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stlc_small5k.lean
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def Ty : Type 1
:= ∀ (Ty : Type)
(ι : Ty)
(arr : Ty → Ty → Ty)
, Ty
def ι : Ty := λ _ ι _ => ι
def arr : Ty → Ty → Ty
:= λ A B Ty ι arr =>
arr (A Ty ι arr) (B Ty ι arr)
def Con : Type 1
:= ∀ (Con : Type)
(nil : Con)
(snoc : Con → Ty → Con)
, Con
def nil : Con
:= λ Con nil snoc => nil
def snoc : Con → Ty → Con
:= λ Γ A Con nil snoc => snoc (Γ Con nil snoc) A
def Var : Con → Ty → Type 1
:= λ Γ A =>
∀ (Var : Con → Ty → Type)
(vz : ∀ Γ A, Var (snoc Γ A) A)
(vs : ∀ Γ B A, Var Γ A → Var (snoc Γ B) A)
, Var Γ A
def vz {Γ A} : Var (snoc Γ A) A
:= λ Var vz vs => vz _ _
def vs {Γ B A} : Var Γ A → Var (snoc Γ B) A
:= λ x Var vz vs => vs _ _ _ (x Var vz vs)
def Tm : Con → Ty → Type 1
:= λ Γ A =>
∀ (Tm : Con → Ty → Type)
(var : ∀ Γ A , Var Γ A → Tm Γ A)
(lam : ∀ Γ A B , Tm (snoc Γ A) B → Tm Γ (arr A B))
(app : ∀ Γ A B , Tm Γ (arr A B) → Tm Γ A → Tm Γ B)
, Tm Γ A
def var {Γ A} : Var Γ A → Tm Γ A
:= λ x Tm var lam app =>
var _ _ x
def lam {Γ A B} : Tm (snoc Γ A) B → Tm Γ (arr A B)
:= λ t Tm var lam app =>
lam _ _ _ (t Tm var lam app)
def app {Γ A B} : Tm Γ (arr A B) → Tm Γ A → Tm Γ B
:= λ t u Tm var lam app =>
app _ _ _
(t Tm var lam app)
(u Tm var lam app)
def v0 {Γ A} : Tm (snoc Γ A) A
:= var vz
def v1 {Γ A B} : Tm (snoc (snoc Γ A) B) A
:= var (vs vz)
def v2 {Γ A B C} : Tm (snoc (snoc (snoc Γ A) B) C) A
:= var (vs (vs vz))
def v3 {Γ A B C D} : Tm (snoc (snoc (snoc (snoc Γ A) B) C) D) A
:= var (vs (vs (vs vz)))
def v4 {Γ A B C D E} : Tm (snoc (snoc (snoc (snoc (snoc Γ A) B) C) D) E) A
:= var (vs (vs (vs (vs vz))))
def test {Γ A} : Tm Γ (arr (arr A A) (arr A A))
:= lam (lam (app v1 (app v1 (app v1 (app v1 (app v1 (app v1 v0)))))))
def Ty1 : Type 1
:= ∀ (Ty1 : Type)
(ι : Ty1)
(arr : Ty1 → Ty1 → Ty1)
, Ty1
def ι1 : Ty1 := λ _ ι1 _ => ι1
def arr1 : Ty1 → Ty1 → Ty1
:= λ A B Ty1 ι1 arr1 =>
arr1 (A Ty1 ι1 arr1) (B Ty1 ι1 arr1)
