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/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.toList_length | [71, 1] | [72, 30] | rw [toList_eq, data_length] | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.length = a.size | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.length = a.size
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.get?_data | [74, 1] | [77, 31] | ext i | C : Type u_1
α : Type u_2
a : Array α
⊢ a.data.get? = a.get? | case h.a
C : Type u_1
α : Type u_2
a : Array α
i : ℕ
a✝ : α
⊢ a✝ ∈ a.data.get? i ↔ a✝ ∈ a.get? i | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.data.get? = a.get?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.get?_data | [74, 1] | [77, 31] | rw [Array.get?_eq_data_get?] | case h.a
C : Type u_1
α : Type u_2
a : Array α
i : ℕ
a✝ : α
⊢ a✝ ∈ a.data.get? i ↔ a✝ ∈ a.get? i | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
C : Type u_1
α : Type u_2
a : Array α
i : ℕ
a✝ : α
⊢ a✝ ∈ a.data.get? i ↔ a✝ ∈ a.get? i
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.get?_toList | [79, 1] | [80, 28] | rw [toList_eq, get?_data] | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.get? = a.get? | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.get? = a.get?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.get?_toListRev | [82, 1] | [84, 75] | rw [toListRev_eq, List.get?_reverse _ (by rwa [data_length]), get?_data] | C : Type u_1
α : Type u_2
a : Array α
i : ℕ
h : i < a.size
⊢ a.toListRev.get? i = a.get? (a.size - 1 - i) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
i : ℕ
h : i < a.size
⊢ a.toListRev.get? i = a.get? (a.size - 1 - i)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.get?_toListRev | [82, 1] | [84, 75] | rwa [data_length] | C : Type u_1
α : Type u_2
a : Array α
i : ℕ
h : i < a.size
⊢ i < a.data.length | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
i : ℕ
h : i < a.size
⊢ i < a.data.length
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | cases a.size.eq_zero_or_pos | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toListRev.head? = a.back? | case inl
C : Type u_1
α : Type u_2
a : Array α
h✝ : a.size = 0
⊢ a.toListRev.head? = a.back?
case inr
C : Type u_1
α : Type u_2
a : Array α
h✝ : a.size > 0
⊢ a.toListRev.head? = a.back? | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toListRev.head? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | case inl h =>
rw [toListRev_eq, back?, ← get?_data]
simp [List.length_eq_zero.mp h] | C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.toListRev.head? = a.back? | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.toListRev.head? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | case inr h =>
rw [← List.get?_zero, get?_toListRev _ _ h, Nat.sub_zero]
rfl | C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.toListRev.head? = a.back? | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.toListRev.head? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | rw [toListRev_eq, back?, ← get?_data] | C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.toListRev.head? = a.back? | C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.data.reverse.head? = a.data.get? (a.size - 1) | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.toListRev.head? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | simp [List.length_eq_zero.mp h] | C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.data.reverse.head? = a.data.get? (a.size - 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size = 0
⊢ a.data.reverse.head? = a.data.get? (a.size - 1)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | rw [← List.get?_zero, get?_toListRev _ _ h, Nat.sub_zero] | C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.toListRev.head? = a.back? | C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.get? (a.size - 1) = a.back? | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.toListRev.head? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.head?_toListRev | [86, 1] | [93, 8] | rfl | C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.get? (a.size - 1) = a.back? | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
h : a.size > 0
⊢ a.get? (a.size - 1) = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.getLast?_toList | [95, 1] | [97, 7] | rw [back?, get?_eq_data_get?, List.getLast?_eq_get?] | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.getLast? = a.back? | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.get? (a.toList.length - 1) = a.data.get? (a.size - 1) | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.getLast? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.getLast?_toList | [95, 1] | [97, 7] | simp | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.get? (a.toList.length - 1) = a.data.get? (a.size - 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.get? (a.toList.length - 1) = a.data.get? (a.size - 1)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.getLast?_data | [99, 1] | [101, 27] | simp [← getLast?_toList] | C : Type u_1
α : Type u_2
a : Array α
⊢ a.data.getLast? = a.back? | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.data.getLast? = a.back?
