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/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | case app ih _ =>
rw [hasType_app] at hσ hτ
obtain ⟨_, h₁, -⟩ := hσ
obtain ⟨_, h₂, -⟩ := hτ
cases ih h₁ h₂
rfl | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaT... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | case fst ih | snd ih =>
simp only [hasType_fst, hasType_snd] at hσ hτ
obtain ⟨σ', hσ⟩ := hσ
obtain ⟨τ', hτ⟩ := hτ
cases ih hσ hτ
rfl | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T]... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ)... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | case case ih₁ _ ih =>
rw [hasType_case] at hσ hτ
obtain ⟨σ₁, σ₂, hσ, hσ₁, _⟩ := hσ
obtain ⟨τ₁, τ₂, hτ, hτ₁, _⟩ := hτ
cases ih hσ hτ
cases ih₁ hσ₁ hτ₁
rfl | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : La... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | all_goals aesop | case const
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T] LambdaTerm.const a✝ ∶ σ
hτ : Γ ⊢[T] LambdaTerm.const a✝ ∶ τ
⊢ σ = τ
case var
p : LambdaParams
U : Type ?u.145218
C : Typ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T] LambdaTerm.const a✝ ∶ σ
hτ : Γ ⊢[T] LambdaTerm.const a✝ ∶ τ
... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | rw [hasType_app] at hσ hτ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaT... | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaT... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨_, h₁, -⟩ := hσ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaT... | case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨_, h₂, -⟩ := hτ | case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U... | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | cases ih h₁ h₂ | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : ... | case intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | rfl | case intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ⊢[T] a✝¹ ∶ τ) → σ = τ
a_ih✝ : ∀ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | simp only [hasType_fst, hasType_snd] at hσ hτ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T]... | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : ∃ σ_1,... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ)... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨σ', hσ⟩ := hσ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
hσ : ∃ σ_1,... | case intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ)... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨τ', hτ⟩ := hτ | case intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ : LambdaType p✝ U✝
... | case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ σ' : LambdaTy... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | cases ih hσ hτ | case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ τ σ' : LambdaTy... | case intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ σ' : Lambd... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | rfl | case intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ U✝
σ σ' : Lambd... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝¹ : p✝.prod = true
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | rw [hasType_case] at hσ hτ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : La... | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : La... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨σ₁, σ₂, hσ, hσ₁, _⟩ := hσ | p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : La... | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | obtain ⟨τ₁, τ₂, hτ, hτ₁, _⟩ := hτ | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝² ∶ τ) → σ = τ
a_ih✝ : ∀ ... | case intro.intro.intro.intro.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝²... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | cases ih hσ hτ | case intro.intro.intro.intro.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T] a✝²... | case intro.intro.intro.intro.intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | cases ih₁ hσ₁ hτ₁ | case intro.intro.intro.intro.intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ⊢[T... | case intro.intro.intro.intro.intro.intro.intro.intro.refl.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro.intro.intro.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Conte... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | rfl | case intro.intro.intro.intro.intro.intro.intro.intro.refl.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ σ) → (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro.intro.intro.intro.intro.refl.refl
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝³ : p✝.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p✝ U✝ C✝
ih₁ : ∀ {Γ : ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | aesop | case elim
