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/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt.intro | [397, 11] | [398, 47] | exact Pos.lt_add_right x z | x y z : Pos
h : x + z = y
⊢ x < x + z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
h : x + z = y
⊢ x < x + z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_stop | [9, 1] | [12, 17] | unfold extract | α : Type u_1
as : List α
stop : Nat
⊢ as.extract stop stop = [] | α : Type u_1
as : List α
stop : Nat
⊢ take (stop - stop) (drop stop as) = [] | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
stop : Nat
⊢ as.extract stop stop = []
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_stop | [9, 1] | [12, 17] | rw [Nat.sub_self] | α : Type u_1
as : List α
stop : Nat
⊢ take (stop - stop) (drop stop as) = [] | α : Type u_1
as : List α
stop : Nat
⊢ take 0 (drop stop as) = [] | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
stop : Nat
⊢ take (stop - stop) (drop stop as) = []
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_stop | [9, 1] | [12, 17] | rw [take_zero] | α : Type u_1
as : List α
stop : Nat
⊢ take 0 (drop stop as) = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
stop : Nat
⊢ take 0 (drop stop as) = []
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | unfold extract | α : Type u_1
as : List α
start stop : Nat
hstart : start < stop
hstop : stop ≤ as.length
⊢ as.extract start stop = as.get ⟨start, ⋯⟩ :: as.extract (start + 1) stop | α : Type u_1
as : List α
start stop : Nat
hstart : start < stop
hstop : stop ≤ as.length
⊢ take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
start stop : Nat
hstart : start < stop
hstop : stop ≤ as.length
⊢ as.extract start stop = as.get ⟨start, ⋯⟩ :: as.extract (start + 1) stop
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | induction start, stop using Nat.recDiag generalizing as with
| zero_zero => contradiction
| succ_zero start => contradiction
| zero_succ stop => match as with | a :: as => simp
| succ_succ start stop ih =>
match as with
| a :: as =>
simp
rw [ih]
exact Nat.lt_of_succ_lt_succ hstart
exact Nat.le_of_su... | α : Type u_1
as : List α
start stop : Nat
hstart : start < stop
hstop : stop ≤ as.length
⊢ take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
start stop : Nat
hstart : start < stop
hstop : stop ≤ as.length
⊢ take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | contradiction | case zero_zero
α : Type u_1
as : List α
hstart : 0 < 0
hstop : 0 ≤ as.length
⊢ take (0 - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (0 - (0 + 1)) (drop (0 + 1) as) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero_zero
α : Type u_1
as : List α
hstart : 0 < 0
hstop : 0 ≤ as.length
⊢ take (0 - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (0 - (0 + 1)) (drop (0 + 1) as)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | contradiction | case succ_zero
α : Type u_1
start : Nat
a✝ :
∀ (as : List α) (hstart : start < 0) (hstop : 0 ≤ as.length),
take (0 - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (0 - (start + 1)) (drop (start + 1) as)
as : List α
hstart : start + 1 < 0
hstop : 0 ≤ as.length
⊢ take (0 - (start + 1)) (drop (start + 1) as) =
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_zero
α : Type u_1
start : Nat
a✝ :
∀ (as : List α) (hstart : start < 0) (hstop : 0 ≤ as.length),
take (0 - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (0 - (start + 1)) (drop (start + 1) as)
as : List α
hstart : start + 1 < 0
hstop : 0 ... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | match as with | a :: as => simp | case zero_succ
α : Type u_1
stop : Nat
a✝ :
∀ (as : List α) (hstart : 0 < stop) (hstop : stop ≤ as.length),
take (stop - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (stop - (0 + 1)) (drop (0 + 1) as)
as : List α
hstart : 0 < stop + 1
hstop : stop + 1 ≤ as.length
⊢ take (stop + 1 - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: tak... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case zero_succ
α : Type u_1
stop : Nat
a✝ :
∀ (as : List α) (hstart : 0 < stop) (hstop : stop ≤ as.length),
take (stop - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (stop - (0 + 1)) (drop (0 + 1) as)
as : List α
hstart : 0 < stop + 1
hstop : stop + 1 ≤ as.le... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | simp | α : Type u_1
stop : Nat
a✝ :
∀ (as : List α) (hstart : 0 < stop) (hstop : stop ≤ as.length),
take (stop - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (stop - (0 + 1)) (drop (0 + 1) as)
as✝ : List α
hstart : 0 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).length
⊢ take (stop + 1 - 0) (drop 0 (a :: as)) = (a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
stop : Nat
a✝ :
∀ (as : List α) (hstart : 0 < stop) (hstop : stop ≤ as.length),
take (stop - 0) (drop 0 as) = as.get ⟨0, ⋯⟩ :: take (stop - (0 + 1)) (drop (0 + 1) as)
as✝ : List α
hstart : 0 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | match as with
| a :: as =>
simp
rw [ih]
exact Nat.lt_of_succ_lt_succ hstart
exact Nat.le_of_succ_le_succ hstop | case succ_succ
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as : List α
hstart : start + 1 < stop + 1
hstop : stop + 1 ≤ as.length
⊢ take (stop + 1 -... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_succ
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as : List α
hstart : start +... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | simp | α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).length
⊢ take ... | α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).length
⊢ take ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | rw [ih] | α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).length
⊢ take ... | case hstart
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).le... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | exact Nat.lt_of_succ_lt_succ hstart | case hstart
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).le... | case hstop
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).len... | Please generate a tactic in lean4 to solve the state.