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | Array.dropLast_toList | [103, 1] | [104, 7] | simp | C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.dropLast = a.pop.toList | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
a : Array α
⊢ a.toList.dropLast = a.pop.toList
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | ToList.lawfulEmptyCollection_iff | [127, 1] | [130, 20] | rw [ToMultiset.lawfulEmptyCollection_iff] | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
⊢ LawfulEmptyCollection C α ↔ toList ∅ = [] | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toList ∅ = [] | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
⊢ LawfulEmptyCollection C α ↔ toList ∅ = []
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | ToList.lawfulEmptyCollection_iff | [127, 1] | [130, 20] | simp [toMultiset] | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toList ∅ = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toList ∅ = []
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | toList_empty | [134, 1] | [137, 49] | rwa [ToList.lawfulEmptyCollection_iff] at inst | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
inst : LawfulEmptyCollection C α
⊢ toList ∅ = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : EmptyCollection C
inst : LawfulEmptyCollection C α
⊢ toList ∅ = []
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | size_eq_size_toArray | [143, 1] | [144, 31] | simp [size_eq_length_toList] | C : Type u_1
α : Type u_2
inst✝ : ToList C α
c : C
⊢ size c = (toArray c).size | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝ : ToList C α
c : C
⊢ size c = (toArray c).size
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | isEmpty_toList | [155, 1] | [156, 84] | rw [isEmpty_eq_decide_size, List.isEmpty_eq_decide_length, size_eq_length_toList] | C : Type u_1
α : Type u_2
inst✝ : ToList C α
c : C
⊢ (toList c).isEmpty = isEmpty c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝ : ToList C α
c : C
⊢ (toList c).isEmpty = isEmpty c
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | front?_isSome | [179, 1] | [181, 85] | rwa [front?_def, List.head?_isSome, ← List.not_isEmpty_iff_ne_nil, isEmpty_toList] | C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : Front C α
c : C
h : ¬isEmpty c = true
⊢ (front? c).isSome = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : Front C α
c : C
h : ¬isEmpty c = true
⊢ (front? c).isSome = true
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | front_def | [183, 1] | [186, 64] | simpa using (front_mem c h).symm | C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : Front C α
c : C
h : ¬isEmpty c = true
⊢ some (front c h) = some ((front? c).get ⋯) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : Front C α
c : C
h : ¬isEmpty c = true
⊢ some (front c h) = some ((front? c).get ⋯)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | back?_isSome | [202, 1] | [204, 87] | rwa [back?_def, List.getLast?_isSome, ← List.not_isEmpty_iff_ne_nil, isEmpty_toList] | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : Back C α
c : C
h : ¬isEmpty c = true
⊢ (back? c).isSome = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : Back C α
c : C
h : ¬isEmpty c = true
⊢ (back? c).isSome = true
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | back_def | [206, 1] | [209, 63] | simpa using (back_mem c h).symm | C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : Back C α
c : C
h : ¬isEmpty c = true
⊢ some (back c h) = some ((back? c).get ⋯) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type u_2
inst✝¹ : ToList C α
inst✝ : Back C α
c : C
h : ¬isEmpty c = true
⊢ some (back c h) = some ((back? c).get ⋯)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | ToList.RandomAccess.get_toArray | [258, 1] | [260, 31] | rw [get_eq_get_toArray] | C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : RandomAccess C α
c : C
i : Fin (toArray c).size
⊢ (toArray c).get i = get c (Fin.cast ⋯ i) | C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : RandomAccess C α
c : C
i : Fin (toArray c).size
⊢ (toArray c).get i = (toArray c).get (Fin.cast ⋯ (Fin.cast ⋯ i)) | Please generate a tactic in lean4 to solve the state.
