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https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_nil
[2135, 1]
[2138, 19]
apply countp_nil
α : Type u_1 inst✝ : BEq α a : α ⊢ countp (fun x => x == a) [] = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : BEq α a : α ⊢ countp (fun x => x == a) [] = 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_cons
[2140, 1]
[2142, 20]
unfold count
α : Type u_1 a : α inst✝ : BEq α head : α tail : List α ⊢ count a (head :: tail) = (if (head == a) = true then 1 else 0) + count a tail
α : Type u_1 a : α inst✝ : BEq α head : α tail : List α ⊢ countp (fun x => x == a) (head :: tail) = (if (head == a) = true then 1 else 0) + countp (fun x => x == a) tail
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 a : α inst✝ : BEq α head : α tail : List α ⊢ count a (head :: tail) = (if (head == a) = true then 1 else 0) + count a tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_cons
[2140, 1]
[2142, 20]
apply countp_cons
α : Type u_1 a : α inst✝ : BEq α head : α tail : List α ⊢ countp (fun x => x == a) (head :: tail) = (if (head == a) = true then 1 else 0) + countp (fun x => x == a) tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 a : α inst✝ : BEq α head : α tail : List α ⊢ countp (fun x => x == a) (head :: tail) = (if (head == a) = true then 1 else 0) + countp (fun x => x == a) tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.countp_append
[2144, 1]
[2148, 117]
induction l₁ with | nil => simp only [nil_append, countp_nil, zero_le, ge_iff_le, nonpos_iff_eq_zero, zero_add] | cons head tail ih => simp only [cons_append, countp_cons, ih, zero_le, ge_iff_le, nonpos_iff_eq_zero, add_assoc]
α✝ : Type u_1 p : α✝ → Bool l₁ l₂ : List α✝ ⊢ countp p (l₁ ++ l₂) = countp p l₁ + countp p l₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 p : α✝ → Bool l₁ l₂ : List α✝ ⊢ countp p (l₁ ++ l₂) = countp p l₁ + countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.countp_append
[2144, 1]
[2148, 117]
simp only [nil_append, countp_nil, zero_le, ge_iff_le, nonpos_iff_eq_zero, zero_add]
case nil α✝ : Type u_1 p : α✝ → Bool l₂ : List α✝ ⊢ countp p ([] ++ l₂) = countp p [] + countp p l₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: case nil α✝ : Type u_1 p : α✝ → Bool l₂ : List α✝ ⊢ countp p ([] ++ l₂) = countp p [] + countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.countp_append
[2144, 1]
[2148, 117]
simp only [cons_append, countp_cons, ih, zero_le, ge_iff_le, nonpos_iff_eq_zero, add_assoc]
case cons α✝ : Type u_1 p : α✝ → Bool l₂ : List α✝ head : α✝ tail : List α✝ ih : countp p (tail ++ l₂) = countp p tail + countp p l₂ ⊢ countp p (head :: tail ++ l₂) = countp p (head :: tail) + countp p l₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: case cons α✝ : Type u_1 p : α✝ → Bool l₂ : List α✝ head : α✝ tail : List α✝ ih : countp p (tail ++ l₂) = countp p tail + countp p l₂ ⊢ countp p (head :: tail ++ l₂) = countp p (head :: tail) + countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_append
[2150, 1]
[2153, 27]
unfold count
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α ⊢ count a (l₁ ++ l₂) = count a l₁ + count a l₂
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α ⊢ countp (fun x => x == a) (l₁ ++ l₂) = countp (fun x => x == a) l₁ + countp (fun x => x == a) l₂
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α ⊢ count a (l₁ ++ l₂) = count a l₁ + count a l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_append
[2150, 1]
[2153, 27]
apply List.countp_append
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α ⊢ countp (fun x => x == a) (l₁ ++ l₂) = countp (fun x => x == a) l₁ + countp (fun x => x == a) l₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α ⊢ countp (fun x => x == a) (l₁ ++ l₂) = countp (fun x => x == a) l₁ + countp (fun x => x == a) l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_countp_le
[2156, 1]
[2161, 11]
have ⟨s,t,heq⟩ := h
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ ⊢ countp p l₁ ≤ countp p l₂
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : s ++ l₁ ++ t = l₂ ⊢ countp p l₁ ≤ countp p l₂
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ ⊢ countp p l₁ ≤ countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_countp_le
[2156, 1]
[2161, 11]
apply_fun countp p at heq
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : s ++ l₁ ++ t = l₂ ⊢ countp p l₁ ≤ countp p l₂
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p (s ++ l₁ ++ t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : s ++ l₁ ++ t = l₂ ⊢ countp p l₁ ≤ countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_countp_le
[2156, 1]
[2161, 11]
simp only [append_assoc, countp_append] at heq
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p (s ++ l₁ ++ t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p (s ++ l₁ ++ t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_countp_le
[2156, 1]
[2161, 11]
rw [← heq]
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p s + (countp p l₁ + countp p t)
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_countp_le
[2156, 1]
[2161, 11]
linarith
α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p s + (countp p l₁ + countp p t)
no goals
Please generate a tactic in lean4 to solve the state. STATE: α✝ : Type u_1 l₁ l₂ : List α✝ p : α✝ → Bool h : l₁ <:+: l₂ s t : List α✝ heq : countp p s + (countp p l₁ + countp p t) = countp p l₂ ⊢ countp p l₁ ≤ countp p s + (countp p l₁ + countp p t) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_count_le
[2163, 1]
[2165, 33]
unfold count
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α h : l₁ <:+: l₂ ⊢ count a l₁ ≤ count a l₂
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α h : l₁ <:+: l₂ ⊢ countp (fun x => x == a) l₁ ≤ countp (fun x => x == a) l₂
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α h : l₁ <:+: l₂ ⊢ count a l₁ ≤ count a l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.isInfix_count_le
[2163, 1]
[2165, 33]
apply List.isInfix_countp_le h
