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sg/mvcgen-
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eba487b7c2 | ||
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e2b500b204 |
@@ -622,12 +622,12 @@ theorem findIdx?_eq_some_le_of_findIdx?_eq_some {xs : Array α} {p q : α → Bo
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/-! ### findFinIdx? -/
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@[grind =]
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theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp
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theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p #[] = none := by simp; rfl
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@[grind =]
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theorem findFinIdx?_singleton {a : α} {p : α → Bool} :
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#[a].findFinIdx? p = if p a then some ⟨0, by simp⟩ else none := by
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simp
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simp; rfl
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-- We can't mark this as a `@[congr]` lemma since the head of the RHS is not `findFinIdx?`.
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theorem findFinIdx?_congr {p : α → Bool} {xs ys : Array α} (w : xs = ys) :
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@@ -801,7 +801,7 @@ theorem idxOf?_eq_map_finIdxOf?_val [BEq α] {xs : Array α} {a : α} :
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xs.idxOf? a = (xs.finIdxOf? a).map (·.val) := by
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simp [idxOf?, finIdxOf?]
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@[grind =] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp
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@[grind =] theorem finIdxOf?_empty [BEq α] : (#[] : Array α).finIdxOf? a = none := by simp; rfl
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@[simp, grind =] theorem finIdxOf?_eq_none_iff [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
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xs.finIdxOf? a = none ↔ a ∉ xs := by
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@@ -1050,7 +1050,7 @@ theorem findFinIdx?_append {xs ys : List α} {p : α → Bool} :
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@[simp, grind =] theorem findFinIdx?_singleton {a : α} {p : α → Bool} :
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[a].findFinIdx? p = if p a then some ⟨0, by simp⟩ else none := by
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simp [findFinIdx?_cons, findFinIdx?_nil]
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simp [findFinIdx?_cons, findFinIdx?_nil]; rfl
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@[simp, grind =] theorem findFinIdx?_eq_none_iff {l : List α} {p : α → Bool} :
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l.findFinIdx? p = none ↔ ∀ x ∈ l, ¬ p x := by
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@@ -311,7 +311,7 @@ theorem drop_length_cons {l : List α} (h : l ≠ []) (a : α) :
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| nil =>
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cases h rfl
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| cons y l ih =>
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simp only [drop]
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simp only [drop, length]
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by_cases h₁ : l = []
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· simp [h₁]
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rw [getLast_cons h₁]
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@@ -182,6 +182,7 @@ private theorem mergeSortTR_run_eq_mergeSort : {n : Nat} → (l : { l : List α
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simp only [mergeSortTR.run, mergeSortTR.run, mergeSort]
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rw [merge_eq_mergeTR]
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rw [mergeSortTR_run_eq_mergeSort, mergeSortTR_run_eq_mergeSort]
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rfl
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-- We don't make this a `@[csimp]` lemma because `mergeSort_eq_mergeSortTR₂` is faster.
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theorem mergeSort_eq_mergeSortTR : @mergeSort = @mergeSortTR := by
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@@ -303,12 +303,12 @@ theorem find?_eq_some_iff_getElem {xs : Vector α n} {p : α → Bool} {b : α}
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/-! ### findFinIdx? -/
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@[grind =]
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theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p (#v[] : Vector α 0) = none := by simp
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theorem findFinIdx?_empty {p : α → Bool} : findFinIdx? p (#v[] : Vector α 0) = none := by simp; rfl
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@[grind =]
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theorem findFinIdx?_singleton {a : α} {p : α → Bool} :
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#[a].findFinIdx? p = if p a then some ⟨0, by simp⟩ else none := by
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simp
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simp; rfl
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@[congr] theorem findFinIdx?_congr {p : α → Bool} {xs : Vector α n} {ys : Vector α n} (w : xs = ys) :
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findFinIdx? p xs = findFinIdx? p ys := by
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@@ -53,7 +53,7 @@ theorem mapM_pure [Monad m] [LawfulMonad m] {xs : Vector α n} (f : α → β) :
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(mk #[] rfl).mapM f = pure #v[] := by
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unfold mapM
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unfold mapM.go
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simp
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simp; rfl
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@[simp, grind =] theorem mapM_append [Monad m] [LawfulMonad m]
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{f : α → m β} {xs : Vector α n} {ys : Vector α n'} :
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@@ -3004,7 +3004,7 @@ Examples:
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* `([] : List String).length = 0`
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* `["green", "brown"].length = 2`
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-/
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@[implicit_reducible] def List.length : List α → Nat
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def List.length : List α → Nat
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| nil => 0
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| cons _ as => HAdd.hAdd (length as) 1
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