STATE:
case hstart
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_step | [14, 1] | [27, 41] | exact Nat.le_of_succ_le_succ hstop | case hstop
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 < stop + 1
a : α
as : List α
hstop : stop + 1 ≤ (a :: as).len... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hstop
α : Type u_1
start stop : Nat
ih :
∀ (as : List α) (hstart : start < stop) (hstop : stop ≤ as.length),
take (stop - start) (drop start as) = as.get ⟨start, ⋯⟩ :: take (stop - (start + 1)) (drop (start + 1) as)
as✝ : List α
hstart : start + 1 ... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_all | [29, 1] | [33, 19] | unfold extract | α : Type u_1
as : List α
⊢ as.extract 0 as.length = as | α : Type u_1
as : List α
⊢ take (as.length - 0) (drop 0 as) = as | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
⊢ as.extract 0 as.length = as
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_all | [29, 1] | [33, 19] | rw [Nat.sub_zero] | α : Type u_1
as : List α
⊢ take (as.length - 0) (drop 0 as) = as | α : Type u_1
as : List α
⊢ take as.length (drop 0 as) = as | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
⊢ take (as.length - 0) (drop 0 as) = as
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_all | [29, 1] | [33, 19] | rw [List.drop] | α : Type u_1
as : List α
⊢ take as.length (drop 0 as) = as | α : Type u_1
as : List α
⊢ take as.length as = as | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
⊢ take as.length (drop 0 as) = as
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.extract_all | [29, 1] | [33, 19] | rw [take_length] | α : Type u_1
as : List α
⊢ take as.length as = as | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
as : List α
⊢ take as.length as = as
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.pure_bind | [51, 9] | [51, 119] | rw [cons_bind, nil_bind, append_nil] | α : Type u_1
β : Type u_2
f : α → List β
a : α
⊢ [a].bind f = f a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
a : α
⊢ [a].bind f = f a
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.bind_assoc | [53, 1] | [56, 61] | induction as with
| nil => rfl
| cons a as H => rw [cons_bind, cons_bind, append_bind, H] | α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
as : List α
⊢ (as.bind f).bind g = as.bind fun a => (f a).bind g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
as : List α
⊢ (as.bind f).bind g = as.bind fun a => (f a).bind g
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.bind_assoc | [53, 1] | [56, 61] | rfl | case nil
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
⊢ ([].bind f).bind g = [].bind fun a => (f a).bind g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
⊢ ([].bind f).bind g = [].bind fun a => (f a).bind g
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/List.lean | List.bind_assoc | [53, 1] | [56, 61] | rw [cons_bind, cons_bind, append_bind, H] | case cons
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
a : α
as : List α
H : (as.bind f).bind g = as.bind fun a => (f a).bind g
⊢ ((a :: as).bind f).bind g = (a :: as).bind fun a => (f a).bind g | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
α : Type u_1
β : Type u_2
γ : Type u_3
f : α → List β
g : β → List γ
a : α
as : List α
H : (as.bind f).bind g = as.bind fun a => (f a).bind g
⊢ ((a :: as).bind f).bind g = (a :: as).bind fun a => (f a).bind g
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.option_eq_iff_eq_unoption | [27, 1] | [30, 37] | constructor | α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ option i = k ↔ i = k.unoption | case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ option i = k → i = k.unoption
case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ i = k.unoption → option i = k | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ option i = k ↔ i = k.unoption
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.option_eq_iff_eq_unoption | [27, 1] | [30, 37] | intro h | case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ option i = k → i = k.unoption | case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : option i = k
⊢ i = k.unoption | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ option i = k → i = k.unoption
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.option_eq_iff_eq_unoption | [27, 1] | [30, 37] | rw [←h, unoption_option] | case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : option i = k
⊢ i = k.unoption | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : option i = k
⊢ i = k.unoption
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.option_eq_iff_eq_unoption | [27, 1] | [30, 37] | intro h | case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ i = k.unoption → option i = k | case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : i = k.unoption