α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α h : l₁ <:+: l₂ ⊢ countp (fun x => x == a) l₁ ≤ countp (fun x => x == a) l₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : BEq α a : α l₁ l₂ : List α h : l₁ <:+: l₂ ⊢ countp (fun x => x == a) l₁ ≤ countp (fun x => x == a) l₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
apply Iff.intro
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ count a l > 0 ↔ a ∈ l
case mp α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ count a l > 0 → a ∈ l case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ count a l > 0 ↔ a ∈ l TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
. intro count_pos induction l with | nil => simp only [count_nil, zero_le, ge_iff_le, nonpos_iff_eq_zero, lt_self_iff_false] at count_pos | cons head tail ih=> simp only [count_cons, beq_iff_eq, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff] at count_pos cases count_pos with | inl hlt => split at hlt case inl heq => simp at heq; simp [heq] case inr heq => simp only at hlt | inr hlt => apply mem_cons.2; right apply ih hlt
case mp α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ count a l > 0 → a ∈ l case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0
case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0
Please generate a tactic in lean4 to solve the state. STATE: case mp α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ count a l > 0 → a ∈ l case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
. intro ain induction l with | nil => simp only [not_mem_nil] at ain | cons head tail ih => cases mem_cons.1 ain with | inl heq => simp only [heq, count_cons, beq_self_eq_true, ite_true, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, true_or] | inr hin => simp only [count_cons, beq_iff_eq, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, ih hin, or_true]
case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mpr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α l : List α ⊢ a ∈ l → count a l > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only [count_nil, zero_le, ge_iff_le, nonpos_iff_eq_zero, lt_self_iff_false] at count_pos
case mp.nil α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α count_pos : count a [] > 0 ⊢ a ∈ []
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mp.nil α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α count_pos : count a [] > 0 ⊢ a ∈ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only [count_cons, beq_iff_eq, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff] at count_pos
case mp.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail count_pos : count a (head :: tail) > 0 ⊢ a ∈ head :: tail
case mp.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail count_pos : (0 < if (head == a) = true then 1 else 0) ∨ 0 < count a tail ⊢ a ∈ head :: tail
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail count_pos : count a (head :: tail) > 0 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
cases count_pos with | inl hlt => split at hlt case inl heq => simp at heq; simp [heq] case inr heq => simp only at hlt | inr hlt => apply mem_cons.2; right apply ih hlt
case mp.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail count_pos : (0 < if (head == a) = true then 1 else 0) ∨ 0 < count a tail ⊢ a ∈ head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail count_pos : (0 < if (head == a) = true then 1 else 0) ∨ 0 < count a tail ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
split at hlt
case mp.cons.inl α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < if (head == a) = true then 1 else 0 ⊢ a ∈ head :: tail
case mp.cons.inl.inl α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail h✝ : (head == a) = true hlt : 0 < 1 ⊢ a ∈ head :: tail case mp.cons.inl.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail h✝ : ¬(head == a) = true hlt : 0 < 0 ⊢ a ∈ head :: tail
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons.inl α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < if (head == a) = true then 1 else 0 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
case inl heq => simp at heq; simp [heq]
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : (head == a) = true hlt : 0 < 1 ⊢ a ∈ head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : (head == a) = true hlt : 0 < 1 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
case inr heq => simp only at hlt
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : ¬(head == a) = true hlt : 0 < 0 ⊢ a ∈ head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : ¬(head == a) = true hlt : 0 < 0 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp at heq
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : (head == a) = true hlt : 0 < 1 ⊢ a ∈ head :: tail
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < 1 heq : head = a ⊢ a ∈ head :: tail
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : (head == a) = true hlt : 0 < 1 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp [heq]
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < 1 heq : head = a ⊢ a ∈ head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < 1 heq : head = a ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only at hlt
α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : ¬(head == a) = true hlt : 0 < 0 ⊢ a ∈ head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail heq : ¬(head == a) = true hlt : 0 < 0 ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
apply mem_cons.2
case mp.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a ∈ head :: tail
case mp.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a = head ∨ a ∈ tail
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a ∈ head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
right
case mp.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a = head ∨ a ∈ tail
case mp.cons.inr.h α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a ∈ tail
