c86b10d141
This PR moves the grind pattern from `Sublist.eq_of_length` to the slightly more general `Sublist.eq_of_length_le`, and adds a grind pattern guard so it only activates if we have a proof of the hypothesis.
117 lines
5.7 KiB
Text
117 lines
5.7 KiB
Text
namespace List
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protected def diff {α} [BEq α] : List α → List α → List α
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| l, [] => l
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| l₁, a :: l₂ => if l₁.elem a then List.diff (l₁.erase a) l₂ else List.diff l₁ l₂
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def Subperm (l₁ l₂ : List α) : Prop := ∃ l, l ~ l₁ ∧ l <+ l₂
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open Perm (swap)
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theorem Perm.subperm_left {l l₁ l₂ : List α} (p : l₁ ~ l₂) : Subperm l l₁ ↔ Subperm l l₂ :=
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sorry
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theorem Sublist.subperm {l₁ l₂ : List α} (s : l₁ <+ l₂) : Subperm l₁ l₂ := sorry
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theorem Subperm.perm_of_length_le {l₁ l₂ : List α} :
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Subperm l₁ l₂ → length l₂ ≤ length l₁ → l₁ ~ l₂ :=
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sorry
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end List
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variable {α : Type} [DecidableEq α] {l₁ l₂ : List α}
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open List
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/--
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error: `grind` failed
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case grind.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1
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α : Type
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inst : DecidableEq α
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l₁ l₂ : List α
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hl : l₂.Subperm l₁
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p : α → Bool
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h : ¬countP p l₁ = countP p (l₁.diff l₂ ++ l₂)
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w : α
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h_2 : ¬count w (l₁.diff l₂ ++ l₂) = count w l₁
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w_1 : α
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h_4 : ¬count w_1 l₁ = count w_1 (l₁.diff l₂ ++ l₂)
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left : l₂ ⊆ l₁
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right : ∀ {a : α}, a ∈ l₂ → a ∈ l₁
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left_1 : filter p l₂ <+ filter p l₁
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w_2 : List α
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left_2 : w_2 <+ l₁
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right_2 : filter p l₂ = filter p w_2
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w_3 : List α
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left_3 : w_3 <+ l₁
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right_3 : filter p l₂ = filter p w_3
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left_4 : l₁.diff l₂ ~ l₁
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right_4 : ∀ (a : α), count a (l₁.diff l₂) = count a l₁
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w_4 : α
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h_11 : ¬count w_4 (l₁.diff l₂ ++ l₂) = count w_4 (l₁.diff l₂)
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w_5 : α
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h_13 : ¬count w_5 (l₁.diff l₂) = count w_5 (l₁.diff l₂ ++ l₂)
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left_5 : l₁.diff l₂ ~ l₂
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right_5 : ∀ (a : α), count a (l₁.diff l₂) = count a l₂
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w_6 : α
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h_16 : ¬count w_6 (l₁.diff l₂ ++ l₂) = count w_6 l₂
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w_7 : α
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h_18 : ¬count w_7 l₂ = count w_7 (l₁.diff l₂ ++ l₂)
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left_6 : l₂ ~ l₁
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right_6 : ∀ (a : α), count a l₂ = count a l₁
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left_7 : l₂ ~ l₁.diff l₂
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right_7 : ∀ (a : α), count a l₂ = count a (l₁.diff l₂)
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left_8 : l₁ ~ l₁.diff l₂
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right_8 : ∀ (a : α), count a l₁ = count a (l₁.diff l₂)
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left_9 : l₁ ~ l₂
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right_9 : ∀ (a : α), count a l₁ = count a l₂
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left_10 : filter p l₁ ~ filter p (l₁.diff l₂ ++ l₂)
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right_10 : ∀ (a : α), count a (filter p l₁) = count a (filter p (l₁.diff l₂ ++ l₂))
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left_11 : filter p (l₁.diff l₂ ++ l₂) ~ filter p l₁