def Con1 : Type 1
:= ∀ (Con1 : Type)
(nil : Con1)
(snoc : Con1 → Ty1 → Con1)
, Con1
def nil1 : Con1
:= λ Con1 nil1 snoc => nil1
def snoc1 : Con1 → Ty1 → Con1
:= λ Γ A Con1 nil1 snoc1 => snoc1 (Γ Con1 nil1 snoc1) A
def Var1 : Con1 → Ty1 → Type 1
:= λ Γ A =>
∀ (Var1 : Con1 → Ty1 → Type)
(vz : ∀ Γ A, Var1 (snoc1 Γ A) A)
(vs : ∀ Γ B A, Var1 Γ A → Var1 (snoc1 Γ B) A)
, Var1 Γ A
def vz1 {Γ A} : Var1 (snoc1 Γ A) A
:= λ Var1 vz1 vs => vz1 _ _
def vs1 {Γ B A} : Var1 Γ A → Var1 (snoc1 Γ B) A
:= λ x Var1 vz1 vs1 => vs1 _ _ _ (x Var1 vz1 vs1)
def Tm1 : Con1 → Ty1 → Type 1
:= λ Γ A =>
∀ (Tm1 : Con1 → Ty1 → Type)
(var : ∀ Γ A , Var1 Γ A → Tm1 Γ A)
(lam : ∀ Γ A B , Tm1 (snoc1 Γ A) B → Tm1 Γ (arr1 A B))
(app : ∀ Γ A B , Tm1 Γ (arr1 A B) → Tm1 Γ A → Tm1 Γ B)
, Tm1 Γ A
def var1 {Γ A} : Var1 Γ A → Tm1 Γ A
:= λ x Tm1 var1 lam app =>
var1 _ _ x
def lam1 {Γ A B} : Tm1 (snoc1 Γ A) B → Tm1 Γ (arr1 A B)
:= λ t Tm1 var1 lam1 app =>
lam1 _ _ _ (t Tm1 var1 lam1 app)
def app1 {Γ A B} : Tm1 Γ (arr1 A B) → Tm1 Γ A → Tm1 Γ B
:= λ t u Tm1 var1 lam1 app1 =>
app1 _ _ _
(t Tm1 var1 lam1 app1)
(u Tm1 var1 lam1 app1)
def v01 {Γ A} : Tm1 (snoc1 Γ A) A
:= var1 vz1
def v11 {Γ A B} : Tm1 (snoc1 (snoc1 Γ A) B) A
:= var1 (vs1 vz1)
def v21 {Γ A B C} : Tm1 (snoc1 (snoc1 (snoc1 Γ A) B) C) A
:= var1 (vs1 (vs1 vz1))
def v31 {Γ A B C D} : Tm1 (snoc1 (snoc1 (snoc1 (snoc1 Γ A) B) C) D) A
:= var1 (vs1 (vs1 (vs1 vz1)))
def v41 {Γ A B C D E} : Tm1 (snoc1 (snoc1 (snoc1 (snoc1 (snoc1 Γ A) B) C) D) E) A
:= var1 (vs1 (vs1 (vs1 (vs1 vz1))))
def test1 {Γ A} : Tm1 Γ (arr1 (arr1 A A) (arr1 A A))
:= lam1 (lam1 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 v01)))))))
def Ty2 : Type 1
:= ∀ (Ty2 : Type)
(ι : Ty2)
(arr : Ty2 → Ty2 → Ty2)
, Ty2
def ι2 : Ty2 := λ _ ι2 _ => ι2
def arr2 : Ty2 → Ty2 → Ty2
:= λ A B Ty2 ι2 arr2 =>
arr2 (A Ty2 ι2 arr2) (B Ty2 ι2 arr2)
def Con2 : Type 1
:= ∀ (Con2 : Type)
(nil : Con2)
(snoc : Con2 → Ty2 → Con2)
, Con2
def nil2 : Con2
:= λ Con2 nil2 snoc => nil2