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a = head ∨ a ∈ tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
apply ih hlt
case mp.cons.inr.h α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a ∈ tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mp.cons.inr.h α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : count a tail > 0 → a ∈ tail hlt : 0 < count a tail ⊢ a ∈ tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only [not_mem_nil] at ain
case mpr.nil α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α ain : a ∈ [] ⊢ count a [] > 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mpr.nil α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a : α ain : a ∈ [] ⊢ count a [] > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
cases mem_cons.1 ain with | inl heq => simp only [heq, count_cons, beq_self_eq_true, ite_true, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, true_or] | inr hin => simp only [count_cons, beq_iff_eq, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, ih hin, or_true]
case mpr.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail ⊢ count a (head :: tail) > 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mpr.cons α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail ⊢ count a (head :: tail) > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only [heq, count_cons, beq_self_eq_true, ite_true, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, true_or]
case mpr.cons.inl α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail heq : a = head ⊢ count a (head :: tail) > 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mpr.cons.inl α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail heq : a = head ⊢ count a (head :: tail) > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.count_pos_iff_mem
[2167, 1]
[2191, 124]
simp only [count_cons, beq_iff_eq, zero_le, ge_iff_le, nonpos_iff_eq_zero, gt_iff_lt, add_pos_iff, ih hin, or_true]
case mpr.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail hin : a ∈ tail ⊢ count a (head :: tail) > 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mpr.cons.inr α : Type u_1 inst✝¹ : BEq α inst✝ : LawfulBEq α a head : α tail : List α ih : a ∈ tail → count a tail > 0 ain : a ∈ head :: tail hin : a ∈ tail ⊢ count a (head :: tail) > 0 TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
induction l with | nil => contradiction | cons head tail ih=> cases delim case nil => simp only [find?, mem_cons, dropLast, append_nil, nil_isInfix, not_true, forall_eq_or_imp, false_and] at h head case cons dhead dtail=> unfold intercalate cases h₂:tail with | nil => subst tail simp only [join, append_nil] apply List.splitOnList_nonmatching have h₃ := (h head (List.mem_singleton_self _)) intro ⟨s,t, hcontr⟩ apply h₃ exists s, (t ++ dropLast (dhead :: dtail)) simp only [append_assoc, cons_append, ← hcontr] | cons mid tail₂ => simp only [join] rw [← List.append_assoc, List.splitOnList_progress, ← List.intercalate, ← h₂, ih] . simp only [singleton_append] . intro e ein apply h subst h₂ simp_all only [find?, mem_cons, ne_eq, not_false_iff, or_true, implies_true, forall_const, forall_true_left, forall_eq_or_imp] . simp only [h₂, ne_eq, not_false_iff] . intro contr apply h head apply List.mem_cons_self exact contr
α : Type u_1 inst✝ : DecidableEq α delim : List α l : List (List α) h : ∀ (e : List α), e ∈ l → ¬delim <:+: e ++ dropLast delim h₂ : l ≠ [] ⊢ splitOnList delim (intercalate delim l) = l
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α delim : List α l : List (List α) h : ∀ (e : List α), e ∈ l → ¬delim <:+: e ++ dropLast delim h₂ : l ≠ [] ⊢ splitOnList delim (intercalate delim l) = l TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
contradiction
case nil α : Type u_1 inst✝ : DecidableEq α delim : List α h : ∀ (e : List α), e ∈ [] → ¬delim <:+: e ++ dropLast delim h₂ : [] ≠ [] ⊢ splitOnList delim (intercalate delim []) = []
no goals
Please generate a tactic in lean4 to solve the state. STATE: case nil α : Type u_1 inst✝ : DecidableEq α delim : List α h : ∀ (e : List α), e ∈ [] → ¬delim <:+: e ++ dropLast delim h₂ : [] ≠ [] ⊢ splitOnList delim (intercalate delim []) = [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
cases delim
case cons α : Type u_1 inst✝ : DecidableEq α delim head : List α tail : List (List α) ih : (∀ (e : List α), e ∈ tail → ¬delim <:+: e ++ dropLast delim) → tail ≠ [] → splitOnList delim (intercalate delim tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬delim <:+: e ++ dropLast delim h₂ : head :: tail ≠ [] ⊢ splitOnList delim (intercalate delim (head :: tail)) = head :: tail
case cons.nil α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] ih : (∀ (e : List α), e ∈ tail → ¬[] <:+: e ++ dropLast []) → tail ≠ [] → splitOnList [] (intercalate [] tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬[] <:+: e ++ dropLast [] ⊢ splitOnList [] (intercalate [] (head :: tail)) = head :: tail case cons.cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] head✝ : α tail✝ : List α ih : (∀ (e : List α), e ∈ tail → ¬head✝ :: tail✝ <:+: e ++ dropLast (head✝ :: tail✝)) → tail ≠ [] → splitOnList (head✝ :: tail✝) (intercalate (head✝ :: tail✝) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬head✝ :: tail✝ <:+: e ++ dropLast (head✝ :: tail✝) ⊢ splitOnList (head✝ :: tail✝) (intercalate (head✝ :: tail✝) (head :: tail)) = head :: tail
Please generate a tactic in lean4 to solve the state. STATE: case cons α : Type u_1 inst✝ : DecidableEq α delim head : List α tail : List (List α) ih : (∀ (e : List α), e ∈ tail → ¬delim <:+: e ++ dropLast delim) → tail ≠ [] → splitOnList delim (intercalate delim tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬delim <:+: e ++ dropLast delim h₂ : head :: tail ≠ [] ⊢ splitOnList delim (intercalate delim (head :: tail)) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
case nil => simp only [find?, mem_cons, dropLast, append_nil, nil_isInfix, not_true, forall_eq_or_imp, false_and] at h head
