||
dsimp; omega
|
||||
rw [List.getElem?_eq_getElem i_in_bounds, List.getElem?_eq_getElem i_in_bounds']
|
||||
simp only [List.get_eq_getElem, Nat.zero_add] at h
|
||||
rw [← Array.getElem_eq_getElem_toList]
|
||||
rw [Array.getElem_toList]
|
||||
simp [h]
|
||||
· have arr_data_length_le_i : arr.toList.length ≤ i := by
|
||||
dsimp; omega
|
||||
|
||||
@@ -497,7 +497,7 @@ theorem deleteOne_preserves_strongAssignmentsInvariant {n : Nat} (f : DefaultFor
|
||||
conv => rhs; rw [Array.size_mk]
|
||||
exact hbound
|
||||
simp only [getElem!, id_eq_idx, Array.length_toList, idx_in_bounds2, ↓reduceDIte,
|
||||
Fin.eta, Array.get_eq_getElem, Array.getElem_eq_getElem_toList, decidableGetElem?] at heq
|
||||
Fin.eta, Array.get_eq_getElem, ← Array.getElem_toList, decidableGetElem?] at heq
|
||||
rw [hidx, hl] at heq
|
||||
simp only [unit, Option.some.injEq, DefaultClause.mk.injEq, List.cons.injEq, and_true] at heq
|
||||
simp only [← heq] at l_ne_b
|
||||
@@ -530,7 +530,7 @@ theorem deleteOne_preserves_strongAssignmentsInvariant {n : Nat} (f : DefaultFor
|
||||
conv => rhs; rw [Array.size_mk]
|
||||
exact hbound
|
||||
simp only [getElem!, id_eq_idx, Array.length_toList, idx_in_bounds2, ↓reduceDIte,
|
||||
Fin.eta, Array.get_eq_getElem, Array.getElem_eq_getElem_toList, decidableGetElem?] at heq
|
||||
Fin.eta, Array.get_eq_getElem, ← Array.getElem_toList, decidableGetElem?] at heq
|
||||
rw [hidx, hl] at heq
|
||||
simp only [unit, Option.some.injEq, DefaultClause.mk.injEq, List.cons.injEq, and_true] at heq
|
||||
have i_eq_l : i = l.1 := by rw [← heq]
|
||||
@@ -590,7 +590,7 @@ theorem deleteOne_preserves_strongAssignmentsInvariant {n : Nat} (f : DefaultFor
|
||||
conv => rhs; rw [Array.size_mk]
|
||||
exact hbound
|
||||
simp only [getElem!, id_eq_idx, Array.length_toList, idx_in_bounds2, ↓reduceDIte,
|
||||
Fin.eta, Array.get_eq_getElem, Array.getElem_eq_getElem_toList, decidableGetElem?] at heq
|
||||
Fin.eta, Array.get_eq_getElem, ← Array.getElem_toList, decidableGetElem?] at heq
|
||||
rw [hidx] at heq
|
||||
simp only [Option.some.injEq] at heq
|
||||
rw [← heq] at hl
|
||||
|
||||
@@ -461,7 +461,7 @@ theorem existsRatHint_of_ratHintsExhaustive {n : Nat} (f : DefaultFormula n)
|
||||
constructor
|
||||
· rw [← Array.mem_toList]
|
||||
apply Array.getElem_mem_toList
|
||||
· rw [← Array.getElem_eq_getElem_toList] at c'_in_f
|
||||
· rw [Array.getElem_toList] at c'_in_f
|
||||
simp only [getElem!, Array.getElem_range, i_lt_f_clauses_size, dite_true,
|
||||
c'_in_f, DefaultClause.contains_iff, Array.get_eq_getElem, decidableGetElem?]
|
||||
simpa [Clause.toList] using negPivot_in_c'
|
||||
@@ -472,8 +472,8 @@ theorem existsRatHint_of_ratHintsExhaustive {n : Nat} (f : DefaultFormula n)
|
||||
dsimp at *
|
||||
omega
|
||||
simp only [List.get_eq_getElem, Array.toList_map, Array.length_toList, List.getElem_map] at h'
|
||||
rw [← Array.getElem_eq_getElem_toList] at h'
|
||||
rw [← Array.getElem_eq_getElem_toList] at c'_in_f
|
||||
rw [Array.getElem_toList] at h'
|
||||
rw [Array.getElem_toList] at c'_in_f
|
||||
exists ⟨j.1, j_in_bounds⟩
|
||||
simp [getElem!, h', i_lt_f_clauses_size, dite_true, c'_in_f, decidableGetElem?]