⊢ option i = k | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
⊢ i = k.unoption → option i = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.option_eq_iff_eq_unoption | [27, 1] | [30, 37] | rw [h, option_unoption] | case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : i = k.unoption
⊢ option i = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α✝ : Type u_1
xs : List α✝
i : Option xs.Index
k : xs.option.Index
h : i = k.unoption
⊢ option i = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.unoption_eq_iff_eq_option | [32, 1] | [35, 37] | constructor | α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k.unoption = i ↔ k = option i | case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k.unoption = i → k = option i
case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k = option i → k.unoption = i | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k.unoption = i ↔ k = option i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.unoption_eq_iff_eq_option | [32, 1] | [35, 37] | intro h | case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k.unoption = i → k = option i | case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k.unoption = i
⊢ k = option i | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k.unoption = i → k = option i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.unoption_eq_iff_eq_option | [32, 1] | [35, 37] | rw [←h, option_unoption] | case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k.unoption = i
⊢ k = option i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k.unoption = i
⊢ k = option i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.unoption_eq_iff_eq_option | [32, 1] | [35, 37] | intro h | case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k = option i → k.unoption = i | case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k = option i
⊢ k.unoption = i | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
⊢ k = option i → k.unoption = i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.unoption_eq_iff_eq_option | [32, 1] | [35, 37] | rw [h, unoption_option] | case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k = option i
⊢ k.unoption = i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α✝ : Type u_1
xs : List α✝
k : xs.option.Index
i : Option xs.Index
h : k = option i
⊢ k.unoption = i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.val_option | [46, 1] | [49, 35] | match i with
| none => rfl
| some i => rw [option, val_map] | α : Type u_1
xs : List α
i : Option xs.Index
⊢ (match i with
| none => none
| some i => some i.val) =
(option i).val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
xs : List α
i : Option xs.Index
⊢ (match i with
| none => none
| some i => some i.val) =
(option i).val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.val_option | [46, 1] | [49, 35] | rfl | α : Type u_1
xs : List α
i : Option xs.Index
⊢ (match none with
| none => none
| some i => some i.val) =
(option none).val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
xs : List α
i : Option xs.Index
⊢ (match none with
| none => none
| some i => some i.val) =
(option none).val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.val_option | [46, 1] | [49, 35] | rw [option, val_map] | α : Type u_1
xs : List α
i✝ : Option xs.Index
i : xs.Index
⊢ (match some i with
| none => none
| some i => some i.val) =
(option (some i)).val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
xs : List α
i✝ : Option xs.Index
i : xs.Index
⊢ (match some i with
| none => none
| some i => some i.val) =
(option (some i)).val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Option.lean | List.Index.val_unoption | [51, 1] | [52, 55] | rw [←option_unoption k, val_option, unoption_option] | α : Type u_1
xs : List α
k : xs.option.Index
⊢ k.val =
match k.unoption with
| none => none
| some k => some k.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
xs : List α
k : xs.option.Index
⊢ k.val =
match k.unoption with
| none => none
| some k => some k.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_bind | [16, 1] | [18, 25] | induction i with simp only [bind, unbind, unappend_append]
| tail _ ih => rw [ih] | α : Type u_1
β : Type u_2
f : α → List β
xs : List α
i : xs.Index
j : (f i.val).Index
⊢ unbind f (bind f ⟨i, j⟩) = ⟨i, j⟩ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
xs : List α
i : xs.Index
j : (f i.val).Index
⊢ unbind f (bind f ⟨i, j⟩) = ⟨i, j⟩
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_bind | [16, 1] | [18, 25] | rw [ih] | case tail
α : Type u_1
β : Type u_2
f : α → List β
xs xs✝ : List α
x✝ : α
a✝ : xs✝.Index