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] ih : (∀ (e : List α), e ∈ tail → ¬[] <:+: e ++ dropLast []) → tail ≠ [] → splitOnList [] (intercalate [] tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬[] <:+: e ++ dropLast [] ⊢ splitOnList [] (intercalate [] (head :: tail)) = head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] ih : (∀ (e : List α), e ∈ tail → ¬[] <:+: e ++ dropLast []) → tail ≠ [] → splitOnList [] (intercalate [] tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬[] <:+: e ++ dropLast [] ⊢ splitOnList [] (intercalate [] (head :: tail)) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
case cons dhead dtail=> unfold intercalate cases h₂:tail with | nil => subst tail simp only [join, append_nil] apply List.splitOnList_nonmatching have h₃ := (h head (List.mem_singleton_self _)) intro ⟨s,t, hcontr⟩ apply h₃ exists s, (t ++ dropLast (dhead :: dtail)) simp only [append_assoc, cons_append, ← hcontr] | cons mid tail₂ => simp only [join] rw [← List.append_assoc, List.splitOnList_progress, ← List.intercalate, ← h₂, ih] . simp only [singleton_append] . intro e ein apply h subst h₂ simp_all only [find?, mem_cons, ne_eq, not_false_iff, or_true, implies_true, forall_const, forall_true_left, forall_eq_or_imp] . simp only [h₂, ne_eq, not_false_iff] . intro contr apply h head apply List.mem_cons_self exact contr
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) (head :: tail)) = head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) (head :: tail)) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
simp only [find?, mem_cons, dropLast, append_nil, nil_isInfix, not_true, forall_eq_or_imp, false_and] at h head
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] ih : (∀ (e : List α), e ∈ tail → ¬[] <:+: e ++ dropLast []) → tail ≠ [] → splitOnList [] (intercalate [] tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬[] <:+: e ++ dropLast [] ⊢ splitOnList [] (intercalate [] (head :: tail)) = head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] ih : (∀ (e : List α), e ∈ tail → ¬[] <:+: e ++ dropLast []) → tail ≠ [] → splitOnList [] (intercalate [] tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬[] <:+: e ++ dropLast [] ⊢ splitOnList [] (intercalate [] (head :: tail)) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
unfold intercalate
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) (head :: tail)) = head :: tail
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) (head :: tail))) = head :: tail
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) (head :: tail)) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
cases h₂:tail with | nil => subst tail simp only [join, append_nil] apply List.splitOnList_nonmatching have h₃ := (h head (List.mem_singleton_self _)) intro ⟨s,t, hcontr⟩ apply h₃ exists s, (t ++ dropLast (dhead :: dtail)) simp only [append_assoc, cons_append, ← hcontr] | cons mid tail₂ => simp only [join] rw [← List.append_assoc, List.splitOnList_progress, ← List.intercalate, ← h₂, ih] . simp only [singleton_append] . intro e ein apply h subst h₂ simp_all only [find?, mem_cons, ne_eq, not_false_iff, or_true, implies_true, forall_const, forall_true_left, forall_eq_or_imp] . simp only [h₂, ne_eq, not_false_iff] . intro contr apply h head apply List.mem_cons_self exact contr
α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) (head :: tail))) = head :: tail
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) (head :: tail))) = head :: tail TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
subst tail
case nil α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₂ : tail = [] ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) [head])) = [head]
case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) [head])) = [head]
Please generate a tactic in lean4 to solve the state. STATE: case nil α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₂ : tail = [] ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) [head])) = [head] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
simp only [join, append_nil]
case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) [head])) = [head]
case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) head = [head]
Please generate a tactic in lean4 to solve the state. STATE: case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) [head])) = [head] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
apply List.splitOnList_nonmatching
case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) head = [head]
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head
Please generate a tactic in lean4 to solve the state. STATE: case nil α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ splitOnList (dhead :: dtail) head = [head] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
have h₃ := (h head (List.mem_singleton_self _))
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head
Please generate a tactic in lean4 to solve the state. STATE: case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
intro ⟨s,t, hcontr⟩
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) ⊢ ¬dhead :: dtail <:+: head TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
apply h₃
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ False
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
exists s, (t ++ dropLast (dhead :: dtail))
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ s ++ dhead :: dtail ++ (t ++ dropLast (dhead :: dtail)) = head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
simp only [append_assoc, cons_append, ← hcontr]
case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ s ++ dhead :: dtail ++ (t ++ dropLast (dhead :: dtail)) = head ++ dropLast (dhead :: dtail)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case nil.h₁ α : Type u_1 inst✝ : DecidableEq α head : List α dhead : α dtail : List α h₂ : [head] ≠ [] ih : (∀ (e : List α), e ∈ [] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → [] ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) []) = [] h : ∀ (e : List α), e ∈ [head] → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) h₃ : ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) s t : List α hcontr : s ++ dhead :: dtail ++ t = head ⊢ s ++ dhead :: dtail ++ (t ++ dropLast (dhead :: dtail)) = head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
