url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elfToString_roundtrip | [2357, 1] | [2370, 59] | . simp only [List.mem_map', forall_exists_index, and_imp, forall_apply_eq_imp_iff₂]
intro a _
apply Int.not_newline_mem_reprΔ | 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 hls
elf : List ℤ
h : ¬elf = []
⊢ List.map Int.reprΔ elf ≠ [] | Please generate a tactic in lean4 to solve the state.
STATE:
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 [ne_eq, List.map_eq_nil, h, not_false_iff] | case hls
elf : List ℤ
h : ¬elf = []
⊢ List.map Int.reprΔ elf ≠ [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 | elves_roundtrip | [2372, 1] | [2406, 61] | induction elves with
| nil => simp only
| cons hd tail ih =>
unfold elvesToString stringToElves
cases tail with
| nil =>
simp only [beq_iff_eq, List.map, List.intercalate_singleton, ite_false, List.append_eq_nil, and_false]
rw [List.splitOnList_nonmatching, List.map_singleton, stringToElf_ignoresTrailing, elfToString_roundtrip]
intro contr
cases List.isInfix_append_split_left contr with
| inl h₁ =>
apply double_newline_not_isInfix_stringToElf hd h₁
| inr h₂ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero] at h₂
have newline_in_elf := List.isInfix_take_of_isInfix_append h₂
simp only [List.take, List.length_nil, zero_add, ge_iff_le, List.lastN_one_eq_getLast,List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_def] at newline_in_elf
apply newline_not_last_elfToString _ newline_in_elf
| cons mid tl =>
simp only [beq_iff_eq, List.map, List.map_eq_nil, IsEmpty.forall_iff,
List.join, ite_false, List.append_eq_nil, and_false, List.intercalate]
rw [List.append_assoc, List.append_assoc, ← List.append_assoc, List.splitOnList_progress, List.map_append,
List.map_singleton, elfToString_roundtrip, List.singleton_append, ←ih, stringToElves, elvesToString, List.intercalate]
. simp only [List.map_eq_nil, beq_iff_eq, List.map, ite_false, List.append_eq_nil, and_false]
. simp only [List.dropLast]
intro contr
cases List.isInfix_append_split_left contr with
| inl h₃ =>
apply double_newline_not_isInfix_stringToElf hd
apply h₃
| inr h₄ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.length_nil] at h₄
have last_contains := List.isInfix_take_of_isInfix_append h₄
simp only [List.take, ge_iff_le, List.lastN_one_eq_getLast, List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_iff] at last_contains
apply newline_not_last_elfToString _ last_contains | elves : List (List ℤ)
⊢ stringToElves (elvesToString elves) = elves | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
⊢ stringToElves (elvesToString elves) = elves
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only | case nil
⊢ stringToElves (elvesToString []) = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
⊢ stringToElves (elvesToString []) = []
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | unfold elvesToString stringToElves | case cons
hd : List ℤ
tail : List (List ℤ)
ih : stringToElves (elvesToString tail) = tail
⊢ stringToElves (elvesToString (hd :: tail)) = hd :: tail | case cons
hd : List ℤ
tail : List (List ℤ)
ih : stringToElves (elvesToString tail) = tail
⊢ (if
((if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]))) =
hd :: tail | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
hd : List ℤ
tail : List (List ℤ)
ih : stringToElves (elvesToString tail) = tail
⊢ stringToElves (elvesToString (hd :: tail)) = hd :: tail
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | cases tail with
| nil =>
simp only [beq_iff_eq, List.map, List.intercalate_singleton, ite_false, List.append_eq_nil, and_false]
rw [List.splitOnList_nonmatching, List.map_singleton, stringToElf_ignoresTrailing, elfToString_roundtrip]
intro contr
cases List.isInfix_append_split_left contr with
| inl h₁ =>
apply double_newline_not_isInfix_stringToElf hd h₁
| inr h₂ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero] at h₂
have newline_in_elf := List.isInfix_take_of_isInfix_append h₂
simp only [List.take, List.length_nil, zero_add, ge_iff_le, List.lastN_one_eq_getLast,List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_def] at newline_in_elf
apply newline_not_last_elfToString _ newline_in_elf
| cons mid tl =>
simp only [beq_iff_eq, List.map, List.map_eq_nil, IsEmpty.forall_iff,
List.join, ite_false, List.append_eq_nil, and_false, List.intercalate]
rw [List.append_assoc, List.append_assoc, ← List.append_assoc, List.splitOnList_progress, List.map_append,
List.map_singleton, elfToString_roundtrip, List.singleton_append, ←ih, stringToElves, elvesToString, List.intercalate]
. simp only [List.map_eq_nil, beq_iff_eq, List.map, ite_false, List.append_eq_nil, and_false]
. simp only [List.dropLast]
intro contr
cases List.isInfix_append_split_left contr with
| inl h₃ =>
apply double_newline_not_isInfix_stringToElf hd
apply h₃