ih : ∀ (j : (f a✝.val).Index), unbind f (bind f ⟨a✝, j⟩) = ⟨a✝, j⟩
j : (f a✝.tail.val).Index
⊢ ⟨(unbind f (bind f ⟨a✝, j⟩)).fst.tail, (unbind f (bind f ⟨a✝, j⟩)).snd⟩ = ⟨a✝.tail, j⟩ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case tail
α : Type u_1
β : Type u_2
f : α → List β
xs xs✝ : List α
x✝ : α
a✝ : xs✝.Index
ih : ∀ (j : (f a✝.val).Index), unbind f (bind f ⟨a✝, j⟩) = ⟨a✝, j⟩
j : (f a✝.tail.val).Index
⊢ ⟨(unbind f (bind f ⟨a✝, j⟩)).fst.tail, (unbind f (bind f ⟨a✝, j⟩)).snd⟩ = ⟨... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | induction xs with
| nil => contradiction
| cons x xs ih =>
rw [unbind]
split
next h => rw [bind, append_inl, ←h, append_unappend]
next h => rw [bind, append_inr, ih, ←h, append_unappend] | α : Type u_1
β : Type u_2
f : α → List β
xs : List α
k : (xs.bind f).Index
⊢ bind f (unbind f k) = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
xs : List α
k : (xs.bind f).Index
⊢ bind f (unbind f k) = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | contradiction | case nil
α : Type u_1
β : Type u_2
f : α → List β
k : ([].bind f).Index
⊢ bind f (unbind f k) = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
α : Type u_1
β : Type u_2
f : α → List β
k : ([].bind f).Index
⊢ bind f (unbind f k) = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | rw [unbind] | case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
⊢ bind f (unbind f k) = k | case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
⊢ bind f
(match k.unappend with
| Sum.inl j => ⟨head, j⟩
| Sum.inr k => ⟨(unbind f k).fst.tail, (unbind f k).snd⟩) =
k | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
⊢ bind f (unbind f k) = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | split | case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
⊢ bind f
(match k.unappend with
| Sum.inl j => ⟨head, j⟩
| Sum.inr k => ⟨(unbind f k).fst.tail, (unbind f k).snd⟩) =
k | case cons.h_1
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
j✝ : (f x).Index
heq✝ : k.unappend = Sum.inl j✝
⊢ bind f ⟨head, j✝⟩ = k
case cons.h_2
α : Type u_1
β : Type u_2
f : α → ... | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
⊢ bind f
(match k.unappend with
| Sum.inl j => ⟨head, j⟩
| Sum.inr k => ⟨(unbind f k).f... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | next h => rw [bind, append_inl, ←h, append_unappend] | case cons.h_1
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
j✝ : (f x).Index
heq✝ : k.unappend = Sum.inl j✝
⊢ bind f ⟨head, j✝⟩ = k
case cons.h_2
α : Type u_1
β : Type u_2
f : α → ... | case cons.h_2
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
k✝ : (map f xs).join.Index
heq✝ : k.unappend = Sum.inr k✝
⊢ bind f ⟨(unbind f k✝).fst.tail, (unbind f k✝).snd⟩ = k | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.h_1
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
j✝ : (f x).Index
heq✝ : k.unappend = Sum.inl j✝
⊢ bind f ⟨he... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | next h => rw [bind, append_inr, ih, ←h, append_unappend] | case cons.h_2
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
k✝ : (map f xs).join.Index
heq✝ : k.unappend = Sum.inr k✝
⊢ bind f ⟨(unbind f k✝).fst.tail, (unbind f k✝).snd⟩ = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons.h_2
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
k✝ : (map f xs).join.Index
heq✝ : k.unappend = Sum.inr k✝
⊢ ... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | rw [bind, append_inl, ←h, append_unappend] | α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
j✝ : (f x).Index
h : k.unappend = Sum.inl j✝
⊢ bind f ⟨head, j✝⟩ = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
j✝ : (f x).Index
h : k.unappend = Sum.inl j✝
⊢ bind f ⟨head, j✝⟩ = k
TACTI... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_unbind | [20, 1] | [27, 61] | rw [bind, append_inr, ih, ←h, append_unappend] | α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
k✝ : (map f xs).join.Index
h : k.unappend = Sum.inr k✝
⊢ bind f ⟨(unbind f k✝).fst.tail, (unbind f k✝).snd⟩ = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (k : (xs.bind f).Index), bind f (unbind f k) = k
k : ((x :: xs).bind f).Index
x✝ : (f x).Index ⊕ (map f xs).join.Index
k✝ : (map f xs).join.Index
h : k.unappend = Sum.inr k✝
⊢ bind f ⟨(unbind f... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_eq_iff_eq_unbind | [29, 1] | [32, 33] | constructor | α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ bind f i = j ↔ i = unbind f j | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ bind f i = j → i = unbind f j