STATE:
C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : RandomAccess C α
c : C
i : Fin (toArray c).size
⊢ (toArray c).get i = get c (Fin.cast ⋯ i)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToList.lean | ToList.RandomAccess.get_toArray | [258, 1] | [260, 31] | rfl | C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : RandomAccess C α
c : C
i : Fin (toArray c).size
⊢ (toArray c).get i = (toArray c).get (Fin.cast ⋯ (Fin.cast ⋯ i)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C✝ : Type u_1
α✝ : Type u_2
C : Type u_3
α : Type u_4
inst✝¹ : ToList C α
inst✝ : RandomAccess C α
c : C
i : Fin (toArray c).size
⊢ (toArray c).get i = (toArray c).get (Fin.cast ⋯ (Fin.cast ⋯ i))
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/Size.lean | isEmpty_eq_decide_size | [31, 1] | [32, 58] | simp only [← isEmpty_iff_size_eq_zero, Bool.decide_coe] | C : Type u_1
α : Type ?u.565
inst✝ : Size C
c : C
⊢ isEmpty c = decide (size c = 0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type ?u.565
inst✝ : Size C
c : C
⊢ isEmpty c = decide (size c = 0)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/Size.lean | isEmpty_eq_size_beq_zero | [34, 1] | [36, 23] | rw [isEmpty_eq_decide_size] | C : Type u_1
α : Type ?u.736
inst✝ : Size C
c : C
⊢ isEmpty c = (size c == 0) | C : Type u_1
α : Type ?u.736
inst✝ : Size C
c : C
⊢ decide (size c = 0) = (size c == 0) | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type ?u.736
inst✝ : Size C
c : C
⊢ isEmpty c = (size c == 0)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/Size.lean | isEmpty_eq_size_beq_zero | [34, 1] | [36, 23] | cases size c <;> rfl | C : Type u_1
α : Type ?u.736
inst✝ : Size C
c : C
⊢ decide (size c = 0) = (size c == 0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
C : Type u_1
α : Type ?u.736
inst✝ : Size C
c : C
⊢ decide (size c = 0) = (size c == 0)
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | toMultiset_of_isEmpty | [50, 1] | [52, 42] | simpa [size_eq_card_toMultiset] using h | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c : C
h : isEmpty c = true
⊢ toMultiset c = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c : C
h : isEmpty c = true
⊢ toMultiset c = 0
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | ToMultiset.not_isEmpty_of_mem | [57, 1] | [59, 85] | simpa [size_eq_card_toMultiset, Multiset.eq_zero_iff_forall_not_mem] using ⟨v, hv⟩ | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c✝ c : C
v : α
hv : v ∈ c
⊢ ¬isEmpty c = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c✝ c : C
v : α
hv : v ∈ c
⊢ ¬isEmpty c = true
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | count_toMultiset_ne_zero | [66, 1] | [67, 50] | simp [count_toMultiset_eq_zero, mem_toMultiset] | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝¹ : ToMultiset C α
c✝ : C
inst✝ : DecidableEq α
a : α
c : C
⊢ Multiset.count a (toMultiset c) ≠ 0 ↔ a ∈ c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝¹ : ToMultiset C α
c✝ : C
inst✝ : DecidableEq α
a : α
c : C
⊢ Multiset.count a (toMultiset c) ≠ 0 ↔ a ∈ c
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | toMultiset_of_isEmpty | [50, 1] | [52, 42] | simpa [size_eq_card_toMultiset] using h | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c : C
h : isEmpty c = true
⊢ toMultiset c = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c : C
h : isEmpty c = true
⊢ toMultiset c = 0
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | ToMultiset.not_isEmpty_of_mem | [57, 1] | [59, 85] | simpa [size_eq_card_toMultiset, Multiset.eq_zero_iff_forall_not_mem] using ⟨v, hv⟩ | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c✝ c : C
v : α
hv : v ∈ c
⊢ ¬isEmpty c = true | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝ : ToMultiset C α
c✝ c : C
v : α
hv : v ∈ c
⊢ ¬isEmpty c = true
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToMultiset.lean | count_toMultiset_ne_zero | [66, 1] | [67, 50] | simp [count_toMultiset_eq_zero, mem_toMultiset] | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝¹ : ToMultiset C α
c✝ : C
inst✝ : DecidableEq α
a : α
c : C
⊢ Multiset.count a (toMultiset c) ≠ 0 ↔ a ∈ c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝¹ : ToMultiset C α
c✝ : C
inst✝ : DecidableEq α
a : α
c : C
⊢ Multiset.count a (toMultiset c) ≠ 0 ↔ a ∈ c
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Forest.lean | Forest.roots_subset_support | [26, 1] | [30, 76] | induction f with
| nil => rfl
| node a c s _ ihs =>