| inr h₄ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.length_nil] at h₄
have last_contains := List.isInfix_take_of_isInfix_append h₄
simp only [List.take, ge_iff_le, List.lastN_one_eq_getLast, List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_iff] at last_contains
apply newline_not_last_elfToString _ last_contains | case cons
hd : List ℤ
tail : List (List ℤ)
ih : stringToElves (elvesToString tail) = tail
⊢ (if
((if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]))) =
hd :: tail | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
hd : List ℤ
tail : List (List ℤ)
ih : stringToElves (elvesToString tail) = tail
⊢ (if
((if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (hd :: tail == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: tail)) ++ [Char.ofNat 10]))) =
hd :: tail
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [beq_iff_eq, List.map, List.intercalate_singleton, ite_false, List.append_eq_nil, and_false] | case cons.nil
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ (if
((if ([hd] == []) = true then []
else List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString [hd]) ++ [Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if ([hd] == []) = true then []
else List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString [hd]) ++ [Char.ofNat 10]))) =
[hd] | case cons.nil
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ List.map stringToElf (List.splitOnList [Char.ofNat 10, Char.ofNat 10] (elfToString hd ++ [Char.ofNat 10])) = [hd] | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ (if
((if ([hd] == []) = true then []
else List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString [hd]) ++ [Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if ([hd] == []) = true then []
else List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString [hd]) ++ [Char.ofNat 10]))) =
[hd]
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | rw [List.splitOnList_nonmatching, List.map_singleton, stringToElf_ignoresTrailing, elfToString_roundtrip] | case cons.nil
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ List.map stringToElf (List.splitOnList [Char.ofNat 10, Char.ofNat 10] (elfToString hd ++ [Char.ofNat 10])) = [hd] | case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10] | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ List.map stringToElf (List.splitOnList [Char.ofNat 10, Char.ofNat 10] (elfToString hd ++ [Char.ofNat 10])) = [hd]
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | intro contr | case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10] | case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | cases List.isInfix_append_split_left contr with
| inl h₁ =>
apply double_newline_not_isInfix_stringToElf hd h₁
| inr h₂ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero] at h₂
have newline_in_elf := List.isInfix_take_of_isInfix_append h₂
simp only [List.take, List.length_nil, zero_add, ge_iff_le, List.lastN_one_eq_getLast,List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_def] at newline_in_elf
apply newline_not_last_elfToString _ newline_in_elf | case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | apply double_newline_not_isInfix_stringToElf hd h₁ | case cons.nil.h₁.inl
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁.inl
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₁ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero] at h₂ | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ :
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ :
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | have newline_in_elf := List.isInfix_take_of_isInfix_append h₂ | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [] + 1) (elfToString hd)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [List.take, List.length_nil, zero_add, ge_iff_le, List.lastN_one_eq_getLast,List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_def] at newline_in_elf | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [] + 1) (elfToString hd)
⊢ False | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [] + 1) (elfToString hd)
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | apply newline_not_last_elfToString _ newline_in_elf | case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.nil.h₁.inr
hd : List ℤ
ih : stringToElves (elvesToString []) = []
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₂ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN (List.length [] + 1) (elfToString hd) ++ [Char.ofNat 10]
newline_in_elf : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [beq_iff_eq, List.map, List.map_eq_nil, IsEmpty.forall_iff,
List.join, ite_false, List.append_eq_nil, and_false, List.intercalate] | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ (if
((if (hd :: mid :: tl == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: mid :: tl)) ++
[Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (hd :: mid :: tl == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: mid :: tl)) ++
[Char.ofNat 10]))) =
hd :: mid :: tl | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(elfToString hd ++
([Char.ofNat 10, Char.ofNat 10] ++
List.join
(List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl))) ++
[Char.ofNat 10])) =
hd :: mid :: tl | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ (if
((if (hd :: mid :: tl == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: mid :: tl)) ++
[Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (hd :: mid :: tl == []) = true then []
else
List.intercalate [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (hd :: mid :: tl)) ++
[Char.ofNat 10]))) =
hd :: mid :: tl
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | rw [List.append_assoc, List.append_assoc, ← List.append_assoc, List.splitOnList_progress, List.map_append,
List.map_singleton, elfToString_roundtrip, List.singleton_append, ←ih, stringToElves, elvesToString, List.intercalate] | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(elfToString hd ++
([Char.ofNat 10, Char.ofNat 10] ++
List.join
(List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl))) ++
[Char.ofNat 10])) =
hd :: mid :: tl | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ hd ::
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl)) ++
[Char.ofNat 10])) =
hd ::
if
((if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]))
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10] | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(elfToString hd ++
([Char.ofNat 10, Char.ofNat 10] ++
List.join
(List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl))) ++
[Char.ofNat 10])) =
hd :: mid :: tl
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | . simp only [List.map_eq_nil, beq_iff_eq, List.map, ite_false, List.append_eq_nil, and_false] | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ hd ::
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl)) ++
[Char.ofNat 10])) =
hd ::
if
((if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]))
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10] | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10] | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ hd ::
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (elfToString mid :: List.map elfToString tl)) ++
[Char.ofNat 10])) =
hd ::
if
((if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]) ==
[]) =
true then
[]
else
List.map stringToElf
(List.splitOnList [Char.ofNat 10, Char.ofNat 10]
(if (mid :: tl == []) = true then []
else
List.join (List.intersperse [Char.ofNat 10, Char.ofNat 10] (List.map elfToString (mid :: tl))) ++
[Char.ofNat 10]))
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10]
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | . simp only [List.dropLast]
intro contr
cases List.isInfix_append_split_left contr with
| inl h₃ =>
apply double_newline_not_isInfix_stringToElf hd
apply h₃
| inr h₄ =>
simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.length_nil] at h₄
have last_contains := List.isInfix_take_of_isInfix_append h₄
simp only [List.take, ge_iff_le, List.lastN_one_eq_getLast, List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_iff] at last_contains
apply newline_not_last_elfToString _ last_contains | case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
⊢ ¬[Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ List.dropLast [Char.ofNat 10, Char.ofNat 10]
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | apply double_newline_not_isInfix_stringToElf hd | case cons.cons.inl
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₃ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ False | case cons.cons.inl
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₃ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inl
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₃ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | apply h₃ | case cons.cons.inl
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₃ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inl
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₃ : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
⊢ [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [List.length_cons, List.length_singleton, ge_iff_le, Nat.succ_sub_succ_eq_sub, tsub_zero, List.length_nil] at h₄ | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ :
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ :
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN (List.length [Char.ofNat 10, Char.ofNat 10] - 1) (elfToString hd) ++ [Char.ofNat 10]
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | have last_contains := List.isInfix_take_of_isInfix_append h₄ | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