simp only [join]
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) (head :: mid :: tail₂))) = head :: mid :: tail₂
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ splitOnList (dhead :: dtail) (head ++ (dhead :: dtail ++ join (intersperse (dhead :: dtail) (mid :: tail₂)))) = head :: mid :: tail₂
Please generate a tactic in lean4 to solve the state. STATE: case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ splitOnList (dhead :: dtail) (join (intersperse (dhead :: dtail) (head :: mid :: tail₂))) = head :: mid :: tail₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
rw [← List.append_assoc, List.splitOnList_progress, ← List.intercalate, ← h₂, ih]
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ splitOnList (dhead :: dtail) (head ++ (dhead :: dtail ++ join (intersperse (dhead :: dtail) (mid :: tail₂)))) = head :: mid :: tail₂
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ [head] ++ tail = head :: tail case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ splitOnList (dhead :: dtail) (head ++ (dhead :: dtail ++ join (intersperse (dhead :: dtail) (mid :: tail₂)))) = head :: mid :: tail₂ TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
. simp only [singleton_append]
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ [head] ++ tail = head :: tail case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ [head] ++ tail = head :: tail case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
. intro e ein apply h subst h₂ simp_all only [find?, mem_cons, ne_eq, not_false_iff, or_true, implies_true, forall_const, forall_true_left, forall_eq_or_imp]
case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case cons.h α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
. simp only [h₂, ne_eq, not_false_iff]
case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
Please generate a tactic in lean4 to solve the state. STATE: case cons.h₂ α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ tail ≠ [] case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.splitOnList_intercalate
[2194, 1]
[2228, 22]
. intro contr apply h head apply List.mem_cons_self exact contr
case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case cons α : Type u_1 inst✝ : DecidableEq α head : List α tail : List (List α) h₂✝ : head :: tail ≠ [] dhead : α dtail : List α ih : (∀ (e : List α), e ∈ tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail)) → tail ≠ [] → splitOnList (dhead :: dtail) (intercalate (dhead :: dtail) tail) = tail h : ∀ (e : List α), e ∈ head :: tail → ¬dhead :: dtail <:+: e ++ dropLast (dhead :: dtail) mid : List α tail₂ : List (List α) h₂ : tail = mid :: tail₂ ⊢ ¬dhead :: dtail <:+: head ++ dropLast (dhead :: dtail) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
convIf.id
[2258, 1]
[2260, 21]
simp[convIf]
α : Sort u_1 P : Prop inst : Decidable P a : α ⊢ a = convIf P inst (fun x => a) fun x => a
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Sort u_1 P : Prop inst : Decidable P a : α ⊢ a = convIf P inst (fun x => a) fun x => a TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
if hempty: elf = [] then intro contr have contr := List.isInfix_length contr simp only [List.length_cons, List.length_singleton, elfToString, hempty, List.map] at contr else unfold elfToString intro contr apply List.not_isInfix_intercalate_by_element ['\n', '\n'] ['\n'] (List.map Int.reprΔ elf) . simp only [List.mem_map', forall_exists_index, and_imp, forall_apply_eq_imp_iff₂] intro a _ contr₂ cases List.isInfix_append_split_right contr₂ with | inl h₁ => cases List.isInfix_append_split_left h₁ with | inl h₂ => have h₃ := List.isInfix_drop_of_isInfix_append h₂ simp only [List.drop, List.singleton_isInfix_iff_mem] at h₃ apply Int.not_newline_mem_reprΔ h₃ | inr h₄ => simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.singleton_append, List.lastN_one_eq_getLast, List.take, List.length,List.getLast?_cons] at h₄ rw [Option.to_list_some] at h₄ have newline_in_repr := List.isInfix_take_of_isInfix_append h₄ simp only [List.take, List.singleton_isInfix_iff_mem, List.mem_singleton] at newline_in_repr rw [List.getLastD_ne_nil] at newline_in_repr apply Int.not_newline_mem_reprΔ (n:=a) rw [newline_in_repr] apply List.getLast_mem apply Int.reprΔ_ne_nil a | inr h₅ => have hlen := List.isInfix_length h₅ simp only at hlen . simp only . simp only [ne_eq, List.map_eq_nil, hempty, not_false_iff] . apply List.isInfix_append_right_of_isInfix apply List.isInfix_append_left_of_isInfix exact contr
elf : List ℤ ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
intro contr
elf : List ℤ hempty : elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf
elf : List ℤ hempty : elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
have contr := List.isInfix_length contr
elf : List ℤ hempty : elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf ⊢ False
elf : List ℤ hempty : elf = [] contr✝ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf contr : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length (elfToString elf) ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
simp only [List.length_cons, List.length_singleton, elfToString, hempty, List.map] at contr
elf : List ℤ hempty : elf = [] contr✝ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf contr : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length (elfToString elf) ⊢ False
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : elf = [] contr✝ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf contr : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length (elfToString elf) ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
unfold elfToString
elf : List ℤ hempty : ¬elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf
elf : List ℤ hempty : ¬elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : ¬elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
intro contr
elf : List ℤ hempty : ¬elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)
elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : ¬elf = [] ⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
apply List.not_isInfix_intercalate_by_element ['\n', '\n'] ['\n'] (List.map Int.reprΔ elf)
elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ False
case h elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ ∀ (e : List Char), e ∈ List.map Int.reprΔ elf → ¬[Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ e ++ [Char.ofNat 10] case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
. simp only [List.mem_map', forall_exists_index, and_imp, forall_apply_eq_imp_iff₂] intro a _ contr₂ cases List.isInfix_append_split_right contr₂ with | inl h₁ => cases List.isInfix_append_split_left h₁ with | inl h₂ => have h₃ := List.isInfix_drop_of_isInfix_append h₂ simp only [List.drop, List.singleton_isInfix_iff_mem] at h₃ apply Int.not_newline_mem_reprΔ h₃ | inr h₄ => simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.singleton_append, List.lastN_one_eq_getLast, List.take, List.length,List.getLast?_cons] at h₄ rw [Option.to_list_some] at h₄ have newline_in_repr := List.isInfix_take_of_isInfix_append h₄ simp only [List.take, List.singleton_isInfix_iff_mem, List.mem_singleton] at newline_in_repr rw [List.getLastD_ne_nil] at newline_in_repr apply Int.not_newline_mem_reprΔ (n:=a) rw [newline_in_repr] apply List.getLast_mem apply Int.reprΔ_ne_nil a | inr h₅ => have hlen := List.isInfix_length h₅ simp only at hlen
case h elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ ∀ (e : List Char), e ∈ List.map Int.reprΔ elf → ¬[Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ e ++ [Char.ofNat 10] case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
Please generate a tactic in lean4 to solve the state. STATE: case h elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ ∀ (e : List Char), e ∈ List.map Int.reprΔ elf → ¬[Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ e ++ [Char.ofNat 10] case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
. simp only
case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
Please generate a tactic in lean4 to solve the state. STATE: case hlen elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.length [Char.ofNat 10, Char.ofNat 10] ≤ 1 + List.length [Char.ofNat 10] case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
. simp only [ne_eq, List.map_eq_nil, hempty, not_false_iff]
case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
Please generate a tactic in lean4 to solve the state. STATE: case hne_nil elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ List.map Int.reprΔ elf ≠ [] case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
. apply List.isInfix_append_right_of_isInfix apply List.isInfix_append_left_of_isInfix exact contr
case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10]
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ⊢ [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) ++ [Char.ofNat 10] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
cases List.isInfix_append_split_left h₁ with | inl h₂ => have h₃ := List.isInfix_drop_of_isInfix_append h₂ simp only [List.drop, List.singleton_isInfix_iff_mem] at h₃ apply Int.not_newline_mem_reprΔ h₃ | inr h₄ => simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.singleton_append, List.lastN_one_eq_getLast, List.take, List.length,List.getLast?_cons] at h₄ rw [Option.to_list_some] at h₄ have newline_in_repr := List.isInfix_take_of_isInfix_append h₄ simp only [List.take, List.singleton_isInfix_iff_mem, List.mem_singleton] at newline_in_repr rw [List.getLastD_ne_nil] at newline_in_repr apply Int.not_newline_mem_reprΔ (n:=a) rw [newline_in_repr] apply List.getLast_mem apply Int.reprΔ_ne_nil a
case h.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] ⊢ False
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
have h₃ := List.isInfix_drop_of_isInfix_append h₂
case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ⊢ False
case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : List.drop (List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: Int.reprΔ a ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
simp only [List.drop, List.singleton_isInfix_iff_mem] at h₃
case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : List.drop (List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: Int.reprΔ a ⊢ False
case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : Char.ofNat 10 ∈ Int.reprΔ a ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : List.drop (List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: Int.reprΔ a ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
apply Int.not_newline_mem_reprΔ h₃
case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : Char.ofNat 10 ∈ Int.reprΔ a ⊢ False
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inl elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a h₃ : Char.ofNat 10 ∈ Int.reprΔ a ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.singleton_append, List.lastN_one_eq_getLast, List.take, List.length,List.getLast?_cons] at h₄
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) ([Char.ofNat 10] ++ Int.reprΔ a) ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] ⊢ False
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: Option.toList (some (List.getLastD (Int.reprΔ a) (Char.ofNat 10))) ++ [Char.ofNat 10] ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) ([Char.ofNat 10] ++ Int.reprΔ a) ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
rw [Option.to_list_some] at h₄
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: Option.toList (some (List.getLastD (Int.reprΔ a) (Char.ofNat 10))) ++ [Char.ofNat 10] ⊢ False