def snoc2 : Con2 → Ty2 → Con2
:= λ Γ A Con2 nil2 snoc2 => snoc2 (Γ Con2 nil2 snoc2) A
def Var2 : Con2 → Ty2 → Type 1
:= λ Γ A =>
∀ (Var2 : Con2 → Ty2 → Type)
(vz : ∀ Γ A, Var2 (snoc2 Γ A) A)
(vs : ∀ Γ B A, Var2 Γ A → Var2 (snoc2 Γ B) A)
, Var2 Γ A
def vz2 {Γ A} : Var2 (snoc2 Γ A) A
:= λ Var2 vz2 vs => vz2 _ _
def vs2 {Γ B A} : Var2 Γ A → Var2 (snoc2 Γ B) A
:= λ x Var2 vz2 vs2 => vs2 _ _ _ (x Var2 vz2 vs2)
def Tm2 : Con2 → Ty2 → Type 1
:= λ Γ A =>
∀ (Tm2 : Con2 → Ty2 → Type)
(var : ∀ Γ A , Var2 Γ A → Tm2 Γ A)
(lam : ∀ Γ A B , Tm2 (snoc2 Γ A) B → Tm2 Γ (arr2 A B))
(app : ∀ Γ A B , Tm2 Γ (arr2 A B) → Tm2 Γ A → Tm2 Γ B)
, Tm2 Γ A
def var2 {Γ A} : Var2 Γ A → Tm2 Γ A
:= λ x Tm2 var2 lam app =>
var2 _ _ x
def lam2 {Γ A B} : Tm2 (snoc2 Γ A) B → Tm2 Γ (arr2 A B)
:= λ t Tm2 var2 lam2 app =>
lam2 _ _ _ (t Tm2 var2 lam2 app)
def app2 {Γ A B} : Tm2 Γ (arr2 A B) → Tm2 Γ A → Tm2 Γ B
:= λ t u Tm2 var2 lam2 app2 =>
app2 _ _ _
(t Tm2 var2 lam2 app2)
(u Tm2 var2 lam2 app2)
def v02 {Γ A} : Tm2 (snoc2 Γ A) A
:= var2 vz2
def v12 {Γ A B} : Tm2 (snoc2 (snoc2 Γ A) B) A
:= var2 (vs2 vz2)
def v22 {Γ A B C} : Tm2 (snoc2 (snoc2 (snoc2 Γ A) B) C) A
:= var2 (vs2 (vs2 vz2))
def v32 {Γ A B C D} : Tm2 (snoc2 (snoc2 (snoc2 (snoc2 Γ A) B) C) D) A
:= var2 (vs2 (vs2 (vs2 vz2)))
def v42 {Γ A B C D E} : Tm2 (snoc2 (snoc2 (snoc2 (snoc2 (snoc2 Γ A) B) C) D) E) A
:= var2 (vs2 (vs2 (vs2 (vs2 vz2))))
def test2 {Γ A} : Tm2 Γ (arr2 (arr2 A A) (arr2 A A))
:= lam2 (lam2 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 v02)))))))
def Ty3 : Type 1
:= ∀ (Ty3 : Type)
(ι : Ty3)
(arr : Ty3 → Ty3 → Ty3)
, Ty3
def ι3 : Ty3 := λ _ ι3 _ => ι3
def arr3 : Ty3 → Ty3 → Ty3
:= λ A B Ty3 ι3 arr3 =>
arr3 (A Ty3 ι3 arr3) (B Ty3 ι3 arr3)
def Con3 : Type 1
:= ∀ (Con3 : Type)
(nil : Con3)
(snoc : Con3 → Ty3 → Con3)
, Con3
def nil3 : Con3
:= λ Con3 nil3 snoc => nil3
def snoc3 : Con3 → Ty3 → Con3
:= λ Γ A Con3 nil3 snoc3 => snoc3 (Γ Con3 nil3 snoc3) A
def Var3 : Con3 → Ty3 → Type 1
:= λ Γ A =>