⊢ False | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN 1 (elfToString hd)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | simp only [List.take, ge_iff_le, List.lastN_one_eq_getLast, List.singleton_isInfix_iff_mem, Option.mem_toList, Option.mem_iff] at last_contains | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN 1 (elfToString hd)
⊢ False | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains :
List.take (List.length [Char.ofNat 10, Char.ofNat 10] - List.length [Char.ofNat 10])
[Char.ofNat 10, Char.ofNat 10] <:+:
List.lastN 1 (elfToString hd)
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | elves_roundtrip | [2372, 1] | [2406, 61] | apply newline_not_last_elfToString _ last_contains | case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.cons.inr
hd mid : List ℤ
tl : List (List ℤ)
ih : stringToElves (elvesToString (mid :: tl)) = mid :: tl
contr : [Char.ofNat 10, Char.ofNat 10] <:+: elfToString hd ++ [Char.ofNat 10]
h₄ : [Char.ofNat 10, Char.ofNat 10] <:+: List.lastN 1 (elfToString hd) ++ [Char.ofNat 10]
last_contains : List.getLast? (elfToString hd) = some (Char.ofNat 10)
⊢ False
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | unfold isSolutionModel | ⊢ isSolutionModel solveOneModel | ⊢ ∀ (elves : List (List ℤ)) (elf : List ℤ), elf ∈ elves → solveOneModel elves ≥ List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ isSolutionModel solveOneModel
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | intro elves elf elfin | ⊢ ∀ (elves : List (List ℤ)) (elf : List ℤ), elf ∈ elves → solveOneModel elves ≥ List.sum elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ solveOneModel elves ≥ List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (elves : List (List ℤ)) (elf : List ℤ), elf ∈ elves → solveOneModel elves ≥ List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | unfold solveOneModel | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ solveOneModel elves ≥ List.sum elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ solveOneModel elves ≥ List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | have hsumin: List.sum elf ∈ (List.map List.sum) elves := by apply List.mem_map'.2; exists elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | have z:= List.le_maximum_of_mem' hsumin | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | apply WithBot.coe_le_coe.1 | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ ↑(List.sum elf) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves))) | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ WithBot.unbot' 0 (List.maximum (List.map List.sum elves)) ≥ List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | apply le_trans z | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ ↑(List.sum elf) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves))) | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ List.maximum (List.map List.sum elves) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves))) | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ ↑(List.sum elf) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves)))
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | apply WithBot.le_coe_unbot' | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ List.maximum (List.map List.sum elves) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
hsumin : List.sum elf ∈ List.map List.sum elves
z : ↑(List.sum elf) ≤ List.maximum (List.map List.sum elves)
⊢ List.maximum (List.map List.sum elves) ≤ ↑(WithBot.unbot' 0 (List.maximum (List.map List.sum elves)))
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | apply List.mem_map'.2 | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ List.sum elf ∈ List.map List.sum elves | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ ∃ a, a ∈ elves ∧ List.sum a = List.sum elf | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ List.sum elf ∈ List.map List.sum elves
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolutionModel_solveOneModel | [2422, 1] | [2430, 30] | exists elf | elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ ∃ a, a ∈ elves ∧ List.sum a = List.sum elf | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
elves : List (List ℤ)
elf : List ℤ
elfin : elf ∈ elves
⊢ ∃ a, a ∈ elves ∧ List.sum a = List.sum elf
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolution_solveOne | [2432, 1] | [2434, 71] | unfold isSolution solveOne | ⊢ isSolution solveOne | ⊢ isSolutionModel ((fun input => solveOneModel (stringToElves input)) ∘ elvesToString) | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ isSolution solveOne
TACTIC:
|
https://github.com/jeremysalwen/advent_of_lean_2022.git | 96035d07c4f9f133fe79fe02cdf5792b597881c0 | One.lean | isSolution_solveOne | [2432, 1] | [2434, 71] | simp [Function.comp, isSolutionModel_solveOneModel, elves_roundtrip] | ⊢ isSolutionModel ((fun input => solveOneModel (stringToElves input)) ∘ elvesToString) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ isSolutionModel ((fun input => solveOneModel (stringToElves input)) ∘ elvesToString)