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ i = unbind f j → bind f i = j | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ bind f i = j ↔ i = unbind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_eq_iff_eq_unbind | [29, 1] | [32, 33] | intro h | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ bind f i = j → i = unbind f j | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : bind f i = j
⊢ i = unbind f j | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ bind f i = j → i = unbind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_eq_iff_eq_unbind | [29, 1] | [32, 33] | rw [←h, unbind_bind] | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : bind f i = j
⊢ i = unbind f j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : bind f i = j
⊢ i = unbind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_eq_iff_eq_unbind | [29, 1] | [32, 33] | intro h | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ i = unbind f j → bind f i = j | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : i = unbind f j
⊢ bind f i = j | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
⊢ i = unbind f j → bind f i = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.bind_eq_iff_eq_unbind | [29, 1] | [32, 33] | rw [h, bind_unbind] | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : i = unbind f j
⊢ bind f i = j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
j : (xs.bind f).Index
h : i = unbind f j
⊢ bind f i = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_eq_iff_eq_bind | [34, 1] | [37, 33] | constructor | α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ unbind f i = j ↔ i = bind f j | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ unbind f i = j → i = bind f j
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ i = bind f j → unbind f i = j | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ unbind f i = j ↔ i = bind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_eq_iff_eq_bind | [34, 1] | [37, 33] | intro h | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ unbind f i = j → i = bind f j | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : unbind f i = j
⊢ i = bind f j | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ unbind f i = j → i = bind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_eq_iff_eq_bind | [34, 1] | [37, 33] | rw [←h, bind_unbind] | case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : unbind f i = j
⊢ i = bind f j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : unbind f i = j
⊢ i = bind f j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_eq_iff_eq_bind | [34, 1] | [37, 33] | intro h | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ i = bind f j → unbind f i = j | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : i = bind f j
⊢ unbind f i = j | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
⊢ i = bind f j → unbind f i = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.unbind_eq_iff_eq_bind | [34, 1] | [37, 33] | rw [h, unbind_bind] | case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : i = bind f j
⊢ unbind f i = j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (xs.bind f).Index
j : (i : xs.Index) × (f i.val).Index
h : i = bind f j
⊢ unbind f i = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | induction xs with
| nil => cases i; contradiction
| cons x xs ih =>
match i with
| ⟨head, j⟩ => rw [bind, val_append_inl]
| ⟨tail i, j⟩ => rw [bind, val_append_inr, ih] | α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
f : α → List β
i : (i : xs.Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | cases i | case nil
α : Type u_1
β : Type u_2
f : α → List β
i : (i : [].Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val | case nil.mk
α : Type u_1
β : Type u_2
f : α → List β
fst✝ : [].Index
snd✝ : (f fst✝.val).Index
⊢ (bind f ⟨fst✝, snd✝⟩).val = ⟨fst✝, snd✝⟩.snd.val | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
α : Type u_1
β : Type u_2
f : α → List β
i : (i : [].Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | contradiction | case nil.mk
α : Type u_1
β : Type u_2
f : α → List β
fst✝ : [].Index
snd✝ : (f fst✝.val).Index
⊢ (bind f ⟨fst✝, snd✝⟩).val = ⟨fst✝, snd✝⟩.snd.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nil.mk
α : Type u_1
β : Type u_2
f : α → List β
fst✝ : [].Index
snd✝ : (f fst✝.val).Index
⊢ (bind f ⟨fst✝, snd✝⟩).val = ⟨fst✝, snd✝⟩.snd.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | match i with
| ⟨head, j⟩ => rw [bind, val_append_inl]
| ⟨tail i, j⟩ => rw [bind, val_append_inr, ih] | case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i : (i : (x :: xs).Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case cons
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i : (i : (x :: xs).Index) × (f i.val).Index
⊢ (bind f i).val = i.snd.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | rw [bind, val_append_inl] | α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i : (i : (x :: xs).Index) × (f i.val).Index