∀ (Var3 : Con3 → Ty3 → Type)
(vz : ∀ Γ A, Var3 (snoc3 Γ A) A)
(vs : ∀ Γ B A, Var3 Γ A → Var3 (snoc3 Γ B) A)
, Var3 Γ A
def vz3 {Γ A} : Var3 (snoc3 Γ A) A
:= λ Var3 vz3 vs => vz3 _ _
def vs3 {Γ B A} : Var3 Γ A → Var3 (snoc3 Γ B) A
:= λ x Var3 vz3 vs3 => vs3 _ _ _ (x Var3 vz3 vs3)
def Tm3 : Con3 → Ty3 → Type 1
:= λ Γ A =>
∀ (Tm3 : Con3 → Ty3 → Type)
(var : ∀ Γ A , Var3 Γ A → Tm3 Γ A)
(lam : ∀ Γ A B , Tm3 (snoc3 Γ A) B → Tm3 Γ (arr3 A B))
(app : ∀ Γ A B , Tm3 Γ (arr3 A B) → Tm3 Γ A → Tm3 Γ B)
, Tm3 Γ A
def var3 {Γ A} : Var3 Γ A → Tm3 Γ A
:= λ x Tm3 var3 lam app =>
var3 _ _ x
def lam3 {Γ A B} : Tm3 (snoc3 Γ A) B → Tm3 Γ (arr3 A B)
:= λ t Tm3 var3 lam3 app =>
lam3 _ _ _ (t Tm3 var3 lam3 app)
def app3 {Γ A B} : Tm3 Γ (arr3 A B) → Tm3 Γ A → Tm3 Γ B
:= λ t u Tm3 var3 lam3 app3 =>
app3 _ _ _
(t Tm3 var3 lam3 app3)
(u Tm3 var3 lam3 app3)
def v03 {Γ A} : Tm3 (snoc3 Γ A) A
:= var3 vz3
def v13 {Γ A B} : Tm3 (snoc3 (snoc3 Γ A) B) A
:= var3 (vs3 vz3)
def v23 {Γ A B C} : Tm3 (snoc3 (snoc3 (snoc3 Γ A) B) C) A
:= var3 (vs3 (vs3 vz3))
def v33 {Γ A B C D} : Tm3 (snoc3 (snoc3 (snoc3 (snoc3 Γ A) B) C) D) A
:= var3 (vs3 (vs3 (vs3 vz3)))
def v43 {Γ A B C D E} : Tm3 (snoc3 (snoc3 (snoc3 (snoc3 (snoc3 Γ A) B) C) D) E) A
:= var3 (vs3 (vs3 (vs3 (vs3 vz3))))
def test3 {Γ A} : Tm3 Γ (arr3 (arr3 A A) (arr3 A A))
:= lam3 (lam3 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 v03)))))))
def Ty4 : Type 1
:= ∀ (Ty4 : Type)
(ι : Ty4)
(arr : Ty4 → Ty4 → Ty4)
, Ty4
def ι4 : Ty4 := λ _ ι4 _ => ι4
def arr4 : Ty4 → Ty4 → Ty4
:= λ A B Ty4 ι4 arr4 =>
arr4 (A Ty4 ι4 arr4) (B Ty4 ι4 arr4)
def Con4 : Type 1
:= ∀ (Con4 : Type)
(nil : Con4)
(snoc : Con4 → Ty4 → Con4)
, Con4
def nil4 : Con4
:= λ Con4 nil4 snoc => nil4
def snoc4 : Con4 → Ty4 → Con4
:= λ Γ A Con4 nil4 snoc4 => snoc4 (Γ Con4 nil4 snoc4) A
def Var4 : Con4 → Ty4 → Type 1
:= λ Γ A =>
∀ (Var4 : Con4 → Ty4 → Type)
(vz : ∀ Γ A, Var4 (snoc4 Γ A) A)
(vs : ∀ Γ B A, Var4 Γ A → Var4 (snoc4 Γ B) A)
, Var4 Γ A