exact Set.insert_subset_insert (Set.subset_union_of_subset_right ihs _) | α : Type u_1
f : Forest α
⊢ f.roots ⊆ f.support | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_1
f : Forest α
⊢ f.roots ⊆ f.support
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Forest.lean | Forest.roots_subset_support | [26, 1] | [30, 76] | rfl | case nil
α : Type u_1
⊢ nil.roots ⊆ nil.support | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
α : Type u_1
⊢ nil.roots ⊆ nil.support
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Forest.lean | Forest.roots_subset_support | [26, 1] | [30, 76] | exact Set.insert_subset_insert (Set.subset_union_of_subset_right ihs _) | case node
α : Type u_1
a : α
c s : Forest α
child_ih✝ : c.roots ⊆ c.support
ihs : s.roots ⊆ s.support
⊢ (node a c s).roots ⊆ (node a c s).support | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case node
α : Type u_1
a : α
c s : Forest α
child_ih✝ : c.roots ⊆ c.support
ihs : s.roots ⊆ s.support
⊢ (node a c s).roots ⊆ (node a c s).support
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToFinset.lean | ToFinset.lawfulEmptyCollection_iff | [34, 1] | [38, 7] | rw [ToMultiset.lawfulEmptyCollection_iff] | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ LawfulEmptyCollection C α ↔ toFinset ∅ = ∅ | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toFinset ∅ = ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ LawfulEmptyCollection C α ↔ toFinset ∅ = ∅
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToFinset.lean | ToFinset.lawfulEmptyCollection_iff | [34, 1] | [38, 7] | change (toFinset (∅ : C)).val = ∅ ↔ _ | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toFinset ∅ = ∅ | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ (toFinset ∅).val = ∅ ↔ toFinset ∅ = ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ ToMultiset.toMultiset ∅ = 0 ↔ toFinset ∅ = ∅
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToFinset.lean | ToFinset.lawfulEmptyCollection_iff | [34, 1] | [38, 7] | simp | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ (toFinset ∅).val = ∅ ↔ toFinset ∅ = ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
⊢ (toFinset ∅).val = ∅ ↔ toFinset ∅ = ∅
TACTIC:
|
https://github.com/negiizhao/Algorithm.git | ae2bb2d101ce546ffe90434d718f919ef346c2ea | Algorithm/Data/Classes/ToFinset.lean | toFinset_empty | [42, 1] | [45, 51] | rwa [ToFinset.lawfulEmptyCollection_iff] at inst | α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
inst : LawfulEmptyCollection C α
⊢ toFinset ∅ = ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α✝ : Type u_1
C : Type u_2
α : Type u_3
inst✝⁴ : ToFinset C α
c : C
inst✝³ : EmptyCollection C
inst✝² : LawfulEmptyCollection C α
inst✝¹ : ToFinset C α
inst✝ : EmptyCollection C
inst : LawfulEmptyCollection C α
⊢ toFinset ∅ = ∅
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/Definitions.lean | PropositionalLogic.HilbertSystem.insertEmpty | [79, 1] | [79, 65] | simp | L✝ : Type u
inst✝³ : DecidableEq L✝
inst✝² : HasMinimalLogicSymbols L✝
L : Type u
inst✝¹ : DecidableEq L
inst✝ : HilbertSystem L
ψ φ : L
⊢ ({φ} ⊢ ψ) → (∅ ∪ {φ} ⊢ ψ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L✝ : Type u
inst✝³ : DecidableEq L✝
inst✝² : HasMinimalLogicSymbols L✝
L : Type u
inst✝¹ : DecidableEq L
inst✝ : HilbertSystem L
ψ φ : L
⊢ ({φ} ⊢ ψ) → (∅ ∪ {φ} ⊢ ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.weakenImp | [29, 1] | [30, 91] | exact λ h => MP (axiomK _ ψ φ) h | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Finset L
ψ φ : L
⊢ (Γ ⊢ ψ) → (Γ ⊢ φ →' ψ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Finset L
ψ φ : L
⊢ (Γ ⊢ ψ) → (Γ ⊢ φ →' ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.weakenContext | [32, 1] | [32, 83] | sorry | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
Γ Δ : Context L
hs : Γ ⊆ Δ
⊢ (Γ ⊢ φ) → (Δ ⊢ φ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
Γ Δ : Context L
hs : Γ ⊆ Δ
⊢ (Γ ⊢ φ) → (Δ ⊢ φ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.weakenContext' | [34, 1] | [34, 86] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
Γ : Context L
⊢ ∅ ⊆ Γ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
Γ : Context L
⊢ ∅ ⊆ Γ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | have s1 : ⊢ (φ →' (φ →' φ) →' φ) := by apply axiomK; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ ∅ ⊢ φ →' φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