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right_11 : ∀ (a : α), count a (filter p (l₁.diff l₂ ++ l₂)) = count a (filter p l₁)
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left_12 : l₁.diff l₂ ++ l₂ ~ l₁.diff l₂ ++ (l₁.diff l₂ ++ l₂)
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right_12 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁.diff l₂ ++ (l₁.diff l₂ ++ l₂))
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left_13 : l₁.diff l₂ ++ l₂ ~ l₂ ++ (l₁.diff l₂ ++ l₂)
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right_13 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₂ ++ (l₁.diff l₂ ++ l₂))
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left_14 : l₁.diff l₂ ++ l₂ ~ l₁.diff l₂ ++ l₂ ++ l₁
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right_14 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁.diff l₂ ++ l₂ ++ l₁)
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left_15 : l₁.diff l₂ ++ l₂ ~ l₁.diff l₂ ++ l₂ ++ (l₁.diff l₂ ++ l₂)
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right_15 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁.diff l₂ ++ l₂ ++ (l₁.diff l₂ ++ l₂))
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left_16 : l₁.diff l₂ ++ l₂ ~ l₁.diff l₂ ++ l₂ ++ l₂
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right_16 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁.diff l₂ ++ l₂ ++ l₂)
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left_17 : l₁.diff l₂ ++ l₂ ~ l₁.diff l₂ ++ l₂ ++ l₁.diff l₂
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right_17 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁.diff l₂ ++ l₂ ++ l₁.diff l₂)
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left_18 : l₁.diff l₂ ++ l₂ ~ l₁ ++ (l₁.diff l₂ ++ l₂)
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right_18 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂) = count a (l₁ ++ (l₁.diff l₂ ++ l₂))
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left_19 : filter p (l₁.diff l₂ ++ l₂) ~ filter p (l₁.diff l₂)
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right_19 : ∀ (a : α), count a (filter p (l₁.diff l₂ ++ l₂)) = count a (filter p (l₁.diff l₂))
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left_20 : filter p (l₁.diff l₂) ~ filter p (l₁.diff l₂ ++ l₂)
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right_20 : ∀ (a : α), count a (filter p (l₁.diff l₂)) = count a (filter p (l₁.diff l₂ ++ l₂))
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left_21 : (filter p (l₁.diff l₂ ++ l₂)).Subperm (filter p l₁)
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right_21 : (filter p (l₁.diff l₂ ++ l₂)).Subperm (filter p (l₁.diff l₂ ++ l₂))
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left_22 : l₁.diff l₂ ++ l₂ ++ l₁.diff l₂ ~ l₁.diff l₂ ++ l₂
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right_22 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂ ++ l₁.diff l₂) = count a (l₁.diff l₂ ++ l₂)
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left_23 : l₁.diff l₂ ++ l₂ ++ l₁ ~ l₁.diff l₂ ++ l₂
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right_23 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂ ++ l₁) = count a (l₁.diff l₂ ++ l₂)
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left_24 : l₁.diff l₂ ++ l₂ ++ l₂ ~ l₁.diff l₂ ++ l₂
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right_24 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂ ++ l₂) = count a (l₁.diff l₂ ++ l₂)
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left_25 : l₁.diff l₂ ++ l₂ ++ (l₁.diff l₂ ++ l₂) ~ l₁.diff l₂ ++ l₂
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right_25 : ∀ (a : α), count a (l₁.diff l₂ ++ l₂ ++ (l₁.diff l₂ ++ l₂)) = count a (l₁.diff l₂ ++ l₂)
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left_26 : l₁ ++ (l₁.diff l₂ ++ l₂) ~ l₁.diff l₂ ++ l₂
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right_26 : ∀ (a : α), count a (l₁ ++ (l₁.diff l₂ ++ l₂)) = count a (l₁.diff l₂ ++ l₂)
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left_27 : l₂ ++ (l₁.diff l₂ ++ l₂) ~ l₁.diff l₂ ++ l₂
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right_27 : ∀ (a : α), count a (l₂ ++ (l₁.diff l₂ ++ l₂)) = count a (l₁.diff l₂ ++ l₂)
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left_28 : l₁.diff l₂ ++ (l₁.diff l₂ ++ l₂) ~ l₁.diff l₂ ++ l₂
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right_28 : ∀ (a : α), count a (l₁.diff l₂ ++ (l₁.diff l₂ ++ l₂)) = count a (l₁.diff l₂ ++ l₂)
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⊢ False
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-/
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#guard_msgs in
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theorem countP_diff (hl : Subperm l₂ l₁) (p : α → Bool) :
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countP p l₁ = countP p (l₁.diff l₂ ++ l₂) := by
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grind -verbose [
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List.Perm.subperm_left,
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List.Sublist.subperm,
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List.Subperm.perm_of_length_le,
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List.Perm.countP_congr,
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List.countP_eq_length_filter
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]
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