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.empty = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ⊢[T] a✝ ∶ τ) → σ = τ
Γ : Context p✝ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type ?u.145218
C : Type ?u.145221
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.empty = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
a_ih✝ : ∀ {Γ : Context p✝ U✝} {σ τ : LambdaType p✝ U... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | induction t generalizing Γ σ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
Δ : Context p U
⊢ Γ ++ Δ ⊢[T] t ∶ σ | case const
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : C✝
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
case var
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaTy... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
Δ : Context p U
⊢ Γ ++ Δ ⊢[T] t ∶ σ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | case var =>
simp only [hasType_var, List.length_append] at h ⊢
obtain ⟨h, rfl⟩ := h
refine ⟨Nat.lt_add_right _ _ _ h, ?_⟩
rw [List.get_append] | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.var a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.var a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | case lambda ih =>
simp only [hasType_lambda] at h ⊢
obtain ⟨σ, rfl, h⟩ := h
exact ⟨σ, rfl, ih h⟩ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.lambda a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | case case ih₁ ih₂ ih =>
simp only [hasType_case] at h ⊢
obtain ⟨σ₁, σ₂, h, h₁, h₂⟩ := h
exact ⟨σ₁, σ₂, ih h, ih₁ h₁, ih₂ h₂⟩ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ++ Δ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : C... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | all_goals aesop | case const
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : C✝
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
case app
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaTy... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : C✝
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
case app
p : LambdaParams
U ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | simp only [hasType_var, List.length_append] at h ⊢ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.var a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : ∃ (h : a✝ < List.length Γ), σ = List.get Γ { val := a✝, isLt := h }
⊢ ∃ (h : a✝ < List.length Γ + List.length Δ),
σ = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.var a✝ ∶ σ
⊢ Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | obtain ⟨h, rfl⟩ := h | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : ∃ (h : a✝ < List.length Γ), σ = List.get Γ { val := a✝, isLt := h }
⊢ ∃ (h : a✝ < List.length Γ + List.length Δ),
σ = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < ... | case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ ∃ (h_1 : a✝ < List.length Γ + List.length Δ),
List.get Γ { val := a✝, isLt := h } = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ))... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
σ : LambdaType p U
h : ∃ (h : a✝ < List.length Γ), σ = List.get Γ { val := a✝, isLt := h }
⊢ ∃ (h : a✝ < List.length Γ + List.length ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | refine ⟨Nat.lt_add_right _ _ _ h, ?_⟩ | case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ ∃ (h_1 : a✝ < List.length Γ + List.length Δ),
List.get Γ { val := a✝, isLt := h } = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ))... | case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ List.get Γ { val := a✝, isLt := h } = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ)) } | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ ∃ (h_1 : a✝ < List.length Γ + List.length Δ),
List.get Γ { val := a✝, isLt := h } = List.get ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | rw [List.get_append] | case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ List.get Γ { val := a✝, isLt := h } = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ)) } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝ : ℕ
Γ : Context p U
h : a✝ < List.length Γ
⊢ List.get Γ { val := a✝, isLt := h } = List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.lengt... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | simp only [hasType_lambda] at h ⊢ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaTerm.lambda a... | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : ∃ σ_1, σ = LambdaType.lamb... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | obtain ⟨σ, rfl, h⟩ := h | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : ∃ σ_1, σ = LambdaType.lamb... | case intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : a✝¹ :: Γ ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | exact ⟨σ, rfl, ih h⟩ | case intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : a✝¹ :: Γ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
ih : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | simp only [hasType_case] at h ⊢ | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ++ Δ ... | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ++ Δ ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : C... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | obtain ⟨σ₁, σ₂, h, h₁, h₂⟩ := h | p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝¹ ∶ σ) → (Γ ++ Δ ... | case intro.intro.intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : C... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | exact ⟨σ₁, σ₂, ih h, ih₁ h₁, ih₂ h₂⟩ | case intro.intro.intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ ⊢[T] a✝² ∶ σ)
ih₂ : ∀ {Γ : Context p U} {σ : LambdaType p U}... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝³ : p.coprod = true
a✝² a✝¹ a✝ : LambdaTerm p U C✝
ih₁ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝² ∶ σ) → (Γ ++ Δ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.append_hasType | [187, 1] | [203, 18] | aesop | case elim
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
a_ih✝ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] a✝ ∶ σ)
Γ : Context p U
σ : LambdaType p U
h : Γ ⊢[T] LambdaT... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type u_2
C : Type ?u.350830
C✝ : Type u_1
T : C✝ → LambdaType p U
Δ : Context p U
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C✝
a_ih✝ : ∀ {Γ : Context p U} {σ : LambdaType p U}, (Γ ⊢[T] a✝ ∶ σ) → (Γ ++ Δ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | induction t generalizing Γ σ | p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ Δ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] t ∶ σ
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ Γ ⊢[T] t ∶ σ | case const
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
ht : LambdaTerm.freeVarRange (LambdaTerm.const a✝) ≤ List.length Γ
⊢ Γ ⊢[T] L... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ Δ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] t ∶ σ
ht : LambdaTerm.freeVarRange t ≤ List.length ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | case var =>
simp only [hasType_var, List.length_append] at h ⊢
obtain ⟨_, rfl⟩ := h
rw [LambdaTerm.freeVarRange_var, Nat.add_one_le_iff] at ht
refine ⟨ht, ?_⟩
rw [List.get_append] | p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
⊢ Γ ⊢[T] LambdaTerm.var a✝... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
ht : LambdaTerm.freeVarRange (... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | all_goals aesop | case const
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
ht : LambdaTerm.freeVarRange (LambdaTerm.const a✝) ≤ List.length Γ
⊢ Γ ⊢[T] L... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.const a✝ ∶ σ
ht : LambdaTerm.... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | simp only [hasType_var, List.length_append] at h ⊢ | p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
⊢ Γ ⊢[T] LambdaTerm.var a✝... | p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
h :
∃ (h : a✝ < List.length Γ + List.length Δ),
σ = List.g... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
h : Γ ++ Δ ⊢[T] LambdaTerm.var a✝ ∶ σ
ht : LambdaTerm.freeVarRange (... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | obtain ⟨_, rfl⟩ := h | p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
h :
∃ (h : a✝ < List.length Γ + List.length Δ),
σ = List.g... | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ ∃ (h : a✝ < List.length Γ),
... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
σ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
h :... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | rw [LambdaTerm.freeVarRange_var, Nat.add_one_le_iff] at ht | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ ∃ (h : a✝ < List.length Γ),
... | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ ∃ (h : a✝ < List.length Γ),
List.get (Γ ++ Δ) { val := a✝, isLt := (_... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : LambdaTerm.freeVarRange (LambdaTerm.var a✝) ≤ List.length Γ
w✝ : a✝ < Lis... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | refine ⟨ht, ?_⟩ | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ ∃ (h : a✝ < List.length Γ),
List.get (Γ ++ Δ) { val := a✝, isLt := (_... | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ)) } ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ ∃ (h : a✝ < ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | rw [List.get_append] | case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ List.get (Γ ++ Δ) { val := a✝, isLt := (_ : a✝ < List.length (Γ ++ Δ)) } ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝ : ℕ
Γ : Context p✝ U✝
ht : a✝ < List.length Γ
w✝ : a✝ < List.length Γ + List.length Δ
⊢ List.get (Γ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_append_hasType | [205, 1] | [214, 18] | aesop | case elim
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝² : p✝.empty = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
a_ih✝ :
∀ {Γ : Context p✝ U✝} {σ : LambdaType p✝ U✝},
(Γ ++ Δ ⊢[T] a✝ ∶ σ) → LambdaTerm.f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type ?u.469890
C : Type ?u.469893
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Δ : Context p✝ U✝
a✝² : p✝.empty = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
a_ih✝ :
∀ {Γ : Context p✝ U✝} {σ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.concat_hasType | [221, 1] | [224, 29] | rw [List.concat_eq_append] | p : LambdaParams
U : Type u_2
C : Type ?u.1008396
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
τ : LambdaType p U
⊢ List.concat Γ τ ⊢[T] t ∶ σ | p : LambdaParams
U : Type u_2
C : Type ?u.1008396
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
τ : LambdaType p U
⊢ Γ ++ [τ] ⊢[T] t ∶ σ | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.1008396
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
τ : LambdaType p U
⊢ List.concat Γ τ ⊢[T] t ∶ σ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.concat_hasType | [221, 1] | [224, 29] | exact append_hasType h [τ] | p : LambdaParams
U : Type u_2
C : Type ?u.1008396
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
τ : LambdaType p U
⊢ Γ ++ [τ] ⊢[T] t ∶ σ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_2
C : Type ?u.1008396
C✝ : Type u_1
T : C✝ → LambdaType p U
Γ : Context p U
t : LambdaTerm p U C✝
σ : LambdaType p U
h : Γ ⊢[T] t ∶ σ
τ : LambdaType p U
⊢ Γ ++ [τ] ⊢[T] t ∶ σ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_concat_hasType | [226, 1] | [229, 39] | rw [List.concat_eq_append] at h | p : LambdaParams
U : Type ?u.1008576
C : Type ?u.1008579
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : List.concat Γ τ ⊢[T] t ∶ σ
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ Γ ⊢[T] t ∶ σ | p : LambdaParams
U : Type ?u.1008576
C : Type ?u.1008579
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ++ [τ] ⊢[T] t ∶ σ
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ Γ ⊢[T] t ∶ σ | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.1008576
C : Type ?u.1008579
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : List.concat Γ τ ⊢[T] t ∶ σ
ht : LambdaTerm... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_of_concat_hasType | [226, 1] | [229, 39] | exact hasType_of_append_hasType h ht | p : LambdaParams
U : Type ?u.1008576
C : Type ?u.1008579
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ++ [τ] ⊢[T] t ∶ σ
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ Γ ⊢[T] t ∶ σ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.1008576
C : Type ?u.1008579
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ++ [τ] ⊢[T] t ∶ σ
ht : LambdaTerm.freeVa... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.concat_hasType_iff | [231, 1] | [234, 30] | rw [List.concat_eq_append] | p : LambdaParams
U : Type ?u.1008897
C : Type ?u.1008900
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ (List.concat Γ τ ⊢[T] t ∶ σ) ↔ (Γ ⊢[T] t ∶ σ) | p : LambdaParams
U : Type ?u.1008897
C : Type ?u.1008900
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ (Γ ++ [τ] ⊢[T] t ∶ σ) ↔ (Γ ⊢[T] t ∶ σ) | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.1008897
C : Type ?u.1008900
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange t ≤ List.length Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.concat_hasType_iff | [231, 1] | [234, 30] | exact append_hasType_iff ht | p : LambdaParams
U : Type ?u.1008897
C : Type ?u.1008900
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange t ≤ List.length Γ
⊢ (Γ ++ [τ] ⊢[T] t ∶ σ) ↔ (Γ ⊢[T] t ∶ σ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.1008897
C : Type ?u.1008900
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
ht : LambdaTerm.freeVarRange t ≤ List.length Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | free_subst_of_not_free | [41, 1] | [42, 33] | rw [subst_eq_of_not_free h] | α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free t
⊢ free (t[v := s]) = free t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free t
⊢ free (t[v := s]) = free t
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | free_subst_eq | [44, 1] | [48, 35] | by_cases h : v ∈ free t | α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t} | case pos
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∈ free t
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t}
case neg
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : Deduction... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t}
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | free_subst_eq | [44, 1] | [48, 35] | simp [free_subst_of_free, h] | case pos
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∈ free t
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∈ free t
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t}
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | free_subst_eq | [44, 1] | [48, 35] | simp [subst_eq_of_not_free, h] | case neg
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free t
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free t
⊢ free (t[v := s]) = free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t}
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | not_mem_free_of_subst | [50, 1] | [52, 11] | rw [free_subst_eq] | α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free s
⊢ v ∉ free (t[v := s]) | α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free s
⊢ v ∉ free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t} | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free s
⊢ v ∉ free (t[v := s])
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/TypeSystem.lean | not_mem_free_of_subst | [50, 1] | [52, 11] | simp_all | α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free s
⊢ v ∉ free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u_2
β : Type u_3
Λ : Type u_4
V : Type u_1
T : Type u_5
inst✝¹ : DeductionSystem α β
inst✝ : TypeSystem α β Λ V T
v : V
s t : Λ
h : v ∉ free s
⊢ v ∉ free t \ {v} ∪ {w | w ∈ free s ∧ v ∈ free t}
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_some | [179, 1] | [181, 38] | cases t <;> simp only [h, replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
t u : LambdaTerm p U C
h : f n t = some u
⊢ replace' f n t = u | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
t u : LambdaTerm p U C
h : f n t = some u
⊢ replace' f n t = u
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_const | [184, 1] | [188, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
c : C
⊢ replace' f n (const c) =
match f n (const c) with
| some u => u
| none => const c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
c : C
⊢ replace' f n (const c) =
match f n (const c) with
| some u => u
| none => const c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_var | [191, 1] | [195, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n m : ℕ
⊢ replace' f n (var m) =
match f n (var m) with
| some u => u
| none => var m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n m : ℕ
⊢ replace' f n (var m) =
match f n (var m) with
| some u => u
| none => var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_lambda | [198, 1] | [202, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.lambda = true
τ : LambdaType p U
t : LambdaTerm p U C
⊢ replace' f n (lambda h τ t) =
match f n (lambda h τ t) with
| some u => u
| none => lambda h τ (replace' f (n + 1) t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.lambda = true
τ : LambdaType p U
t : LambdaTerm p U C
⊢ replace' f n (lambda h τ t) =
match f n (lambda h τ t) with
| some u => u
| none =>... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_app | [205, 1] | [209, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.lambda = true
l r : LambdaTerm p U C
⊢ replace' f n (app h l r) =
match f n (app h l r) with
| some u => u
| none => app h (replace' f n l) (replace' f n r) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.lambda = true
l r : LambdaTerm p U C
⊢ replace' f n (app h l r) =
match f n (app h l r) with
| some u => u
| none => app h (replace' f n l)... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_pair | [212, 1] | [216, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
l r : LambdaTerm p U C
⊢ replace' f n (pair h l r) =
match f n (pair h l r) with
| some u => u
| none => pair h (replace' f n l) (replace' f n r) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
l r : LambdaTerm p U C
⊢ replace' f n (pair h l r) =
match f n (pair h l r) with
| some u => u
| none => pair h (replace' f n l... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_fst | [219, 1] | [223, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
t : LambdaTerm p U C
⊢ replace' f n (fst h t) =
match f n (fst h t) with
| some u => u
| none => fst h (replace' f n t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
t : LambdaTerm p U C
⊢ replace' f n (fst h t) =
match f n (fst h t) with
| some u => u
| none => fst h (replace' f n t)
TACTIC:... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_snd | [226, 1] | [230, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
t : LambdaTerm p U C
⊢ replace' f n (snd h t) =
match f n (snd h t) with
| some u => u
| none => snd h (replace' f n t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.prod = true
t : LambdaTerm p U C
⊢ replace' f n (snd h t) =
match f n (snd h t) with
| some u => u
| none => snd h (replace' f n t)
TACTIC:... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_inl | [233, 1] | [237, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
τ : LambdaType p U
l : LambdaTerm p U C
⊢ replace' f n (inl h τ l) =
match f n (inl h τ l) with
| some u => u
| none => inl h τ (replace' f n l) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
τ : LambdaType p U
l : LambdaTerm p U C
⊢ replace' f n (inl h τ l) =
match f n (inl h τ l) with
| some u => u
| none => inl h... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_inr | [240, 1] | [244, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
τ : LambdaType p U
r : LambdaTerm p U C
⊢ replace' f n (inr h τ r) =
match f n (inr h τ r) with
| some u => u
| none => inr h τ (replace' f n r) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
τ : LambdaType p U
r : LambdaTerm p U C
⊢ replace' f n (inr h τ r) =
match f n (inr h τ r) with
| some u => u
| none => inr h... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_case | [247, 1] | [251, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
l r t : LambdaTerm p U C
⊢ replace' f n (case h l r t) =
match f n (case h l r t) with
| some u => u
| none => case h (replace' f (n + 1) l) (replace' f (n + 1) r) (replace' f n t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.coprod = true
l r t : LambdaTerm p U C
⊢ replace' f n (case h l r t) =
match f n (case h l r t) with
| some u => u
| none => case h (replac... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_star | [254, 1] | [258, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.unit = true
⊢ replace' f n (star h) =
match f n (star h) with
| some u => u
| none => star h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.unit = true
⊢ replace' f n (star h) =
match f n (star h) with
| some u => u
| none => star h
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.replace'_elim | [261, 1] | [265, 26] | simp only [replace'] | p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.empty = true
τ : LambdaType p U
t : LambdaTerm p U C
⊢ replace' f n (elim h τ t) =
match f n (elim h τ t) with
| some u => u
| none => elim h τ (replace' f n t) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
f : ℕ → LambdaTerm p U C → Option (LambdaTerm p U C)
n : ℕ
h : p.empty = true
τ : LambdaType p U
t : LambdaTerm p U C
⊢ replace' f n (elim h τ t) =
match f n (elim h τ t) with
| some u => u
| none => elim... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | induction u generalizing n <;> rw [freeVarRange] at h | p : LambdaParams
U : Type u_1
C : Type u_2
t u : LambdaTerm p U C
n : ℕ
h : freeVarRange u ≤ n
⊢ replace' (instantiateFun t) n u = u | case const
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' (instantiateFun t) n (const a✝) = const a✝
case var
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝ n : ℕ
h : a✝ + 1 ≤ n
⊢ replace' (instantiateFun t) n (var a✝) = var a✝
case lambda
p : Lam... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
t u : LambdaTerm p U C
n : ℕ
h : freeVarRange u ≤ n
⊢ replace' (instantiateFun t) n u = u
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | case var m =>
rw [Nat.add_one_le_iff] at h
rw [replace'_var, instantiateFun]
aesop | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m + 1 ≤ n
⊢ replace' (instantiateFun t) n (var m) = var m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m + 1 ≤ n
⊢ replace' (instantiateFun t) n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | all_goals aesop | case const
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' (instantiateFun t) n (const a✝) = const a✝
case lambda
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVar... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' (instantiateFun t) n (const a✝) = const a✝
case lambda
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝² : p.lambda = true
a✝¹ : La... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | rw [Nat.add_one_le_iff] at h | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m + 1 ≤ n
⊢ replace' (instantiateFun t) n (var m) = var m | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ replace' (instantiateFun t) n (var m) = var m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m + 1 ≤ n
⊢ replace' (instantiateFun t) n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | rw [replace'_var, instantiateFun] | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ replace' (instantiateFun t) n (var m) = var m | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => some (if m = n then t else if m < n then var m else var (m - 1))
| x => none with
| some u => u
| none => var m) =
var m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ replace' (instantiateFun t) n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | aesop | p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => some (if m = n then t else if m < n then var m else var (m - 1))
| x => none with
| some u => u
| none => var m) =
var m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => some (if m = n then t else if m < n then var m else var (m - 1))
| x => none with
| some u => u
| none => var m) =... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.instantiate'_eq_of_freeVarRange_le | [287, 1] | [295, 18] | aesop | case elim
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVarRange a✝ ≤ n → replace' (instantiateFun t) n a✝ = a✝
n : ℕ
h : freeVarRange a✝ ≤ n
⊢ replace' (instantiateFun t) n (elim a✝² a✝¹ a✝) = elim a✝² a✝¹ a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type u_1
C : Type u_2
t : LambdaTerm p U C
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVarRange a✝ ≤ n → replace' (instantiateFun t) n a✝ = a✝
n : ℕ
h : freeVarRange a✝ ≤ n
⊢ replace' (... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | induction u generalizing n <;> rw [freeVarRange] at h | p : LambdaParams
U : Type u_1
C : Type u_2
u : LambdaTerm p U C
n : ℕ
h : freeVarRange u ≤ n
⊢ replace' liftFun n u = u | case const
p : LambdaParams
U : Type u_1
C : Type u_2
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' liftFun n (const a✝) = const a✝
case var
p : LambdaParams
U : Type u_1
C : Type u_2
a✝ n : ℕ
h : a✝ + 1 ≤ n
⊢ replace' liftFun n (var a✝) = var a✝
case lambda
p : LambdaParams
U : Type u_1
C : Type u_2
a✝² : p.lambda = true
a✝¹ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
u : LambdaTerm p U C
n : ℕ
h : freeVarRange u ≤ n
⊢ replace' liftFun n u = u
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | case var m =>
rw [Nat.add_one_le_iff] at h
rw [replace'_var, liftFun]
simp only
rw [if_neg]
rw [not_le]
exact h | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m + 1 ≤ n
⊢ replace' liftFun n (var m) = var m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m + 1 ≤ n
⊢ replace' liftFun n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | all_goals aesop | case const
p : LambdaParams
U : Type u_1
C : Type u_2
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' liftFun n (const a✝) = const a✝
case lambda
p : LambdaParams
U : Type u_1
C : Type u_2
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVarRange a✝ ≤ n → replace' liftFun n a✝ = a✝
n : ℕ
h : f... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type u_1
C : Type u_2
a✝ : C
n : ℕ
h : 0 ≤ n
⊢ replace' liftFun n (const a✝) = const a✝
case lambda
p : LambdaParams
U : Type u_1
C : Type u_2
a✝² : p.lambda = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ),... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | rw [Nat.add_one_le_iff] at h | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m + 1 ≤ n
⊢ replace' liftFun n (var m) = var m | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ replace' liftFun n (var m) = var m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m + 1 ≤ n
⊢ replace' liftFun n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | rw [replace'_var, liftFun] | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ replace' liftFun n (var m) = var m | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => if n ≤ m then some (var (m + 1)) else none
| x => none with
| some u => u
| none => var m) =
var m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ replace' liftFun n (var m) = var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | simp only | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => if n ≤ m then some (var (m + 1)) else none
| x => none with
| some u => u
| none => var m) =
var m | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match if n ≤ m then some (var (m + 1)) else none with
| some u => u
| none => var m) =
var m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match
match var m with
| var m => if n ≤ m then some (var (m + 1)) else none
| x => none with
| some u => u
| none => var m) =
var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | rw [if_neg] | p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match if n ≤ m then some (var (m + 1)) else none with
| some u => u
| none => var m) =
var m | case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ ¬n ≤ m | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ (match if n ≤ m then some (var (m + 1)) else none with
| some u => u
| none => var m) =
var m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | rw [not_le] | case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ ¬n ≤ m | case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ m < n | Please generate a tactic in lean4 to solve the state.
STATE:
case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ ¬n ≤ m
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | exact h | case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ m < n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case hnc
p : LambdaParams
U : Type u_1
C : Type u_2
m n : ℕ
h : m < n
⊢ m < n
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/LambdaCalculus.lean | LambdaCalculi.LambdaTerm.lift'_eq_of_freeVarRange_le | [309, 1] | [320, 18] | aesop | case elim
p : LambdaParams
U : Type u_1
C : Type u_2
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVarRange a✝ ≤ n → replace' liftFun n a✝ = a✝
n : ℕ
h : freeVarRange a✝ ≤ n
⊢ replace' liftFun n (elim a✝² a✝¹ a✝) = elim a✝² a✝¹ a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type u_1
C : Type u_2
a✝² : p.empty = true
a✝¹ : LambdaType p U
a✝ : LambdaTerm p U C
a_ih✝ : ∀ (n : ℕ), freeVarRange a✝ ≤ n → replace' liftFun n a✝ = a✝
n : ℕ
h : freeVarRange a✝ ≤ n
⊢ replace' liftFun n (elim a✝² a✝¹ a✝) = eli... |
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Power.lean | MyNat.pow_zero | [19, 1] | [19, 47] | rfl | m : ℕ
⊢ m ^ 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
m : ℕ
⊢ m ^ 0 = 1
TACTIC:
|
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Power.lean | MyNat.pow_succ | [21, 1] | [21, 64] | rfl | m n : ℕ
⊢ m ^ succ n = m ^ n * m | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
m n : ℕ
⊢ m ^ succ n = m ^ n * m
TACTIC:
|
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Addition.lean | MyNat.add_zero | [17, 1] | [17, 51] | rfl | a : ℕ
⊢ a + 0 = a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
⊢ a + 0 = a
TACTIC:
|
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Addition.lean | MyNat.add_succ | [22, 1] | [22, 71] | rfl | a d : ℕ
⊢ a + succ d = succ (a + d) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a d : ℕ
⊢ a + succ d = succ (a + d)
TACTIC:
|
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Multiplication.lean | MyNat.mul_zero | [15, 1] | [15, 51] | rfl | a : ℕ
⊢ a * 0 = 0 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℕ
⊢ a * 0 = 0
TACTIC:
|
https://github.com/PatrickMassot/GaloisConnectionGame.git | c25799a01b35601b41ddb8be28903f5d7ef2c521 | NNG/MyNat/Multiplication.lean | MyNat.mul_succ | [17, 1] | [17, 68] | rfl | a b : ℕ
⊢ a * succ b = a * b + a | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℕ
⊢ a * succ b = a * b + a
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Conal/Language.lean | ν | [167, 1] | [169, 29] | induction f with
| universal => exact unit? | α : Type u
P : dLang α
f : Lang P
⊢ Dec (dLang.ν P) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type u
P : dLang α
f : Lang P
⊢ Dec (dLang.ν P)
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Conal/Language.lean | ν | [167, 1] | [169, 29] | exact unit? | case universal
α : Type u
P : dLang α
⊢ Dec (dLang.ν fun x => PUnit) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case universal
α : Type u
P : dLang α
⊢ Dec (dLang.ν fun x => PUnit)
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Std/Ltac.lean | anda | [90, 9] | [94, 27] | intro a | a : Prop
⊢ a → a ∧ a | a✝ : Prop
a : a✝
⊢ a✝ ∧ a✝ | Please generate a tactic in lean4 to solve the state.
STATE:
a : Prop
⊢ a → a ∧ a
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Std/Ltac.lean | anda | [90, 9] | [94, 27] | apply And.intro | a✝ : Prop
a : a✝
⊢ a✝ ∧ a✝ | case left
a✝ : Prop
a : a✝
⊢ a✝
case right
a✝ : Prop
a : a✝
⊢ a✝ | Please generate a tactic in lean4 to solve the state.
STATE:
a✝ : Prop
a : a✝
⊢ a✝ ∧ a✝
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Std/Ltac.lean | anda | [90, 9] | [94, 27] | case left => assumption | a✝ : Prop
a : a✝
⊢ a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a✝ : Prop
a : a✝
⊢ a✝
TACTIC:
|
https://github.com/katydid/proofs.git | 8105af686a3bdf193909567f5165835001240640 | Katydid/Std/Ltac.lean | anda | [90, 9] | [94, 27] | case right => assumption | a✝ : Prop
a : a✝
⊢ a✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
a✝ : Prop
a : a✝
⊢ a✝
TACTIC:
|
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