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: Option.toList (some (List.getLastD (Int.reprΔ a) (Char.ofNat 10))) ++ [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
have newline_in_repr := List.isInfix_take_of_isInfix_append h₄
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] ⊢ False
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
simp only [List.take, List.singleton_isInfix_iff_mem, List.mem_singleton] at newline_in_repr
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ⊢ False
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10]) [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
rw [List.getLastD_ne_nil] at newline_in_repr
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ False
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ False case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
apply Int.not_newline_mem_reprΔ (n:=a)
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ False case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ Char.ofNat 10 ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ False case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
rw [newline_in_repr]
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ Char.ofNat 10 ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ List.getLast (Int.reprΔ a) ?h.inl.inr ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ Char.ofNat 10 ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
apply List.getLast_mem
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ List.getLast (Int.reprΔ a) ?h.inl.inr ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr✝ : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) newline_in_repr : Char.ofNat 10 = List.getLast (Int.reprΔ a) ?h.inl.inr ⊢ List.getLast (Int.reprΔ a) ?h.inl.inr ∈ Int.reprΔ a case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
apply Int.reprΔ_ne_nil a
case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ []
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] case h.inl.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ List.take (List.length [Char.ofNat 10, Char.ofNat 10] - 1) [Char.ofNat 10] h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: [List.getLastD (Int.reprΔ a) (Char.ofNat 10)] ++ [Char.ofNat 10] newline_in_repr : Char.ofNat 10 = List.getLastD (Int.reprΔ a) (Char.ofNat 10) ⊢ Int.reprΔ a ≠ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
have hlen := List.isInfix_length h₅
case h.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₅ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ⊢ False
case h.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₅ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] hlen : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length [Char.ofNat 10] ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: case h.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₅ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
double_newline_not_isInfix_stringToElf
[2282, 1]
[2319, 18]
simp only at hlen
case h.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₅ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] hlen : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length [Char.ofNat 10] ⊢ False
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h.inr elf : List ℤ hempty : ¬elf = [] contr : [Char.ofNat 10, Char.ofNat 10] <:+: List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) a : ℤ a✝ : a ∈ elf contr₂ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] ++ Int.reprΔ a ++ [Char.ofNat 10] h₅ : [Char.ofNat 10, Char.ofNat 10] <:+: [Char.ofNat 10] hlen : List.length [Char.ofNat 10, Char.ofNat 10] ≤ List.length [Char.ofNat 10] ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
if hnil: elf = [] then simp only [hnil, ne_eq] else unfold elfToString intro contr have h₂ := List.getLast?_some contr rw [List.getLast_intercalate] at h₂ . simp only [List.getLast_map _ hnil] at h₂ revert h₂ generalize_proofs hnil' intro h₂ have mem := List.getLast_mem hnil' rw [h₂] at mem apply Int.not_newline_mem_reprΔ apply mem . intro contr have gl := List.getLast?_some contr rw [List.getLast_map] at gl apply Int.reprΔ_ne_nil apply gl apply hnil . exact '\n'
elf : List ℤ ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10)
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
simp only [hnil, ne_eq]
elf : List ℤ hnil : elf = [] ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10)
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : elf = [] ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
unfold elfToString
elf : List ℤ hnil : ¬elf = [] ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10)
elf : List ℤ hnil : ¬elf = [] ⊢ List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) ≠ some (Char.ofNat 10)
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] ⊢ List.getLast? (elfToString elf) ≠ some (Char.ofNat 10) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
intro contr
elf : List ℤ hnil : ¬elf = [] ⊢ List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) ≠ some (Char.ofNat 10)
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] ⊢ List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) ≠ some (Char.ofNat 10) TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
have h₂ := List.getLast?_some contr
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) ⊢ False
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
rw [List.getLast_intercalate] at h₂
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ False
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂✝ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 h₂ : List.getLast (List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False)) (_ : List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False) = [] → False) = Char.ofNat 10 ⊢ False case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ False TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
. simp only [List.getLast_map _ hnil] at h₂ revert h₂ generalize_proofs hnil' intro h₂ have mem := List.getLast_mem hnil' rw [h₂] at mem apply Int.not_newline_mem_reprΔ apply mem
