daa4fd9955
This PR reviews the implicitness of arguments across List/Array/Vector, generally trying to make arguments implicit where possible, although sometimes correcting propositional arguments which were incorrectly implicit to explicit.
95 lines
2.8 KiB
Text
95 lines
2.8 KiB
Text
theorem all_eq_not_any_not (l : List α) (p : α → Bool) :
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l.all p = !l.any fun x => binderNameHint x p (!p x)
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:= List.all_eq_not_any_not
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/--
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error: tactic 'fail' failed
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names : List String
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⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
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-/
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#guard_msgs in
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example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
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rw [all_eq_not_any_not]
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fail
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/--
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error: tactic 'fail' failed
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names : List String
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⊢ (names.any fun name => !"Waldo".isPrefixOf name) = false
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-/
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#guard_msgs in
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example (names : List String) : names.all (fun name => "Waldo".isPrefixOf name) = true := by
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simp [all_eq_not_any_not, -List.any_eq_false]
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fail
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def List.myAll (p : α → Bool) (xs : List α) : Bool := !(xs.any fun x => !p x)
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theorem myAll_eq_not_any_not (l : List α) (p : α → Bool) :
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l.myAll p = !l.any fun x => binderNameHint x p (!p x)
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:= rfl
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/--
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error: tactic 'fail' failed
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names : List String
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⊢ (!names.any fun name => !"Waldo".isPrefixOf name) = true
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-/
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#guard_msgs in
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example (names : List String) : names.myAll (fun name => "Waldo".isPrefixOf name) = true := by
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dsimp [myAll_eq_not_any_not]
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fail
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-- Check if we can pick the second binder by providing arguments to `f` in `binderNameHint`
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-- (It will beta-reduce it)
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-- Why this not in standard lib (maybe with the more complex form of recognizing lambdas that
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-- ignore arguments?)
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@[simp]
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theorem List.mapIdx_eq_map (l : List α) (f : α → β) : (l.mapIdx fun _ x => f x) = l.map f := by
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induction l <;> simp_all
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set_option linter.unusedVariables false in
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theorem zipWith_eq_map_idx_zipWith (l1 : List α) (l2 : List β) (f : α → β → γ) :
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List.zipWith f l1 l2 = (List.zip l1 l2).mapIdx
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(fun i ⟨a, b⟩ => binderNameHint a f <| binderNameHint b (f a) <| f a b)
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:= by simp [List.zip_eq_zipWith, List.map_zipWith]
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/--
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error: tactic 'fail' failed
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l1 l2 : List Nat
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⊢ (List.mapIdx
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(fun i x =>
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match x with
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| (x, y) => x + y)
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(l1.zip l2)).isEmpty =
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true
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-/
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#guard_msgs in
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example (l1 l2 : List Nat) :
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(List.zipWith (fun x y => x + y) l1 l2).isEmpty := by
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rw [zipWith_eq_map_idx_zipWith]
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fail
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-- For now, binder name hints do not work in other tactics, like `apply`
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-- (but at least `simp` or `dsimp` removes them)
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theorem myAll_eq_not_any_not_iff {l : List α} {p : α → Bool} :
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l.myAll p ↔ !l.any fun x => binderNameHint x p (!p x)
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:= by simp [myAll_eq_not_any_not]
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/--
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error: unsolved goals
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names : List String
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⊢ (!names.any fun x => !"Waldo".isPrefixOf x) = true
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---
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info: names : List String
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⊢ (!names.any fun x => binderNameHint x (fun name => "Waldo".isPrefixOf name) !"Waldo".isPrefixOf x) = true
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-/
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#guard_msgs in
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example (names : List String) : names.myAll (fun name => "Waldo".isPrefixOf name) = true := by
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apply myAll_eq_not_any_not_iff.mpr
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trace_state
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dsimp
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done
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