j : (f head.val).Index
⊢ (bind f ⟨head, j⟩).val = ⟨head, j⟩.snd.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i : (i : (x :: xs).Index) × (f i.val).Index
j : (f head.val).Index
⊢ (bind f ⟨head, j⟩).val = ⟨head, j⟩.snd.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_bind | [48, 1] | [54, 51] | rw [bind, val_append_inr, ih] | α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i✝ : (i : (x :: xs).Index) × (f i.val).Index
i : xs.Index
j : (f i.tail.val).Index
⊢ (bind f ⟨i.tail, j⟩).val = ⟨i.tail, j⟩.snd.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
x : α
xs : List α
ih : ∀ (i : (i : xs.Index) × (f i.val).Index), (bind f i).val = i.snd.val
i✝ : (i : (x :: xs).Index) × (f i.val).Index
i : xs.Index
j : (f i.tail.val).Index
⊢ (bind f ⟨i.tail, j⟩).val = ⟨i.tail, j⟩.sn... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Bind.lean | List.Index.val_unbind | [56, 1] | [57, 47] | rw [←bind_unbind f i, val_bind, unbind_bind] | α : Type u_1
β : Type u_2
f : α → List β
xs : List α
i : (xs.bind f).Index
⊢ (unbind f i).snd.val = i.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
f : α → List β
xs : List α
i : (xs.bind f).Index
⊢ (unbind f i).snd.val = i.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_arr | [18, 1] | [19, 27] | rw [arr, unarr, unpi_pi] | α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
⊢ (arr h).unarr = h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
⊢ (arr h).unarr = h
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_unarr | [21, 1] | [22, 27] | rw [arr, unarr, pi_unpi] | α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
⊢ arr k.unarr = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
⊢ arr k.unarr = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_eq_iff_eq_unarr | [24, 1] | [27, 31] | constructor | α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ arr h = k ↔ h = k.unarr | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ arr h = k → h = k.unarr
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ h = k.unarr → arr h = k | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ arr h = k ↔ h = k.unarr
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_eq_iff_eq_unarr | [24, 1] | [27, 31] | intro h | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ arr h = k → h = k.unarr | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : arr h✝ = k
⊢ h✝ = k.unarr | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ arr h = k → h = k.unarr
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_eq_iff_eq_unarr | [24, 1] | [27, 31] | rw [←h, unarr_arr] | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : arr h✝ = k
⊢ h✝ = k.unarr | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : arr h✝ = k
⊢ h✝ = k.unarr
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_eq_iff_eq_unarr | [24, 1] | [27, 31] | intro h | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ h = k.unarr → arr h = k | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : h✝ = k.unarr
⊢ arr h✝ = k | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h : xs.Index → ys.Index
k : (xs.arr ys).Index
⊢ h = k.unarr → arr h = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.arr_eq_iff_eq_unarr | [24, 1] | [27, 31] | rw [h, arr_unarr] | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : h✝ = k.unarr
⊢ arr h✝ = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
h✝ : xs.Index → ys.Index
k : (xs.arr ys).Index
h : h✝ = k.unarr
⊢ arr h✝ = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_eq_iff_eq_arr | [29, 1] | [32, 31] | constructor | α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k.unarr = h ↔ k = arr h | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k.unarr = h → k = arr h
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k = arr h → k.unarr = h | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k.unarr = h ↔ k = arr h
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_eq_iff_eq_arr | [29, 1] | [32, 31] | intro h | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k.unarr = h → k = arr h | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k.unarr = h✝
⊢ k = arr h✝ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k.unarr = h → k = arr h
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_eq_iff_eq_arr | [29, 1] | [32, 31] | rw [←h, arr_unarr] | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k.unarr = h✝
⊢ k = arr h✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k.unarr = h✝
⊢ k = arr h✝
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_eq_iff_eq_arr | [29, 1] | [32, 31] | intro h | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k = arr h → k.unarr = h | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k = arr h✝