def vz4 {Γ A} : Var4 (snoc4 Γ A) A
:= λ Var4 vz4 vs => vz4 _ _
def vs4 {Γ B A} : Var4 Γ A → Var4 (snoc4 Γ B) A
:= λ x Var4 vz4 vs4 => vs4 _ _ _ (x Var4 vz4 vs4)
def Tm4 : Con4 → Ty4 → Type 1
:= λ Γ A =>
∀ (Tm4 : Con4 → Ty4 → Type)
(var : ∀ Γ A , Var4 Γ A → Tm4 Γ A)
(lam : ∀ Γ A B , Tm4 (snoc4 Γ A) B → Tm4 Γ (arr4 A B))
(app : ∀ Γ A B , Tm4 Γ (arr4 A B) → Tm4 Γ A → Tm4 Γ B)
, Tm4 Γ A
def var4 {Γ A} : Var4 Γ A → Tm4 Γ A
:= λ x Tm4 var4 lam app =>
var4 _ _ x
def lam4 {Γ A B} : Tm4 (snoc4 Γ A) B → Tm4 Γ (arr4 A B)
:= λ t Tm4 var4 lam4 app =>
lam4 _ _ _ (t Tm4 var4 lam4 app)
def app4 {Γ A B} : Tm4 Γ (arr4 A B) → Tm4 Γ A → Tm4 Γ B
:= λ t u Tm4 var4 lam4 app4 =>
app4 _ _ _
(t Tm4 var4 lam4 app4)
(u Tm4 var4 lam4 app4)
def v04 {Γ A} : Tm4 (snoc4 Γ A) A
:= var4 vz4
def v14 {Γ A B} : Tm4 (snoc4 (snoc4 Γ A) B) A
:= var4 (vs4 vz4)
def v24 {Γ A B C} : Tm4 (snoc4 (snoc4 (snoc4 Γ A) B) C) A
:= var4 (vs4 (vs4 vz4))
def v34 {Γ A B C D} : Tm4 (snoc4 (snoc4 (snoc4 (snoc4 Γ A) B) C) D) A
:= var4 (vs4 (vs4 (vs4 vz4)))
def v44 {Γ A B C D E} : Tm4 (snoc4 (snoc4 (snoc4 (snoc4 (snoc4 Γ A) B) C) D) E) A
:= var4 (vs4 (vs4 (vs4 (vs4 vz4))))
def test4 {Γ A} : Tm4 Γ (arr4 (arr4 A A) (arr4 A A))
:= lam4 (lam4 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 v04)))))))
def Ty5 : Type 1
:= ∀ (Ty5 : Type)
(ι : Ty5)
(arr : Ty5 → Ty5 → Ty5)
, Ty5
def ι5 : Ty5 := λ _ ι5 _ => ι5
def arr5 : Ty5 → Ty5 → Ty5
:= λ A B Ty5 ι5 arr5 =>
arr5 (A Ty5 ι5 arr5) (B Ty5 ι5 arr5)
def Con5 : Type 1
:= ∀ (Con5 : Type)
(nil : Con5)
(snoc : Con5 → Ty5 → Con5)
, Con5
def nil5 : Con5
:= λ Con5 nil5 snoc => nil5
def snoc5 : Con5 → Ty5 → Con5
:= λ Γ A Con5 nil5 snoc5 => snoc5 (Γ Con5 nil5 snoc5) A
def Var5 : Con5 → Ty5 → Type 1
:= λ Γ A =>
∀ (Var5 : Con5 → Ty5 → Type)
(vz : ∀ Γ A, Var5 (snoc5 Γ A) A)
(vs : ∀ Γ B A, Var5 Γ A → Var5 (snoc5 Γ B) A)
, Var5 Γ A
def vz5 {Γ A} : Var5 (snoc5 Γ A) A
:= λ Var5 vz5 vs => vz5 _ _
def vs5 {Γ B A} : Var5 Γ A → Var5 (snoc5 Γ B) A
:= λ x Var5 vz5 vs5 => vs5 _ _ _ (x Var5 vz5 vs5)