⊢ ∅ ⊢ φ →' φ | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | have s2 : ⊢ ((φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ) := by apply axiomS; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
⊢ ∅ ⊢ φ →' φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | have s3 : ⊢ ((φ →' φ →' φ) →' φ →' φ) := MP s2 s1 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | have s4 : ⊢ (φ →' φ →' φ) := by apply axiomK; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
⊢ ∅ ⊢ φ →' φ | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | have s5 : ⊢ (φ →' φ) := MP s3 s4 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
⊢ ∅ ⊢ φ →' φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
s5 : ∅ ⊢ φ →' φ
⊢ ∅ ⊢ φ →' φ | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | assumption | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
s5 : ∅ ⊢ φ →' φ
⊢ ∅ ⊢ φ →' φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
s4 : ∅ ⊢ φ →' φ →' φ
s5 : ∅ ⊢ φ →' φ
⊢ ∅ ⊢ φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | apply axiomK | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ ∅ ⊢ φ →' (φ →' φ) →' φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ ∅ ⊢ φ →' (φ →' φ) →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | apply axiomS | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
⊢ ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
⊢ ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id_imp' | [37, 1] | [43, 14] | apply axiomK | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ →' φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
s1 : ∅ ⊢ φ →' (φ →' φ) →' φ
s2 : ∅ ⊢ (φ →' (φ →' φ) →' φ) →' (φ →' φ →' φ) →' φ →' φ
s3 : ∅ ⊢ (φ →' φ →' φ) →' φ →' φ
⊢ ∅ ⊢ φ →' φ →' φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.id | [48, 1] | [49, 52] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ φ ∈ {φ} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
φ : L
⊢ φ ∈ {φ}
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | apply Iff.intro | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) ↔ (Γ ∪ {φ} ⊢ ψ) | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) → (Γ ∪ {φ} ⊢ ψ)
case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ) | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) ↔ (Γ ∪ {φ} ⊢ ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | . intro h;
have h1 : (Γ ∪ {φ}) ⊢ (φ →' ψ) := weakenContext Γ (Γ ∪ {φ}) (subset_union_left _ _) h;
have h2 := context (Γ ∪ {φ}) φ (by simp);
exact MP h1 h2; | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) → (Γ ∪ {φ} ⊢ ψ)
case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ) | case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) → (Γ ∪ {φ} ⊢ ψ)
case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | . admit | case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | intro h | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) → (Γ ∪ {φ} ⊢ ψ) | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ⊢ φ →' ψ) → (Γ ∪ {φ} ⊢ ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | have h1 : (Γ ∪ {φ}) ⊢ (φ →' ψ) := weakenContext Γ (Γ ∪ {φ}) (subset_union_left _ _) h | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | have h2 := context (Γ ∪ {φ}) φ (by simp) | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
h2 : Γ ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ} ⊢ ψ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ} ⊢ ψ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | exact MP h1 h2 | case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
h2 : Γ ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ} ⊢ ψ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
h2 : Γ ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ} ⊢ ψ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
⊢ φ ∈ Γ ∪ {φ} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
h : Γ ⊢ φ →' ψ
h1 : Γ ∪ {φ} ⊢ φ →' ψ
⊢ φ ∈ Γ ∪ {φ}
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.deduction | [51, 1] | [57, 10] | admit | case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ : L
⊢ (Γ ∪ {φ} ⊢ ψ) → (Γ ⊢ φ →' ψ)
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | simp [deduction] | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ φ →' ¬'¬'φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ φ →' ¬'¬'φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | have s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | have s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥' := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | have s3 := MP s2 s1 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