⊢ k.unarr = h✝ | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h : xs.Index → ys.Index
⊢ k = arr h → k.unarr = h
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Arr.lean | List.Index.unarr_eq_iff_eq_arr | [29, 1] | [32, 31] | rw [h, unarr_arr] | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k = arr h✝
⊢ k.unarr = h✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
k : (xs.arr ys).Index
h✝ : xs.Index → ys.Index
h : k = arr h✝
⊢ k.unarr = h✝
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_prod | [19, 1] | [21, 30] | simp only [prod, unprod] | α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ (prod i).unprod = i | α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ ((unbind (fun x => List.map (Prod.mk x) ys)
(bind (fun x => List.map (Prod.mk x) ys) ⟨i.fst, map (Prod.mk i.fst.val) i.snd⟩)).fst,
unmap
(Prod.mk
(unbind (fun x => List.map (Prod.mk x) ys)
(bind... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ (prod i).unprod = i
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_prod | [19, 1] | [21, 30] | rw [unbind_bind, unmap_map] | α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ ((unbind (fun x => List.map (Prod.mk x) ys)
(bind (fun x => List.map (Prod.mk x) ys) ⟨i.fst, map (Prod.mk i.fst.val) i.snd⟩)).fst,
unmap
(Prod.mk
(unbind (fun x => List.map (Prod.mk x) ys)
(bind... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ ((unbind (fun x => List.map (Prod.mk x) ys)
(bind (fun x => List.map (Prod.mk x) ys) ⟨i.fst, map (Prod.mk i.fst.val) i.snd⟩)).fst,
unmap
(Prod.mk
(un... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_unprod | [23, 1] | [25, 30] | simp only [prod, unprod] | α : Type u_2
β : Type u_1
xs : List α
ys : List β
k : (xs.prod ys).Index
⊢ prod k.unprod = k | α : Type u_2
β : Type u_1
xs : List α
ys : List β
k : (xs.prod ys).Index
⊢ bind (fun x => List.map (Prod.mk x) ys)
⟨(unbind (fun x => List.map (Prod.mk x) ys) k).fst,
map (Prod.mk (unbind (fun x => List.map (Prod.mk x) ys) k).fst.val)
(unmap (Prod.mk (unbind (fun x => List.map (Prod.mk x) ys) k)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_1
xs : List α
ys : List β
k : (xs.prod ys).Index
⊢ prod k.unprod = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_unprod | [23, 1] | [25, 30] | rw [map_unmap, bind_unbind] | α : Type u_2
β : Type u_1
xs : List α
ys : List β
k : (xs.prod ys).Index
⊢ bind (fun x => List.map (Prod.mk x) ys)
⟨(unbind (fun x => List.map (Prod.mk x) ys) k).fst,
map (Prod.mk (unbind (fun x => List.map (Prod.mk x) ys) k).fst.val)
(unmap (Prod.mk (unbind (fun x => List.map (Prod.mk x) ys) k)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_1
xs : List α
ys : List β
k : (xs.prod ys).Index
⊢ bind (fun x => List.map (Prod.mk x) ys)
⟨(unbind (fun x => List.map (Prod.mk x) ys) k).fst,
map (Prod.mk (unbind (fun x => List.map (Prod.mk x) ys) k).fst.val)
... |
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_eq_iff_eq_unprod | [27, 1] | [30, 33] | constructor | α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ prod i = k ↔ i = k.unprod | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ prod i = k → i = k.unprod
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ i = k.unprod → prod i = k | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ prod i = k ↔ i = k.unprod
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_eq_iff_eq_unprod | [27, 1] | [30, 33] | intro h | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ prod i = k → i = k.unprod | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : prod i = k
⊢ i = k.unprod | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ prod i = k → i = k.unprod
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_eq_iff_eq_unprod | [27, 1] | [30, 33] | rw [←h, unprod_prod] | case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : prod i = k
⊢ i = k.unprod | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : prod i = k
⊢ i = k.unprod
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_eq_iff_eq_unprod | [27, 1] | [30, 33] | intro h | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ i = k.unprod → prod i = k | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : i = k.unprod
⊢ prod i = k | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
⊢ i = k.unprod → prod i = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.prod_eq_iff_eq_unprod | [27, 1] | [30, 33] | rw [h, prod_unprod] | case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : i = k.unprod
⊢ prod i = k | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
k : (xs.prod ys).Index
h : i = k.unprod
⊢ prod i = k