def Tm5 : Con5 → Ty5 → Type 1
:= λ Γ A =>
∀ (Tm5 : Con5 → Ty5 → Type)
(var : ∀ Γ A , Var5 Γ A → Tm5 Γ A)
(lam : ∀ Γ A B , Tm5 (snoc5 Γ A) B → Tm5 Γ (arr5 A B))
(app : ∀ Γ A B , Tm5 Γ (arr5 A B) → Tm5 Γ A → Tm5 Γ B)
, Tm5 Γ A
def var5 {Γ A} : Var5 Γ A → Tm5 Γ A
:= λ x Tm5 var5 lam app =>
var5 _ _ x
def lam5 {Γ A B} : Tm5 (snoc5 Γ A) B → Tm5 Γ (arr5 A B)
:= λ t Tm5 var5 lam5 app =>
lam5 _ _ _ (t Tm5 var5 lam5 app)
def app5 {Γ A B} : Tm5 Γ (arr5 A B) → Tm5 Γ A → Tm5 Γ B
:= λ t u Tm5 var5 lam5 app5 =>
app5 _ _ _
(t Tm5 var5 lam5 app5)
(u Tm5 var5 lam5 app5)
def v05 {Γ A} : Tm5 (snoc5 Γ A) A
:= var5 vz5
def v15 {Γ A B} : Tm5 (snoc5 (snoc5 Γ A) B) A
:= var5 (vs5 vz5)
def v25 {Γ A B C} : Tm5 (snoc5 (snoc5 (snoc5 Γ A) B) C) A
:= var5 (vs5 (vs5 vz5))
def v35 {Γ A B C D} : Tm5 (snoc5 (snoc5 (snoc5 (snoc5 Γ A) B) C) D) A
:= var5 (vs5 (vs5 (vs5 vz5)))
def v45 {Γ A B C D E} : Tm5 (snoc5 (snoc5 (snoc5 (snoc5 (snoc5 Γ A) B) C) D) E) A
:= var5 (vs5 (vs5 (vs5 (vs5 vz5))))
def test5 {Γ A} : Tm5 Γ (arr5 (arr5 A A) (arr5 A A))
:= lam5 (lam5 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 v05)))))))
def Ty6 : Type 1
:= ∀ (Ty6 : Type)
(ι : Ty6)
(arr : Ty6 → Ty6 → Ty6)
, Ty6
def ι6 : Ty6 := λ _ ι6 _ => ι6
def arr6 : Ty6 → Ty6 → Ty6
:= λ A B Ty6 ι6 arr6 =>
arr6 (A Ty6 ι6 arr6) (B Ty6 ι6 arr6)
def Con6 : Type 1
:= ∀ (Con6 : Type)
(nil : Con6)
(snoc : Con6 → Ty6 → Con6)
, Con6
def nil6 : Con6
:= λ Con6 nil6 snoc => nil6
def snoc6 : Con6 → Ty6 → Con6
:= λ Γ A Con6 nil6 snoc6 => snoc6 (Γ Con6 nil6 snoc6) A
def Var6 : Con6 → Ty6 → Type 1
:= λ Γ A =>
∀ (Var6 : Con6 → Ty6 → Type)
(vz : ∀ Γ A, Var6 (snoc6 Γ A) A)
(vs : ∀ Γ B A, Var6 Γ A → Var6 (snoc6 Γ B) A)
, Var6 Γ A
def vz6 {Γ A} : Var6 (snoc6 Γ A) A
:= λ Var6 vz6 vs => vz6 _ _
def vs6 {Γ B A} : Var6 Γ A → Var6 (snoc6 Γ B) A
:= λ x Var6 vz6 vs6 => vs6 _ _ _ (x Var6 vz6 vs6)
def Tm6 : Con6 → Ty6 → Type 1
:= λ Γ A =>
∀ (Tm6 : Con6 → Ty6 → Type)
(var : ∀ Γ A , Var6 Γ A → Tm6 Γ A)