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | refine ⟨?_, ?_⟩ | t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | case refine_1
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1
case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | { use 3380*t^2 + 416*t + 13
ring } | case refine_1
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1
case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1
case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | { use 1300*t^2 + 160*t + 5
ring } | case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | use 3380*t^2 + 416*t + 13 | case refine_1
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1 | case refine_1
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 5 * (3380 * t ^ 2 + 416 * t + 13) | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
t : ℕ
⊢ 5 ∣ 4 * (65 * t + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | ring | case refine_1
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 5 * (3380 * t ^ 2 + 416 * t + 13) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 5 * (3380 * t ^ 2 + 416 * t + 13)
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | use 1300*t^2 + 160*t + 5 | case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1 | case refine_2
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 13 * (1300 * t ^ 2 + 160 * t + 5) | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
t : ℕ
⊢ 13 ∣ 4 * (65 * t + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | divides_of_cong_four | [32, 1] | [38, 11] | ring | case refine_2
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 13 * (1300 * t ^ 2 + 160 * t + 5) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
t : ℕ
⊢ 4 * (65 * t + 4) ^ 2 + 1 = 13 * (1300 * t ^ 2 + 160 * t + 5)
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | intro N | ⊢ ∀ (N : ℕ), ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 | N : ℕ
⊢ ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | use 65 * N + 4 | N : ℕ
⊢ ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 | N : ℕ
⊢ 65 * N + 4 > N ∧ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
N : ℕ
⊢ ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | refine ⟨?_, ?_⟩ | N : ℕ
⊢ 65 * N + 4 > N ∧ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | case refine_1
N : ℕ
⊢ 65 * N + 4 > N
case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
N : ℕ
⊢ 65 * N + 4 > N ∧ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | { linarith } | case refine_1
N : ℕ
⊢ 65 * N + 4 > N
case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
N : ℕ
⊢ 65 * N + 4 > N
case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | { apply divides_of_cong_four } | case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | linarith | case refine_1
N : ℕ
⊢ 65 * N + 4 > N | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
N : ℕ
⊢ 65 * N + 4 > N
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | arb_large_soln | [41, 1] | [47, 33] | apply divides_of_cong_four | case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
N : ℕ
⊢ 5 ∣ 4 * (65 * N + 4) ^ 2 + 1 ∧ 13 ∣ 4 * (65 * N + 4) ^ 2 + 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | refine ⟨?_, ?_⟩ | S : Set ℕ
⊢ Set.Infinite S ↔ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | case refine_1
S : Set ℕ
⊢ Set.Infinite S → ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S | Please generate a tactic in lean4 to solve the state.
STATE:
S : Set ℕ
⊢ Set.Infinite S ↔ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | { intro h
have h2 := Set.Infinite.exists_nat_lt h
intro n
rcases h2 n with ⟨m, hm, h3⟩
use m
exact ⟨h3, hm⟩
} | case refine_1
S : Set ℕ
⊢ Set.Infinite S → ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S | case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Set ℕ
⊢ Set.Infinite S → ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | { contrapose!
intro h
rw [Set.not_infinite] at h
let S2 : Finset ℕ := Set.Finite.toFinset h
have h2 : ∃ B, ∀n ∈ S2, n ≤ B
{ use Finset.sup S2 id
intro n hn
apply Finset.le_sup hn }
cases' h2 with N hN
use N
have h3 : ∀n : ℕ, n ∈ S ↔ n ∈ S2 := by
intro n
exact (Set.Finite.mem_toFinset h).symm
intros n hn h4
rw [h3] at h4
specialize hN n h4
linarith
} | case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intro h | case refine_1
S : Set ℕ
⊢ Set.Infinite S → ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | case refine_1
S : Set ℕ
h : Set.Infinite S
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Set ℕ
⊢ Set.Infinite S → ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | have h2 := Set.Infinite.exists_nat_lt h | case refine_1
S : Set ℕ
h : Set.Infinite S
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Set ℕ
h : Set.Infinite S
