Theorem: List.takeWhile₂_eq_takeWhile₂TR
File: .lake/packages/batteries/Batteries/Data/List/Basic.lean

Proof steps:
state_before: ⊢ @takeWhile₂ = @takeWhile₂TR
state_after: case h.h.h.h.h
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
⊢ takeWhile₂ R as bs = takeWhile₂TR R as bs
tactic: funext α β R as bs
state_before: case h.h.h.h.h
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
⊢ takeWhile₂ R as bs = takeWhile₂TR R as bs
state_after: case h.h.h.h.h
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
⊢ takeWhile₂ R as bs = takeWhile₂TR.go R as bs [] []
tactic: simp [takeWhile₂TR]
state_before: α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
as : List α
bs : List β
acca : List α
accb : List β
⊢ takeWhile₂TR.go R as bs acca accb =
    (acca.reverse ++ (takeWhile₂ R as bs).fst, accb.reverse ++ (takeWhile₂ R as bs).snd)
state_after: α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
as : List α
bs : List β
acca : List α
accb : List β
⊢ (match as, bs, acca, accb with
    | a :: as, b :: bs, acca, accb =>
      bif R a b then takeWhile₂TR.go R as bs (a :: acca) (b :: accb) else (acca.reverse, accb.reverse)
    | x, x_1, acca, accb => (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (match as, bs with
          | a :: as, b :: bs =>
            if R a b = true then
              match takeWhile₂ R as bs with
              | (as', bs') => (a :: as', b :: bs')
            else ([], [])
          | x, x_1 => ([], [])).fst,
      accb.reverse ++
        (match as, bs with
          | a :: as, b :: bs =>
            if R a b = true then
              match takeWhile₂ R as bs with
              | (as', bs') => (a :: as', b :: bs')
            else ([], [])
          | x, x_1 => ([], [])).snd)
tactic: unfold takeWhile₂TR.go takeWhile₂
state_before: α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
as : List α
bs : List β
acca : List α
accb : List β
⊢ (match as, bs, acca, accb with
    | a :: as, b :: bs, acca, accb =>
      bif R a b then takeWhile₂TR.go R as bs (a :: acca) (b :: accb) else (acca.reverse, accb.reverse)
    | x, x_1, acca, accb => (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (match as, bs with
          | a :: as, b :: bs =>
            if R a b = true then
              match takeWhile₂ R as bs with
              | (as', bs') => (a :: as', b :: bs')
            else ([], [])
          | x, x_1 => ([], [])).fst,
      accb.reverse ++
        (match as, bs with
          | a :: as, b :: bs =>
            if R a b = true then
              match takeWhile₂ R as bs with
              | (as', bs') => (a :: as', b :: bs')
            else ([], [])
          | x, x_1 => ([], [])).snd)
state_after: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a✝ : α
as✝ : List α
b✝ : β
bs✝ : List β
⊢ (bif R a✝ b✝ then takeWhile₂TR.go R as✝ bs✝ (a✝ :: acca) (b✝ :: accb) else (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a✝ b✝ = true then (a✝ :: (takeWhile₂ R as✝ bs✝).fst, b✝ :: (takeWhile₂ R as✝ bs✝).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a✝ b✝ = true then (a✝ :: (takeWhile₂ R as✝ bs✝).fst, b✝ :: (takeWhile₂ R as✝ bs✝).snd) else ([], [])).snd)
tactic: split <;> simp
state_before: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a✝ : α
as✝ : List α
b✝ : β
bs✝ : List β
⊢ (bif R a✝ b✝ then takeWhile₂TR.go R as✝ bs✝ (a✝ :: acca) (b✝ :: accb) else (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a✝ b✝ = true then (a✝ :: (takeWhile₂ R as✝ bs✝).fst, b✝ :: (takeWhile₂ R as✝ bs✝).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a✝ b✝ = true then (a✝ :: (takeWhile₂ R as✝ bs✝).fst, b✝ :: (takeWhile₂ R as✝ bs✝).snd) else ([], [])).snd)
state_after: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a : α
as : List α
b : β
bs : List β
⊢ (bif R a b then takeWhile₂TR.go R as bs (a :: acca) (b :: accb) else (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).snd)
tactic: rename_i a as b bs
state_before: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a : α
as : List α
b : β
bs : List β
⊢ (bif R a b then takeWhile₂TR.go R as bs (a :: acca) (b :: accb) else (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).snd)
state_after: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a : α
as : List α
b : β
bs : List β
⊢ (match R a b with
    | true => takeWhile₂TR.go R as bs (a :: acca) (b :: accb)
    | false => (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).snd)
tactic: unfold cond
state_before: case h_1
α : Type u_2
β : Type u_1
R : α → β → Bool
as✝ : List α
bs✝ : List β
acca : List α
accb : List β
x✝³ : List α
x✝² : List β
x✝¹ : List α
x✝ : List β
a : α
as : List α
b : β
bs : List β
⊢ (match R a b with
    | true => takeWhile₂TR.go R as bs (a :: acca) (b :: accb)
    | false => (acca.reverse, accb.reverse)) =
    (acca.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).fst,
      accb.reverse ++
        (if R a b = true then (a :: (takeWhile₂ R as bs).fst, b :: (takeWhile₂ R as bs).snd) else ([], [])).snd)
state_after: no goals
tactic: cases R a b <;> simp [go as bs]
state_before: case h.h.h.h.h
α : Type u_2
β : Type u_1
R : α → β → Bool
as : List α
bs : List β
⊢ takeWhile₂ R as bs = takeWhile₂TR.go R as bs [] []
state_after: no goals
tactic: exact (go as bs [] []).symm