f3baff8dce
This PR follows up on #7103 which changes the generaliziation behavior of `induction`, to keep `fun_induction` in sync. Also fixes a `Syntax` indexing off-by-one error.
208 lines
5 KiB
Text
208 lines
5 KiB
Text
/-!
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Checks the generalization behavior of `fun_induction`.
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In particular that it behaves the same as `induction … using ….induct`.
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-/
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variable (xs ys : List Nat)
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variable (P : ∀ {α}, List α → Prop)
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs✝.zip ys✝)
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⊢ P ((x✝ :: xs✝).zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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⊢ P (t✝.zip x✝¹)
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-/
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#guard_msgs in
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example : P (List.zip xs ys) := by
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fun_induction List.zipWith _ xs ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys✝)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip x✝¹)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction List.zipWith _ xs ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip ys)
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip ys)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction List.zipWith _ xs (ys.take 2)
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : xs✝.isEmpty = true → P (xs✝.zip ys)
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h : (x✝ :: xs✝).isEmpty = true
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⊢ P ((x✝ :: xs✝).zip ys)
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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h : t✝.isEmpty = true
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⊢ P (t✝.zip ys)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs, ys.take 2 using List.zipWith.induct
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs.zip ys✝)
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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⊢ P (xs.zip x✝¹)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction List.zipWith _ (xs.take 2) ys
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/--
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error: unsolved goals
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case case1
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : P (xs.zip ys✝)
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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xs ys : List Nat
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P : {α : Type} → List α → Prop
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h : xs.isEmpty = true
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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⊢ P (xs.zip x✝¹)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs.take 2, ys using List.zipWith.induct
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/--
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error: unsolved goals
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case case1
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : ∀ (xs : List Nat), xs.isEmpty = true → P (xs.zip ys✝)
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip x✝¹)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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fun_induction List.zipWith _ (xs.take 2) ys generalizing xs
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/--
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error: unsolved goals
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case case1
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P : {α : Type} → List α → Prop
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x✝ : Nat
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xs✝ : List Nat
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y✝ : Nat
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ys✝ : List Nat
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ih1✝ : ∀ (xs : List Nat), xs.isEmpty = true → P (xs.zip ys✝)
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip (y✝ :: ys✝))
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case case2
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P : {α : Type} → List α → Prop
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t✝ x✝¹ : List Nat
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x✝ : ∀ (x : Nat) (xs : List Nat) (y : Nat) (ys : List Nat), t✝ = x :: xs → x✝¹ = y :: ys → False
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xs : List Nat
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h : xs.isEmpty = true
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⊢ P (xs.zip x✝¹)
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-/
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#guard_msgs in
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example (h : xs.isEmpty) : P (List.zip xs ys) := by
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induction xs.take 2, ys using List.zipWith.induct generalizing xs
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