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intro n | case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S | case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n : ℕ
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | rcases h2 n with ⟨m, hm, h3⟩ | case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n : ℕ
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S | case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n : ℕ
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | use m | case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S | case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ m > n ∧ m ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ ∃ n_1, n_1 > n ∧ n_1 ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | exact ⟨h3, hm⟩ | case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ m > n ∧ m ∈ S | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_1.intro.intro
S : Set ℕ
h : Set.Infinite S
h2 : ∀ (n : ℕ), ∃ m, m ∈ S ∧ n < m
n m : ℕ
hm : m ∈ S
h3 : n < m
⊢ m > n ∧ m ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | contrapose! | case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S | case refine_2
S : Set ℕ
⊢ ¬Set.Infinite S → ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
⊢ (∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S) → Set.Infinite S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intro h | case refine_2
S : Set ℕ
⊢ ¬Set.Infinite S → ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2
S : Set ℕ
h : ¬Set.Infinite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
⊢ ¬Set.Infinite S → ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | rw [Set.not_infinite] at h | case refine_2
S : Set ℕ
h : ¬Set.Infinite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2
S : Set ℕ
h : Set.Finite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
h : ¬Set.Infinite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | let S2 : Finset ℕ := Set.Finite.toFinset h | case refine_2
S : Set ℕ
h : Set.Finite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
h : Set.Finite S
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | have h2 : ∃ B, ∀n ∈ S2, n ≤ B | case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | { use Finset.sup S2 id
intro n hn
apply Finset.le_sup hn } | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | cases' h2 with N hN | case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
h2 : ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | use N | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∃ N, ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | have h3 : ∀n : ℕ, n ∈ S ↔ n ∈ S2 := by
intro n
exact (Set.Finite.mem_toFinset h).symm | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intros n hn h4 | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
⊢ ∀ (n : ℕ), n > N → ¬n ∈ S
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | rw [h3] at h4 | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S
⊢ False | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S
⊢ False
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | specialize hN n h4 | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
⊢ False | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
hN : n ≤ N
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
⊢ False
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | linarith | case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
hN : n ≤ N
⊢ False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case refine_2.intro
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
h3 : ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
n : ℕ
hn : n > N
h4 : n ∈ S2
hN : n ≤ N
⊢ False
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | use Finset.sup S2 id | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∀ (n : ℕ), n ∈ S2 → n ≤ Finset.sup S2 id | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∃ B, ∀ (n : ℕ), n ∈ S2 → n ≤ B
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intro n hn | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∀ (n : ℕ), n ∈ S2 → n ≤ Finset.sup S2 id | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
n : ℕ
hn : n ∈ S2
⊢ n ≤ Finset.sup S2 id | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
⊢ ∀ (n : ℕ), n ∈ S2 → n ≤ Finset.sup S2 id
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | apply Finset.le_sup hn | case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
n : ℕ
hn : n ∈ S2
⊢ n ≤ Finset.sup S2 id | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
n : ℕ
hn : n ∈ S2
⊢ n ≤ Finset.sup S2 id
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | intro n | S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∀ (n : ℕ), n ∈ S ↔ n ∈ S2 | S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
n : ℕ
⊢ n ∈ S ↔ n ∈ S2 | Please generate a tactic in lean4 to solve the state.