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂✝ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 h₂ : List.getLast (List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False)) (_ : List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False) = [] → False) = Char.ofNat 10 ⊢ False case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂✝ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 h₂ : List.getLast (List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False)) (_ : List.getLast (List.map Int.reprΔ elf) (_ : List.map Int.reprΔ elf = [] → False) = [] → False) = Char.ofNat 10 ⊢ False case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
. intro contr have gl := List.getLast?_some contr rw [List.getLast_map] at gl apply Int.reprΔ_ne_nil apply gl apply hnil
case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
Please generate a tactic in lean4 to solve the state. STATE: case not_nil elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ List.getLast? (List.map Int.reprΔ elf) ≠ some [] elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
newline_not_last_elfToString
[2322, 1]
[2344, 17]
. exact '\n'
elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ hnil : ¬elf = [] contr : List.getLast? (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) = some (Char.ofNat 10) h₂ : List.getLast (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)) (_ : ¬List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf) = []) = Char.ofNat 10 ⊢ Char TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
stringToElf_ignoresTrailing
[2348, 1]
[2351, 63]
simp only [stringToElf, ne_eq, decide_not, List.find?, List.not_mem_nil, beq_iff_eq, IsEmpty.forall_iff, forall_const, List.splitOn_last, List.filter_append, decide_True, Bool.not_true, not_false_iff, List.filter_cons_of_neg, List.filter_nil, List.append_nil]
s : List Char ⊢ stringToElf (s ++ [Char.ofNat 10]) = stringToElf s
no goals
Please generate a tactic in lean4 to solve the state. STATE: s : List Char ⊢ stringToElf (s ++ [Char.ofNat 10]) = stringToElf s TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
List.intercalate_singleton
[2353, 1]
[2355, 100]
rw [List.intercalate, List.intersperse_singleton, List.join_cons, List.join_nil, List.append_nil]
α : Type u_1 sep elem : List α ⊢ intercalate sep [elem] = elem
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type u_1 sep elem : List α ⊢ intercalate sep [elem] = elem TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
if h:elf = [] then simp only [h] else unfold stringToElf elfToString rw [List.splitOn_intercalate, List.filter_eq_self.2, List.map_map] . unfold Function.comp simp only [String.toIntΔ_inv_IntreprΔ, List.map_id''] . simp only [List.mem_map', ne_eq, decide_not, Bool.not_eq_true', decide_eq_false_iff_not, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂, Int.reprΔ_ne_nil, not_false_iff, implies_true, forall_const] . simp only [List.mem_map', forall_exists_index, and_imp, forall_apply_eq_imp_iff₂] intro a _ apply Int.not_newline_mem_reprΔ . simp only [ne_eq, List.map_eq_nil, h, not_false_iff]
elf : List ℤ ⊢ stringToElf (elfToString elf) = elf
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ ⊢ stringToElf (elfToString elf) = elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
simp only [h]
elf : List ℤ h : elf = [] ⊢ stringToElf (elfToString elf) = elf
no goals
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ h : elf = [] ⊢ stringToElf (elfToString elf) = elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
unfold stringToElf elfToString
elf : List ℤ h : ¬elf = [] ⊢ stringToElf (elfToString elf) = elf
elf : List ℤ h : ¬elf = [] ⊢ List.map String.toIntΔ (List.filter (fun x => decide (x ≠ [])) (List.splitOn (Char.ofNat 10) (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)))) = elf
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ h : ¬elf = [] ⊢ stringToElf (elfToString elf) = elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
rw [List.splitOn_intercalate, List.filter_eq_self.2, List.map_map]
elf : List ℤ h : ¬elf = [] ⊢ List.map String.toIntΔ (List.filter (fun x => decide (x ≠ [])) (List.splitOn (Char.ofNat 10) (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)))) = elf
elf : List ℤ h : ¬elf = [] ⊢ List.map (String.toIntΔ ∘ Int.reprΔ) elf = elf elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ []
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ h : ¬elf = [] ⊢ List.map String.toIntΔ (List.filter (fun x => decide (x ≠ [])) (List.splitOn (Char.ofNat 10) (List.intercalate [Char.ofNat 10] (List.map Int.reprΔ elf)))) = elf TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
. unfold Function.comp simp only [String.toIntΔ_inv_IntreprΔ, List.map_id'']
elf : List ℤ h : ¬elf = [] ⊢ List.map (String.toIntΔ ∘ Int.reprΔ) elf = elf elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ []
elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ []
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ h : ¬elf = [] ⊢ List.map (String.toIntΔ ∘ Int.reprΔ) elf = elf elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ [] TACTIC:
https://github.com/jeremysalwen/advent_of_lean_2022.git
96035d07c4f9f133fe79fe02cdf5792b597881c0
One.lean
elfToString_roundtrip
[2357, 1]
[2370, 59]
. simp only [List.mem_map', ne_eq, decide_not, Bool.not_eq_true', decide_eq_false_iff_not, forall_exists_index, and_imp, forall_apply_eq_imp_iff₂, Int.reprΔ_ne_nil, not_false_iff, implies_true, forall_const]
elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ []
case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ []
Please generate a tactic in lean4 to solve the state. STATE: elf : List ℤ h : ¬elf = [] ⊢ ∀ (a : List Char), a ∈ List.map Int.reprΔ elf → decide (a ≠ []) = true case hx elf : List ℤ h : ¬elf = [] ⊢ ∀ (l : List Char), l ∈ List.map Int.reprΔ elf → ¬Char.ofNat 10 ∈ l case hls elf : List ℤ h : ¬elf = [] ⊢ List.map Int.reprΔ elf ≠ [] TACTIC: