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/ImperialCollegeLondon/formalising-mathematics-2024.git | b732ed1352e87b4474b0520d1383994e069f8057 | FormalisingMathematics2024/Section20representationTheory/Sheet2.lean | Section20sheet2.RepMap.id_comp | [94, 1] | [94, 65] | sorry | k : Type
inst✝⁷ : Field k
G : Type
inst✝⁶ : Group G
V : Type
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module k V
W : Type
inst✝³ : AddCommGroup W
inst✝² : Module k W
ρ : Representation k G V
σ : Representation k G W
X : Type
inst✝¹ : AddCommGroup X
inst✝ : Module k X
φ : RepMap ρ σ
⊢ comp (id σ) φ = φ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k : Type
inst✝⁷ : Field k
G : Type
inst✝⁶ : Group G
V : Type
inst✝⁵ : AddCommGroup V
inst✝⁴ : Module k V
W : Type
inst✝³ : AddCommGroup W
inst✝² : Module k W
ρ : Representation k G V
σ : Representation k G W
X : Type
inst✝¹ : AddCommGroup X
inst✝ : Module k X... |
https://github.com/ImperialCollegeLondon/formalising-mathematics-2024.git | b732ed1352e87b4474b0520d1383994e069f8057 | FormalisingMathematics2024/Section20representationTheory/Sheet2.lean | Section20sheet2.RepMap.comp_assoc | [96, 1] | [98, 54] | sorry | k : Type
inst✝⁹ : Field k
G : Type
inst✝⁸ : Group G
V : Type
inst✝⁷ : AddCommGroup V
inst✝⁶ : Module k V
W : Type
inst✝⁵ : AddCommGroup W
inst✝⁴ : Module k W
ρ : Representation k G V
σ : Representation k G W
X : Type
inst✝³ : AddCommGroup X
inst✝² : Module k X
τ : Representation k G X
Y : Type
inst✝¹ : AddCommGroup Y
i... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
k : Type
inst✝⁹ : Field k
G : Type
inst✝⁸ : Group G
V : Type
inst✝⁷ : AddCommGroup V
inst✝⁶ : Module k V
W : Type
inst✝⁵ : AddCommGroup W
inst✝⁴ : Module k W
ρ : Representation k G V
σ : Representation k G W
X : Type
inst✝³ : AddCommGroup X
inst✝² : Module k ... |
https://github.com/ImperialCollegeLondon/formalising-mathematics-2024.git | b732ed1352e87b4474b0520d1383994e069f8057 | FormalisingMathematics2024/Section15numberTheory/Sheet5.lean | Section15Sheet5.sixteen_pow_sixtyfour_mod_nineteen | [29, 1] | [29, 80] | rfl | ⊢ 16 ^ 64 = 16 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ 16 ^ 64 = 16
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | constructor | p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.const c ∶ σ) ↔ σ = T c | case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.const c ∶ σ) → σ = T c
case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.const c ∶ σ) ↔ σ = T c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.const c ∶ σ) → σ = T c | case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const c ∶ σ
⊢ σ = T c | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.const c ∶ σ) → σ = T c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const c ∶ σ
⊢ σ = T c | case mp.const
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ T c = T c | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const c ∶ σ
⊢ σ = T c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | rfl | case mp.const
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ T c = T c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.const
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ T c = T c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | rintro rfl | case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ σ = T c → (Γ ⊢[T] LambdaTerm.const c ∶ σ) | case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ Γ ⊢[T] LambdaTerm.const c ∶ T c | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
σ : LambdaType p✝ U✝
⊢ σ = T c → (Γ ⊢[T] LambdaTerm.const c ∶ σ)
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_const | [34, 1] | [40, 17] | exact .const | case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ Γ ⊢[T] LambdaTerm.const c ∶ T c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.15403
C : Type ?u.15406
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
c : C✝
⊢ Γ ⊢[T] LambdaTerm.const c ∶ T c
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | constructor | p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.var n ∶ σ) ↔ ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h } | case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.var n ∶ σ) → ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h }
case mpr
p : LambdaParams
U : Type ?u.162... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.var n ∶ σ) ↔ ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, i... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.var n ∶ σ) → ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h } | case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.var n ∶ σ
⊢ ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h } | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.var n ∶ σ) → ∃ (h : n < List.length Γ), σ = List.get Γ { val... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.var n ∶ σ
⊢ ∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h } | case mp.var
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h✝ : n < List.length Γ
⊢ ∃ (h : n < List.length Γ), List.get Γ { val := n, isLt := h✝ } = List.get Γ { val := n, isLt := h } | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.var n ∶ σ
⊢ ∃ (h : n < List.length Γ), σ = List.get Γ { val... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | exact ⟨_, rfl⟩ | case mp.var
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h✝ : n < List.length Γ
⊢ ∃ (h : n < List.length Γ), List.get Γ { val := n, isLt := h✝ } = List.get Γ { val := n, isLt := h } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.var
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h✝ : n < List.length Γ
⊢ ∃ (h : n < List.length Γ), List.get Γ { val := n, isLt := h✝ } = List.get... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | rintro ⟨h, rfl⟩ | case mpr
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h }) → (Γ ⊢[T] LambdaTerm.var n ∶ σ) | case mpr.intro
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h : n < List.length Γ
⊢ Γ ⊢[T] LambdaTerm.var n ∶ List.get Γ { val := n, isLt := h } | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
σ : LambdaType p✝ U✝
⊢ (∃ (h : n < List.length Γ), σ = List.get Γ { val := n, isLt := h }) → (Γ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_var | [43, 1] | [49, 17] | exact .var h | case mpr.intro
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h : n < List.length Γ
⊢ Γ ⊢[T] LambdaTerm.var n ∶ List.get Γ { val := n, isLt := h } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
p : LambdaParams
U : Type ?u.16248
C : Type ?u.16251
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
n : ℕ
h : n < List.length Γ
⊢ Γ ⊢[T] LambdaTerm.var n ∶ List.get Γ { val := n, isLt := h }
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | constructor | p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.lambda h ρ t ∶ τ) ↔ ∃ σ, τ = LambdaType.lambda h ρ σ ∧ (ρ :: Γ ⊢[T] t... | case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.lambda h ρ t ∶ τ) → ∃ σ, τ = LambdaType.lambda h ρ σ ∧ (ρ :: ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.lambda h... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | intro h | case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.lambda h ρ t ∶ τ) → ∃ σ, τ = LambdaType.lambda h ρ σ ∧ (ρ :: ... | case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.lambda h✝ ρ t ∶ τ
⊢ ∃ σ, τ = LambdaType.lambda h✝ ρ σ ∧ (ρ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | cases h | case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.lambda h✝ ρ t ∶ τ
⊢ ∃ σ, τ = LambdaType.lambda h✝ ρ σ ∧ (ρ ... | case mp.lambda
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
a✝ : ρ :: Γ ⊢[T] t ∶ σ✝
⊢ ∃ σ, LambdaType.lambda h✝ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTer... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | exact ⟨_, rfl, by assumption⟩ | case mp.lambda
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
a✝ : ρ :: Γ ⊢[T] t ∶ σ✝
⊢ ∃ σ, LambdaType.lambda h✝ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.lambda
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.lambd... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | assumption | p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
a✝ : ρ :: Γ ⊢[T] t ∶ σ✝
⊢ ρ :: Γ ⊢[T] t ∶ σ✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
a✝ : ρ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | rintro ⟨σ, rfl, h⟩ | case mpr
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, τ = LambdaType.lambda h ρ σ ∧ (ρ :: Γ ⊢[T] t ∶ σ)) → (Γ ⊢[T] LambdaTerm.l... | case mpr.intro.intro
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : ρ :: Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.lambda h✝ ρ t ∶ LambdaType... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, τ = LambdaTy... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_lambda | [52, 1] | [59, 20] | exact .lambda h | case mpr.intro.intro
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : ρ :: Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.lambda h✝ ρ t ∶ LambdaType... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
p : LambdaParams
U : Type ?u.17183
C : Type ?u.17186
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
ρ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : ρ :... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | constructor | p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) ↔ ∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h σ τ) ∧ (Γ ⊢[T] u ∶ σ) | case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) → ∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h σ τ) ∧ (Γ ⊢[T] u ∶ σ)
cas... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) ↔ ∃ σ, (Γ ⊢[... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | intro h | case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) → ∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h σ τ) ∧ (Γ ⊢[T] u ∶ σ) | case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.app h✝ t u ∶ τ
⊢ ∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h✝ σ τ) ∧ (Γ ⊢[T] u ∶ σ) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) → ∃ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | cases h | case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.app h✝ t u ∶ τ
⊢ ∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h✝ σ τ) ∧ (Γ ⊢[T] u ∶ σ) | case mp.app
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ : Γ ⊢[T] u ∶ τ✝
a✝ : Γ ⊢[T] t ∶ LambdaType.lambda... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.app h✝ t u ∶ τ
⊢ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | exact ⟨_, by assumption, by assumption⟩ | case mp.app
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ : Γ ⊢[T] u ∶ τ✝
a✝ : Γ ⊢[T] t ∶ LambdaType.lambda... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.app
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaTyp... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | assumption | p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ : Γ ⊢[T] u ∶ τ✝
a✝ : Γ ⊢[T] t ∶ LambdaType.lambda h✝ τ✝ τ
⊢ Γ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | assumption | p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ : Γ ⊢[T] u ∶ τ✝
a✝ : Γ ⊢[T] t ∶ LambdaType.lambda h✝ τ✝ τ
⊢ Γ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.lambda = true
τ✝ : LambdaType p✝ U✝
a✝¹ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | rintro ⟨σ, h₁, h₂⟩ | case mpr
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h σ τ) ∧ (Γ ⊢[T] u ∶ σ)) → (Γ ⊢[T] LambdaTerm.app h t u ∶ τ) | case mpr.intro.intro
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ LambdaType.lambda h σ τ
h₂ : Γ ⊢[T] u ∶ σ
⊢ Γ ⊢[T] LambdaTerm.app h t ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, (Γ ⊢[T] t ∶ LambdaType.lambda h... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_app | [62, 1] | [69, 21] | exact .app h₁ h₂ | case mpr.intro.intro
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ LambdaType.lambda h σ τ
h₂ : Γ ⊢[T] u ∶ σ
⊢ Γ ⊢[T] LambdaTerm.app h t ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
p : LambdaParams
U : Type ?u.18239
C : Type ?u.18242
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.lambda = true
t u : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ LambdaTyp... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | constructor | p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.pair h t u ∶ τ) ↔ ∃ σ₁ σ₂, τ = LambdaType.prod h σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢[T] u ∶ σ₂) | case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.pair h t u ∶ τ) → ∃ σ₁ σ₂, τ = LambdaType.prod h σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢[T]... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.pair h t u ∶ τ) ↔ ∃ σ₁ σ₂, τ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | intro h | case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.pair h t u ∶ τ) → ∃ σ₁ σ₂, τ = LambdaType.prod h σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢[T]... | case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.pair h✝ t u ∶ τ
⊢ ∃ σ₁ σ₂, τ = LambdaType.prod h✝ σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.pair h t u ∶ τ) → ∃ σ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | cases h | case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.pair h✝ t u ∶ τ
⊢ ∃ σ₁ σ₂, τ = LambdaType.prod h✝ σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢... | case mp.pair
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ ⊢[T] u ∶ τ✝
⊢ ∃ σ₁ σ₂, LambdaType.prod h✝ σ✝ τ✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.pair h✝ t u ∶ τ
⊢ ∃... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | exact ⟨_, _, rfl, by assumption, by assumption⟩ | case mp.pair
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ ⊢[T] u ∶ τ✝
⊢ ∃ σ₁ σ₂, LambdaType.prod h✝ σ✝ τ✝... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.pair
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | assumption | p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ ⊢[T] u ∶ τ✝
⊢ Γ ⊢[T] t ∶ σ✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | assumption | p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ ⊢[T] u ∶ τ✝
⊢ Γ ⊢[T] u ∶ τ✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ✝ τ✝ : LambdaType p✝ U✝
h✝ : p✝.prod = true
a✝¹ : Γ ⊢[T] t ∶ σ✝
a✝ : Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | rintro ⟨σ₁, σ₂, rfl, h₁, h₂⟩ | case mpr
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ₁ σ₂, τ = LambdaType.prod h σ₁ σ₂ ∧ (Γ ⊢[T] t ∶ σ₁) ∧ (Γ ⊢[T] u ∶ σ₂)) → (Γ ⊢[T] LambdaTerm.pair... | case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ₁ σ₂ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ σ₁
h₂ : Γ ⊢[T] u ∶ σ₂
⊢ Γ ⊢[T] LambdaTerm.pair h t u ∶ Lam... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ₁ σ₂, τ = LambdaType.prod h σ₁ σ₂ ∧... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_pair | [72, 1] | [79, 22] | exact .pair h₁ h₂ | case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ₁ σ₂ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ σ₁
h₂ : Γ ⊢[T] u ∶ σ₂
⊢ Γ ⊢[T] LambdaTerm.pair h t u ∶ Lam... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.19287
C : Type ?u.19290
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t u : LambdaTerm p✝ U✝ C✝
σ₁ σ₂ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | constructor | p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) ↔ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h τ σ | case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) → ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h τ σ
case mpr
p : LambdaParams
U : ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) ↔ ∃ σ, Γ ⊢[T] t ∶ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) → ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h τ σ | case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.fst h✝ t ∶ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h✝ τ σ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) → ∃ σ, Γ ⊢... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.fst h✝ t ∶ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h✝ τ σ | case mp.fst
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
τ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ τ τ✝
⊢ ∃ σ, Γ ⊢[T] t ∶ L... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.fst h✝ t ∶ τ
⊢ ∃ σ, Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | exact ⟨_, by assumption⟩ | case mp.fst
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
τ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ τ τ✝
⊢ ∃ σ, Γ ⊢[T] t ∶ L... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.fst
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
τ✝ : LambdaType p✝ U... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | assumption | p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
τ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ τ τ✝
⊢ Γ ⊢[T] t ∶ LambdaType.prod h ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
τ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | rintro ⟨σ, h⟩ | case mpr
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h τ σ) → (Γ ⊢[T] LambdaTerm.fst h t ∶ τ) | case mpr.intro
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ τ σ
⊢ Γ ⊢[T] LambdaTerm.fst h✝ t ∶ τ | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h τ σ) →... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_fst | [82, 1] | [89, 17] | exact .fst h | case mpr.intro
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ τ σ
⊢ Γ ⊢[T] LambdaTerm.fst h✝ t ∶ τ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
p : LambdaParams
U : Type ?u.20413
C : Type ?u.20416
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | constructor | p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) ↔ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h σ τ | case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) → ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h σ τ
case mpr
p : LambdaParams
U : ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) ↔ ∃ σ, Γ ⊢[T] t ∶ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) → ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h σ τ | case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.snd h✝ t ∶ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h✝ σ τ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) → ∃ σ, Γ ⊢... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.snd h✝ t ∶ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h✝ σ τ | case mp.snd
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
σ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ σ✝ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ L... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.snd h✝ t ∶ τ
⊢ ∃ σ, Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | exact ⟨_, by assumption⟩ | case mp.snd
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
σ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ σ✝ τ
⊢ ∃ σ, Γ ⊢[T] t ∶ L... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.snd
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
σ✝ : LambdaType p✝ U... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | assumption | p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
σ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T] t ∶ LambdaType.prod h✝ σ✝ τ
⊢ Γ ⊢[T] t ∶ LambdaType.prod h ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h✝ : p✝.prod = true
σ✝ : LambdaType p✝ U✝
a✝ : Γ ⊢[T... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | rintro ⟨σ, h⟩ | case mpr
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h σ τ) → (Γ ⊢[T] LambdaTerm.snd h t ∶ τ) | case mpr.intro
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ σ τ
⊢ Γ ⊢[T] LambdaTerm.snd h✝ t ∶ τ | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
⊢ (∃ σ, Γ ⊢[T] t ∶ LambdaType.prod h σ τ) →... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_snd | [92, 1] | [99, 17] | exact .snd h | case mpr.intro
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ σ τ
⊢ Γ ⊢[T] LambdaTerm.snd h✝ t ∶ τ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
p : LambdaParams
U : Type ?u.21356
C : Type ?u.21359
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.prod = true
t : LambdaTerm p✝ U✝ C✝
τ σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.prod h✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | constructor | p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inl h τ t ∶ σ) ↔ ∃ ρ, σ = LambdaType.coprod h ρ τ ∧ (Γ ⊢[T] t ∶ ρ) | case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inl h τ t ∶ σ) → ∃ ρ, σ = LambdaType.coprod h ρ τ ∧ (Γ ⊢[T] t... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inl h τ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inl h τ t ∶ σ) → ∃ ρ, σ = LambdaType.coprod h ρ τ ∧ (Γ ⊢[T] t... | case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.inl h✝ τ t ∶ σ
⊢ ∃ ρ, σ = LambdaType.coprod h✝ ρ τ ∧ (Γ ⊢[T... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.inl h✝ τ t ∶ σ
⊢ ∃ ρ, σ = LambdaType.coprod h✝ ρ τ ∧ (Γ ⊢[T... | case mp.inl
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[T] t ∶ σ✝
⊢ ∃ ρ, LambdaType.coprod h✝ σ✝ τ = L... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTer... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | exact ⟨_, rfl, by assumption⟩ | case mp.inl
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[T] t ∶ σ✝
⊢ ∃ ρ, LambdaType.coprod h✝ σ✝ τ = L... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.inl
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod =... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | assumption | p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[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.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | rintro ⟨σ, rfl, h⟩ | case mpr
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ ρ, σ = LambdaType.coprod h ρ τ ∧ (Γ ⊢[T] t ∶ ρ)) → (Γ ⊢[T] LambdaTerm.inl h ... | case mpr.intro.intro
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.inl h✝ τ t ∶ LambdaType.coprod ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ ρ, σ = LambdaTy... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inl | [102, 1] | [109, 17] | exact .inl h | case mpr.intro.intro
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.inl h✝ τ t ∶ LambdaType.coprod ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
p : LambdaParams
U : Type ?u.22299
C : Type ?u.22302
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | constructor | p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inr h τ t ∶ σ) ↔ ∃ ρ, σ = LambdaType.coprod h τ ρ ∧ (Γ ⊢[T] t ∶ ρ) | case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inr h τ t ∶ σ) → ∃ ρ, σ = LambdaType.coprod h τ ρ ∧ (Γ ⊢[T] t... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inr h τ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | intro h | case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.inr h τ t ∶ σ) → ∃ ρ, σ = LambdaType.coprod h τ ρ ∧ (Γ ⊢[T] t... | case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.inr h✝ τ t ∶ σ
⊢ ∃ ρ, σ = LambdaType.coprod h✝ τ ρ ∧ (Γ ⊢[T... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | cases h | case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.inr h✝ τ t ∶ σ
⊢ ∃ ρ, σ = LambdaType.coprod h✝ τ ρ ∧ (Γ ⊢[T... | case mp.inr
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[T] t ∶ τ✝
⊢ ∃ ρ, LambdaType.coprod h✝ τ τ✝ = L... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTer... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | refine ⟨_, rfl, by assumption⟩ | case mp.inr
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[T] t ∶ τ✝
⊢ ∃ ρ, LambdaType.coprod h✝ τ τ✝ = L... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.inr
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod =... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | assumption | p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ ⊢[T] t ∶ τ✝
⊢ Γ ⊢[T] t ∶ τ✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ✝ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
a✝ : Γ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | rintro ⟨σ, rfl, h⟩ | case mpr
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ ρ, σ = LambdaType.coprod h τ ρ ∧ (Γ ⊢[T] t ∶ ρ)) → (Γ ⊢[T] LambdaTerm.inr h ... | case mpr.intro.intro
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.inr h✝ τ t ∶ LambdaType.coprod ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ ρ, σ = LambdaTy... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_inr | [112, 1] | [119, 17] | exact .inr h | case mpr.intro.intro
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ σ
⊢ Γ ⊢[T] LambdaTerm.inr h✝ τ t ∶ LambdaType.coprod ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro
p : LambdaParams
U : Type ?u.23350
C : Type ?u.23353
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | constructor | p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.case h l r t ∶ σ) ↔
∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂) ∧ (τ₁ :: Γ ⊢[T... | case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.case h l r t ∶ σ) →
∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂) ∧ (τ₁ ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.case h l r t ∶ σ) ↔
∃... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | intro h | case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.case h l r t ∶ σ) →
∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂) ∧ (τ₁ ... | case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.case h✝ l r t ∶ σ
⊢ ∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁ τ₂) ∧ (τ₁ :... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.case h l r t ∶ σ)... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | cases h | case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.case h✝ l r t ∶ σ
⊢ ∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁ τ₂) ∧ (τ₁ :... | case mp.case
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ U✝
a✝² : Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁✝ τ₂✝... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.case h✝ l r t ∶... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | refine ⟨_, _, by assumption, by assumption, by assumption⟩ | case mp.case
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ U✝
a✝² : Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁✝ τ₂✝... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.case
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : L... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | assumption | p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ U✝
a✝² : Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁✝ τ₂✝
a✝¹ : τ₁✝ ::... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | assumption | p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ U✝
a✝² : Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁✝ τ₂✝
a✝¹ : τ₁✝ ::... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | assumption | p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ U✝
a✝² : Γ ⊢[T] t ∶ LambdaType.coprod h✝ τ₁✝ τ₂✝
a✝¹ : τ₁✝ ::... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h✝ : p✝.coprod = true
τ₁✝ τ₂✝ : LambdaType p✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | rintro ⟨τ₁, τ₂, h₁, h₂, h₃⟩ | case mpr
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂) ∧ (τ₁ :: Γ ⊢[T] l ∶ σ) ∧ (τ₂ :: Γ ⊢[T] r ∶ σ)) ... | case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ τ₁ τ₂ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂
h₂ : τ₁ :: Γ ⊢[T] l ∶ σ
h₃... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (∃ τ₁ τ₂, (Γ ⊢[T] t ∶ LambdaType.co... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_case | [122, 1] | [129, 25] | exact .case h₁ h₂ h₃ | case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ τ₁ τ₂ : LambdaType p✝ U✝
h₁ : Γ ⊢[T] t ∶ LambdaType.coprod h τ₁ τ₂
h₂ : τ₁ :: Γ ⊢[T] l ∶ σ
h₃... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro.intro.intro.intro
p : LambdaParams
U : Type ?u.24401
C : Type ?u.24404
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.coprod = true
l r t : LambdaTerm p✝ U✝ C✝
σ τ₁ τ₂ : LambdaType p✝ U✝
h₁ : Γ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | constructor | p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.star h ∶ σ) ↔ σ = LambdaType.unit h | case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.star h ∶ σ) → σ = LambdaType.unit h
case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.star h ∶ σ) ↔ σ = LambdaType.unit h
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | intro h | case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.star h ∶ σ) → σ = LambdaType.unit h | case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.unit = true
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.star h✝ ∶ σ
⊢ σ = LambdaType.unit h✝ | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.star h ∶ σ) → σ = LambdaType.unit h
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | cases h | case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.unit = true
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.star h✝ ∶ σ
⊢ σ = LambdaType.unit h✝ | case mp.star
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h h✝ : p✝.unit = true
⊢ LambdaType.unit h✝ = LambdaType.unit h | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.unit = true
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.star h✝ ∶ σ
⊢ σ = LambdaType.unit h✝
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | rfl | case mp.star
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h h✝ : p✝.unit = true
⊢ LambdaType.unit h✝ = LambdaType.unit h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.star
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h h✝ : p✝.unit = true
⊢ LambdaType.unit h✝ = LambdaType.unit h
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | rintro rfl | case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ σ = LambdaType.unit h → (Γ ⊢[T] LambdaTerm.star h ∶ σ) | case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
⊢ Γ ⊢[T] LambdaTerm.star h ∶ LambdaType.unit h | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
σ : LambdaType p✝ U✝
⊢ σ = LambdaType.unit h → (Γ ⊢[T] LambdaTerm.star h ∶ σ)
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_star | [132, 1] | [138, 16] | exact .star | case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
⊢ Γ ⊢[T] LambdaTerm.star h ∶ LambdaType.unit h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.25589
C : Type ?u.25592
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.unit = true
⊢ Γ ⊢[T] LambdaTerm.star h ∶ LambdaType.unit h
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | constructor | p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.elim h τ t ∶ σ) ↔ σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h) | case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.elim h τ t ∶ σ) → σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h)
cas... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.elim h τ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | intro h | case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.elim h τ t ∶ σ) → σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h) | case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.elim h✝ τ t ∶ σ
⊢ σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h✝) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ (Γ ⊢[T] LambdaTerm.e... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | cases h | case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.elim h✝ τ t ∶ σ
⊢ σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h✝) | case mp.elim
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
h✝ : p✝.empty = true
a✝ : Γ ⊢[T] t ∶ LambdaType.empty h✝
⊢ τ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h) | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | exact ⟨rfl, by assumption⟩ | case mp.elim
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
h✝ : p✝.empty = true
a✝ : Γ ⊢[T] t ∶ LambdaType.empty h✝
⊢ τ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp.elim
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
h✝ : p✝.empty = true
a✝ : Γ ⊢[T] t ∶ L... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | assumption | p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
h✝ : p✝.empty = true
a✝ : Γ ⊢[T] t ∶ LambdaType.empty h✝
⊢ Γ ⊢[T] t ∶ LambdaType.empty h | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
h✝ : p✝.empty = true
a✝ : Γ ⊢[T] t ∶ LambdaType.emp... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | rintro ⟨rfl, h⟩ | case mpr
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ σ = τ ∧ (Γ ⊢[T] t ∶ LambdaType.empty h) → (Γ ⊢[T] LambdaTerm.elim h τ t ∶ σ) | case mpr.intro
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.empty h✝
⊢ Γ ⊢[T] LambdaTerm.elim h✝ σ t ∶ σ | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h : p✝.empty = true
τ : LambdaType p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
⊢ σ = τ ∧ (Γ ⊢[T] t ∶... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.hasType_elim | [141, 1] | [147, 18] | exact .elim h | case mpr.intro
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.empty h✝
⊢ Γ ⊢[T] LambdaTerm.elim h✝ σ t ∶ σ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr.intro
p : LambdaParams
U : Type ?u.26427
C : Type ?u.26430
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
h✝ : p✝.empty = true
t : LambdaTerm p✝ U✝ C✝
σ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ LambdaType.empty h✝
... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | induction t generalizing Γ τ | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ τ
⊢ LambdaTerm.freeVarRange t ≤ List.length Γ | case const
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ τ
⊢ LambdaTerm.freeVarRange (LambdaTerm.const a✝) ≤ List.length Γ
case var
p : LambdaParams
U : Type ?u... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
Γ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] t ∶ τ
⊢ LambdaTerm.freeVarRange t ≤ List.length Γ
TACTIC:
|
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | case lambda ih =>
simp at h ⊢
obtain ⟨σ, rfl, h⟩ := h
exact ih h | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.length Γ
Γ : Context ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | case case ih₁ ih₂ ih =>
simp at h ⊢
obtain ⟨τ₁, τ₂, h, h₁, h₂⟩ := h
exact ⟨⟨ih₁ h₁, ih₂ h₂⟩, ih h⟩ | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.length Γ
ih₂ : ∀ {Γ : Context p✝ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaT... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | all_goals aesop | case const
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ τ
⊢ LambdaTerm.freeVarRange (LambdaTerm.const a✝) ≤ List.length Γ
case var
p : LambdaParams
U : Type ?u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case const
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝ : C✝
Γ : Context p✝ U✝
τ : LambdaType p✝ U✝
h : Γ ⊢[T] LambdaTerm.const a✝ ∶ τ
⊢ LambdaTerm.freeVarRange (LambdaTerm.con... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | simp at h ⊢ | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.length Γ
Γ : Context ... | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.length Γ
Γ : Context ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | obtain ⟨σ, rfl, h⟩ := h | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.length Γ
Γ : Context ... | case intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.leng... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | exact ih h | case intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.leng... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
C✝ : Type u_1
p✝ : LambdaParams
U✝ : Type u_2
T : C✝ → LambdaType p✝ U✝
a✝² : p✝.lambda = true
a✝¹ : LambdaType p✝ U✝
a✝ : LambdaTerm p✝ U✝ C✝
ih : ∀ {Γ : Context p✝ U✝} {τ : LambdaType p✝ ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | simp at h ⊢ | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.length Γ
ih₂ : ∀ {Γ : Context p✝ ... | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.length Γ
ih₂ : ∀ {Γ : Context p✝ ... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaT... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | obtain ⟨τ₁, τ₂, h, h₁, h₂⟩ := h | p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.length Γ
ih₂ : ∀ {Γ : Context p✝ ... | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.leng... | Please generate a tactic in lean4 to solve the state.
STATE:
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaT... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | exact ⟨⟨ih₁ h₁, ih₂ h₂⟩, ih h⟩ | case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝² ∶ τ) → LambdaTerm.freeVarRange a✝² ≤ List.leng... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.intro.intro.intro
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.freeVarRange_le_length | [150, 1] | [160, 18] | aesop | case elim
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, (Γ ⊢[T] a✝ ∶ τ) → LambdaTerm.freeVarRange a✝ ≤ List.length Γ
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case elim
p : LambdaParams
U : Type ?u.27425
C : Type ?u.27428
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✝} {τ : LambdaType p✝ U✝}, ... |
https://github.com/zeramorphic/lambda_calculi.git | 1b485231bf1e4f70be77b658b3c448b98084b5d2 | LambdaCalculi/HasType.lean | LambdaCalculi.eq_of_hasType | [163, 1] | [184, 18] | induction t generalizing Γ σ τ | 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✝
Γ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T] t ∶ σ
hτ : Γ ⊢[T] t ∶ τ
⊢ σ = τ | 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... | 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✝
Γ : Context p✝ U✝
t : LambdaTerm p✝ U✝ C✝
σ τ : LambdaType p✝ U✝
hσ : Γ ⊢[T] t ∶ σ
hτ : Γ ⊢[T] t ∶ τ
⊢ σ = τ
TACTIC:
|
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