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_eq_iff_eq_prod | [32, 1] | [35, 33] | constructor | α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i.unprod = j ↔ i = prod j | case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i.unprod = j → i = prod j
case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i = prod j → i.unprod = j | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i.unprod = j ↔ i = prod j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_eq_iff_eq_prod | [32, 1] | [35, 33] | intro h | case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i.unprod = j → i = prod j | case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i.unprod = j
⊢ i = prod j | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i.unprod = j → i = prod j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_eq_iff_eq_prod | [32, 1] | [35, 33] | rw [←h, prod_unprod] | case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i.unprod = j
⊢ i = prod j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i.unprod = j
⊢ i = prod j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_eq_iff_eq_prod | [32, 1] | [35, 33] | intro h | case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i = prod j → i.unprod = j | case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i = prod j
⊢ i.unprod = j | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
⊢ i = prod j → i.unprod = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.unprod_eq_iff_eq_prod | [32, 1] | [35, 33] | rw [h, unprod_prod] | case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i = prod j
⊢ i.unprod = j | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
j : xs.Index × ys.Index
h : i = prod j
⊢ i.unprod = j
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.val_prod | [46, 1] | [47, 31] | rw [prod, val_bind, val_map] | α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ (prod i).val = (i.fst.val, i.snd.val) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
β : Type u_2
xs : List α
ys : List β
i : xs.Index × ys.Index
⊢ (prod i).val = (i.fst.val, i.snd.val)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Index/Prod.lean | List.Index.val_unprod | [49, 1] | [50, 45] | rw [←prod_unprod i, val_prod, unprod_prod] | α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
⊢ (i.unprod.fst.val, i.unprod.snd.val) = i.val | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_1
xs : List α
ys : List β
i : (xs.prod ys).Index
⊢ (i.unprod.fst.val, i.unprod.snd.val) = i.val
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.add_add_add_comm | [14, 11] | [18, 53] | rw [Int.add_assoc] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ + i₂ + (j₁ + j₂) = i₁ + (i₂ + (j₁ + j₂)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ + i₂ + (j₁ + j₂) = i₁ + (i₂ + (j₁ + j₂))
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.add_add_add_comm | [14, 11] | [18, 53] | rw [Int.add_left_comm i₂ j₁ j₂] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ + (i₂ + (j₁ + j₂)) = i₁ + (j₁ + (i₂ + j₂)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ + (i₂ + (j₁ + j₂)) = i₁ + (j₁ + (i₂ + j₂))
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.add_add_add_comm | [14, 11] | [18, 53] | rw [Int.add_assoc] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ + (j₁ + (i₂ + j₂)) = i₁ + j₁ + (i₂ + j₂) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ + (j₁ + (i₂ + j₂)) = i₁ + j₁ + (i₂ + j₂)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.mul_mul_mul_comm | [20, 11] | [24, 53] | rw [Int.mul_assoc] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ * i₂ * (j₁ * j₂) = i₁ * (i₂ * (j₁ * j₂)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ * i₂ * (j₁ * j₂) = i₁ * (i₂ * (j₁ * j₂))
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.mul_mul_mul_comm | [20, 11] | [24, 53] | rw [Int.mul_left_comm i₂ j₁ j₂] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ * (i₂ * (j₁ * j₂)) = i₁ * (j₁ * (i₂ * j₂)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ * (i₂ * (j₁ * j₂)) = i₁ * (j₁ * (i₂ * j₂))
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.mul_mul_mul_comm | [20, 11] | [24, 53] | rw [Int.mul_assoc] | i₁ i₂ j₁ j₂ : Int
⊢ i₁ * (j₁ * (i₂ * j₂)) = i₁ * j₁ * (i₂ * j₂) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i₁ i₂ j₁ j₂ : Int
⊢ i₁ * (j₁ * (i₂ * j₂)) = i₁ * j₁ * (i₂ * j₂)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.mk_self | [28, 1] | [31, 45] | induction m with
| zero => rfl
| succ m ih => rw [succ_mk_succ]; exact ih | m : Nat
⊢ m ⊖ m = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
m : Nat
⊢ m ⊖ m = 0
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Int/Lemmas.lean | Int.mk_self | [28, 1] | [31, 45] | 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:
|
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