|
||||
|
||||
|
||||
@@ -1133,25 +1133,24 @@ theorem nodup_derivedLits {n : Nat} (f : DefaultFormula n)
|
||||
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k
|
||||
simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
|
||||
simp only [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li, li_eq_lj] at h3
|
||||
simp only [List.get_eq_getElem, Array.getElem_eq_getElem_toList, not_true_eq_false] at h3
|
||||
simp only [List.get_eq_getElem, ← Array.getElem_toList, not_true_eq_false] at h3
|
||||
· next k_ne_i =>
|
||||
have i_ne_k : ⟨i.1, i_in_bounds⟩ ≠ k := by intro i_eq_k; simp only [← i_eq_k, not_true] at k_ne_i
|
||||
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k
|
||||
simp +decide [Fin.getElem_fin, derivedLits_arr_def, ne_eq,
|
||||
Array.getElem_eq_getElem_toList, li] at h3
|
||||
simp +decide [Fin.getElem_fin, derivedLits_arr_def, ne_eq, li] at h3
|
||||
· by_cases li.2 = true
|
||||
· next li_eq_true =>
|
||||
have i_ne_k2 : ⟨i.1, i_in_bounds⟩ ≠ k2 := by
|
||||
intro i_eq_k2
|
||||
rw [← i_eq_k2] at k2_eq_false
|
||||
simp only [List.get_eq_getElem] at k2_eq_false
|
||||
simp [derivedLits_arr_def, Array.getElem_eq_getElem_toList, k2_eq_false, li] at li_eq_true
|
||||
simp [derivedLits_arr_def, k2_eq_false, li] at li_eq_true
|
||||
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
|
||||
intro j_eq_k2
|
||||
rw [← j_eq_k2] at k2_eq_false
|
||||
simp only [List.get_eq_getElem] at k2_eq_false
|
||||
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_getElem_toList] at li_eq_lj
|
||||
simp [derivedLits_arr_def, Array.getElem_eq_getElem_toList, k2_eq_false, li_eq_lj, li] at li_eq_true
|
||||
simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
|
||||
simp [derivedLits_arr_def, k2_eq_false, li_eq_lj, li] at li_eq_true
|
||||
by_cases ⟨i.1, i_in_bounds⟩ = k1
|
||||
· next i_eq_k1 =>
|
||||
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
|
||||
@@ -1160,12 +1159,11 @@ theorem nodup_derivedLits {n : Nat} (f : DefaultFormula n)
|
||||
simp only [Fin.mk.injEq] at i_eq_k1
|
||||
exact i_ne_j (Fin.eq_of_val_eq i_eq_k1)
|
||||
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
|
||||
simp [li, li_eq_lj, derivedLits_arr_def, Array.getElem_eq_getElem_toList] at h3
|
||||
simp [li, li_eq_lj, derivedLits_arr_def] at h3
|
||||
· next i_ne_k1 =>
|
||||
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
|
||||
apply h3
|
||||
simp +decide only [Fin.getElem_fin, Array.getElem_eq_getElem_toList,
|
||||
ne_eq, derivedLits_arr_def, li]
|
||||
simp +decide only [Fin.getElem_fin, ne_eq, derivedLits_arr_def, li]
|
||||
rfl
|
||||
· next li_eq_false =>
|
||||
simp only [Bool.not_eq_true] at li_eq_false
|
||||
@@ -1173,13 +1171,13 @@ theorem nodup_derivedLits {n : Nat} (f : DefaultFormula n)
|
||||
intro i_eq_k1
|
||||
rw [← i_eq_k1] at k1_eq_true
|
||||
simp only [List.get_eq_getElem] at k1_eq_true
|
||||
simp [derivedLits_arr_def, Array.getElem_eq_getElem_toList, k1_eq_true, li] at li_eq_false
|
||||
simp [derivedLits_arr_def, k1_eq_true, li] at li_eq_false
|
||||
have j_ne_k1 : ⟨j.1, j_in_bounds⟩ ≠ k1 := by
|
||||
intro j_eq_k1
|
||||
rw [← j_eq_k1] at k1_eq_true
|
||||
simp only [List.get_eq_getElem] at k1_eq_true
|
||||
simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_getElem_toList] at li_eq_lj