s3 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | assumption | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
s3 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
s2 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
s3 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.DNI | [61, 1] | [66, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ
⊢ Γ ∪ {φ} ∪ {φ →' ⊥'} ⊢ φ →' ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | simp [deduction] | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ¬'φ) →' ¬'φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ¬'φ) →' ¬'φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | have s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥' := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | have s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | have s3 := MP s1 s2 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | have s4 := MP s3 s2 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
s4 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | assumption | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
s4 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
s2 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
s3 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' ⊥'
s4 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.CM₁ | [68, 1] | [74, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ →' φ →' ⊥'
⊢ Γ ∪ {φ →' φ →' ⊥'} ∪ {φ} ⊢ φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.RAA | [76, 1] | [76, 49] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ⊥') →' ¬'φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ⊥') →' ¬'φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | simp [deduction] | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ψ) →' ¬'ψ →' ¬'φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ψ) →' ¬'ψ →' ¬'φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | have s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | have s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | have s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥' := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | have s4 := MP s2 s1 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | have s5 := MP s3 s4 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
s5 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | assumption | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
s5 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
s3 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ
s5 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₁ | [78, 1] | [85, 14] | simp | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ φ →' ψ
⊢ Γ ∪ {φ →' ψ} ∪ {ψ →' ⊥'} ∪ {φ} ⊢ ψ →' ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | simp [deduction] | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ¬'ψ) →' ψ →' ¬'φ | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ⊢ (φ →' ¬'ψ) →' ψ →' ¬'φ
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | have s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | have s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | have s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥' := by simp; | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | have s4 := MP s3 s1 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | have s5 := MP s4 s2 | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
s5 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
https://github.com/SnO2WMaN/lean4-propositional-logic.git | 01e7b1a79bbbe2b5aa55cc4806cff3eb45efd7cb | PropositionalLogic/HilbertSystem/HPM₀.lean | PropositionalLogic.HilbertSystem.HPM₀.Con₂ | [87, 1] | [94, 14] | assumption | L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
s5 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
L : Type u
inst✝⁵ : DecidableEq L
inst✝⁴ : HasArrow L
inst✝³ : HasBot L
inst✝² : HasLnot L
inst✝¹ : HilbertSystem L
inst✝ : HPM₀ L
Γ : Context L
φ ψ χ : L
s1 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ
s2 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ
s3 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ φ →' ψ →' ⊥'
s4 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ψ →' ⊥'
s5 : Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
⊢ Γ ∪ {φ →' ψ →' ⊥'} ∪ {ψ} ∪ {φ} ⊢ ⊥'
TACTIC:
|
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