STATE:
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
⊢ ∀ (n : ℕ), n ∈ S ↔ n ∈ S2
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_iff_arb_large | [51, 1] | [77, 4] | exact (Set.Finite.mem_toFinset h).symm | S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
n : ℕ
⊢ n ∈ S ↔ n ∈ S2 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
S : Set ℕ
h : Set.Finite S
S2 : Finset ℕ := Set.Finite.toFinset h
N : ℕ
hN : ∀ (n : ℕ), n ∈ S2 → n ≤ N
n : ℕ
⊢ n ∈ S ↔ n ∈ S2
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_set_of_solutions | [81, 1] | [83, 23] | rw [infinite_iff_arb_large] | ⊢ Set.Infinite { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 } | ⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 } | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ Set.Infinite { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 }
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NumberTheory3Solutions.lean | infinite_set_of_solutions | [81, 1] | [83, 23] | exact arb_large_soln | ⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 }
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.mul_eq_of_eq_inv_mul | [43, 1] | [45, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
h : b = a⁻¹ * c
⊢ a * b = c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
h : b = a⁻¹ * c
⊢ a * b = c
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.mul_one | [48, 1] | [50, 8] | sorry | G : Type
inst✝ : MyGroup G
a✝ b c a : G
⊢ a * 1 = a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a✝ b c a : G
⊢ a * 1 = a
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.mul_inv_self | [53, 1] | [54, 8] | sorry | G : Type
inst✝ : MyGroup G
a✝ b c a : G
⊢ a * a⁻¹ = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a✝ b c a : G
⊢ a * a⁻¹ = 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.inv_mul_cancel_left | [80, 1] | [81, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
⊢ a⁻¹ * (a * b) = b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
⊢ a⁻¹ * (a * b) = b
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.mul_inv_cancel_left | [83, 1] | [84, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
⊢ a * (a⁻¹ * b) = b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
⊢ a * (a⁻¹ * b) = b
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.left_inv_eq_right_inv | [93, 1] | [95, 8] | sorry | G : Type
inst✝ : MyGroup G
a✝ b✝ c✝ a b c : G
h1 : b * a = 1
h2 : a * c = 1
⊢ b = c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a✝ b✝ c✝ a b c : G
h1 : b * a = 1
h2 : a * c = 1
⊢ b = c
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.one_inv | [105, 1] | [106, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
⊢ 1⁻¹ = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
⊢ 1⁻¹ = 1
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.inv_inv | [108, 1] | [109, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
⊢ a⁻¹⁻¹ = a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
⊢ a⁻¹⁻¹ = a
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/GroupTheory.lean | MyGroup.mul_inv_rev | [111, 1] | [112, 8] | sorry | G : Type
inst✝ : MyGroup G
a b c : G
⊢ (a * b)⁻¹ = b⁻¹ * a⁻¹ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
G : Type
inst✝ : MyGroup G
a b c : G
⊢ (a * b)⁻¹ = b⁻¹ * a⁻¹
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.add_zero | [59, 1] | [60, 6] | rfl | n : MyNat
⊢ n + 0 = n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n : MyNat
⊢ n + 0 = n
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.add_succ | [63, 1] | [64, 6] | rfl | n m : MyNat
⊢ n + succ m = succ (n + m) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
n m : MyNat
⊢ n + succ m = succ (n + m)
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.easy | [69, 1] | [70, 6] | rfl | ⊢ two + two = four | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ two + two = four
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.easy2 | [73, 1] | [74, 6] | rfl | ⊢ two + one = one + two | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ two + one = one + two
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | induction' n with d hd | n : MyNat
⊢ 0 + n = n | case zero
⊢ 0 + 0 = 0
case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d | Please generate a tactic in lean4 to solve the state.
STATE:
n : MyNat
⊢ 0 + n = n
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | { rfl } | case zero
⊢ 0 + 0 = 0
case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d | case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
⊢ 0 + 0 = 0
case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | { rw [add_succ] rw [hd] } | case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | rfl | case zero
⊢ 0 + 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
⊢ 0 + 0 = 0
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | rw [add_succ] | case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d | case succ
d : MyNat
hd : 0 + d = d
⊢ succ (0 + d) = succ d | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
d : MyNat
hd : 0 + d = d
⊢ 0 + succ d = succ d
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.zero_add | [88, 1] | [92, 14] | rw [hd] | case succ
d : MyNat
hd : 0 + d = d
⊢ succ (0 + d) = succ d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
d : MyNat
hd : 0 + d = d
⊢ succ (0 + d) = succ d
TACTIC:
|
https://github.com/kbuzzard/IISc-experiments.git | f2f2d7d14b3ec1957fcdd38cc0e3657df6850047 | IIScExperiments/Solutions/NatAddMulSolutions.lean | MyNat.succ_add | [96, 1] | [101, 34] | induction' b with d hd | a b : MyNat
⊢ succ a + b = succ (a + b) | case zero
a : MyNat
⊢ succ a + 0 = succ (a + 0)
case succ
a d : MyNat
hd : succ a + d = succ (a + d)
⊢ succ a + succ d = succ (a + succ d) | Please generate a tactic in lean4 to solve the state.
STATE:
a b : MyNat
⊢ succ a + b = succ (a + b)
TACTIC:
|
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