|
||||
simp [derivedLits_arr_def, Array.getElem_eq_getElem_toList, k1_eq_true, li_eq_lj, li] at li_eq_false
|
||||
simp only [derivedLits_arr_def, Fin.getElem_fin] at li_eq_lj
|
||||
simp [derivedLits_arr_def, k1_eq_true, li_eq_lj, li] at li_eq_false
|
||||
by_cases ⟨i.1, i_in_bounds⟩ = k2
|
||||
· next i_eq_k2 =>
|
||||
have j_ne_k2 : ⟨j.1, j_in_bounds⟩ ≠ k2 := by
|
||||
@@ -1188,10 +1186,10 @@ theorem nodup_derivedLits {n : Nat} (f : DefaultFormula n)
|
||||
simp only [Fin.mk.injEq] at i_eq_k2
|
||||
exact i_ne_j (Fin.eq_of_val_eq i_eq_k2)
|
||||
specialize h3 ⟨j.1, j_in_bounds⟩ j_ne_k1 j_ne_k2
|
||||
simp [li, li_eq_lj, derivedLits_arr_def, Array.getElem_eq_getElem_toList] at h3
|
||||
simp [li, li_eq_lj, derivedLits_arr_def] at h3
|
||||
· next i_ne_k2 =>
|
||||
specialize h3 ⟨i.1, i_in_bounds⟩ i_ne_k1 i_ne_k2
|
||||
simp +decide [Array.getElem_eq_getElem_toList, derivedLits_arr_def, li] at h3
|
||||
simp +decide [derivedLits_arr_def, li] at h3
|
||||
|
||||
theorem restoreAssignments_performRupCheck_base_case {n : Nat} (f : DefaultFormula n)
|
||||
(f_assignments_size : f.assignments.size = n)
|
||||
@@ -1225,7 +1223,7 @@ theorem restoreAssignments_performRupCheck_base_case {n : Nat} (f : DefaultFormu
|
||||
constructor
|
||||
· apply Nat.zero_le
|
||||
· constructor
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_getElem_toList, ← j_eq_i]
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, ← j_eq_i]
|
||||
rfl
|
||||
· apply And.intro h1 ∘ And.intro h2
|
||||
intro k _ k_ne_j
|
||||
@@ -1237,7 +1235,7 @@ theorem restoreAssignments_performRupCheck_base_case {n : Nat} (f : DefaultFormu
|
||||
apply Fin.ne_of_val_ne
|
||||
simp only
|
||||
exact Fin.val_ne_of_ne k_ne_j
|
||||
simp only [Fin.getElem_fin, Array.getElem_eq_getElem_toList, ne_eq, derivedLits_arr_def]
|
||||
simp only [Fin.getElem_fin, ne_eq, derivedLits_arr_def]
|
||||
exact h3 ⟨k.1, k_in_bounds⟩ k_ne_j
|
||||
· apply Or.inr ∘ Or.inr
|
||||
have j1_lt_derivedLits_arr_size : j1.1 < derivedLits_arr.size := by
|
||||
@@ -1251,11 +1249,11 @@ theorem restoreAssignments_performRupCheck_base_case {n : Nat} (f : DefaultFormu
|
||||
⟨j2.1, j2_lt_derivedLits_arr_size⟩,
|
||||
i_gt_zero, Nat.zero_le j1.1, Nat.zero_le j2.1, ?_⟩
|
||||
constructor
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_getElem_toList, ← j1_eq_i]
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, ← j1_eq_i]
|
||||
rw [← j1_eq_true]
|
||||
rfl
|
||||
· constructor
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, Array.getElem_eq_getElem_toList, ← j2_eq_i]
|
||||
· simp only [derivedLits_arr_def, Fin.getElem_fin, ← j2_eq_i]
|
||||
rw [← j2_eq_false]
|
||||
rfl
|
||||
· apply And.intro h1 ∘ And.intro h2
|
||||
@@ -1272,7 +1270,7 @@ theorem restoreAssignments_performRupCheck_base_case {n : Nat} (f : DefaultFormu
|
||||
apply Fin.ne_of_val_ne
|
||||
simp only
|
||||
exact Fin.val_ne_of_ne k_ne_j2
|
||||
simp only [Fin.getElem_fin, Array.getElem_eq_getElem_toList, ne_eq, derivedLits_arr_def]
|
||||
simp only [Fin.getElem_fin, ne_eq, derivedLits_arr_def]
|
||||
exact h3 ⟨k.1, k_in_bounds⟩ k_ne_j1 k_ne_j2
|
||||
|
||||
theorem restoreAssignments_performRupCheck {n : Nat} (f : DefaultFormula n) (f_assignments_size : f.assignments.size = n)
|
||||
|
||||
Reference in New Issue
Block a user