(lam : ∀ Γ A B , Tm6 (snoc6 Γ A) B → Tm6 Γ (arr6 A B))
(app : ∀ Γ A B , Tm6 Γ (arr6 A B) → Tm6 Γ A → Tm6 Γ B)
, Tm6 Γ A
def var6 {Γ A} : Var6 Γ A → Tm6 Γ A
:= λ x Tm6 var6 lam app =>
var6 _ _ x
def lam6 {Γ A B} : Tm6 (snoc6 Γ A) B → Tm6 Γ (arr6 A B)
:= λ t Tm6 var6 lam6 app =>
lam6 _ _ _ (t Tm6 var6 lam6 app)
def app6 {Γ A B} : Tm6 Γ (arr6 A B) → Tm6 Γ A → Tm6 Γ B
:= λ t u Tm6 var6 lam6 app6 =>
app6 _ _ _
(t Tm6 var6 lam6 app6)
(u Tm6 var6 lam6 app6)
def v06 {Γ A} : Tm6 (snoc6 Γ A) A
:= var6 vz6
def v16 {Γ A B} : Tm6 (snoc6 (snoc6 Γ A) B) A
:= var6 (vs6 vz6)
def v26 {Γ A B C} : Tm6 (snoc6 (snoc6 (snoc6 Γ A) B) C) A
:= var6 (vs6 (vs6 vz6))
def v36 {Γ A B C D} : Tm6 (snoc6 (snoc6 (snoc6 (snoc6 Γ A) B) C) D) A
:= var6 (vs6 (vs6 (vs6 vz6)))
def v46 {Γ A B C D E} : Tm6 (snoc6 (snoc6 (snoc6 (snoc6 (snoc6 Γ A) B) C) D) E) A
:= var6 (vs6 (vs6 (vs6 (vs6 vz6))))
def test6 {Γ A} : Tm6 Γ (arr6 (arr6 A A) (arr6 A A))
:= lam6 (lam6 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 v06)))))))
def Ty7 : Type 1
:= ∀ (Ty7 : Type)
(ι : Ty7)
(arr : Ty7 → Ty7 → Ty7)
, Ty7
def ι7 : Ty7 := λ _ ι7 _ => ι7
def arr7 : Ty7 → Ty7 → Ty7
:= λ A B Ty7 ι7 arr7 =>
arr7 (A Ty7 ι7 arr7) (B Ty7 ι7 arr7)
def Con7 : Type 1
:= ∀ (Con7 : Type)
(nil : Con7)
(snoc : Con7 → Ty7 → Con7)
, Con7
def nil7 : Con7
:= λ Con7 nil7 snoc => nil7
def snoc7 : Con7 → Ty7 → Con7
:= λ Γ A Con7 nil7 snoc7 => snoc7 (Γ Con7 nil7 snoc7) A
def Var7 : Con7 → Ty7 → Type 1
:= λ Γ A =>
∀ (Var7 : Con7 → Ty7 → Type)
(vz : ∀ Γ A, Var7 (snoc7 Γ A) A)
(vs : ∀ Γ B A, Var7 Γ A → Var7 (snoc7 Γ B) A)
, Var7 Γ A
def vz7 {Γ A} : Var7 (snoc7 Γ A) A
:= λ Var7 vz7 vs => vz7 _ _
def vs7 {Γ B A} : Var7 Γ A → Var7 (snoc7 Γ B) A
:= λ x Var7 vz7 vs7 => vs7 _ _ _ (x Var7 vz7 vs7)
def Tm7 : Con7 → Ty7 → Type 1
:= λ Γ A =>
∀ (Tm7 : Con7 → Ty7 → Type)
(var : ∀ Γ A , Var7 Γ A → Tm7 Γ A)
(lam : ∀ Γ A B , Tm7 (snoc7 Γ A) B → Tm7 Γ (arr7 A B))
(app : ∀ Γ A B , Tm7 Γ (arr7 A B) → Tm7 Γ A → Tm7 Γ B)
, Tm7 Γ A
def var7 {Γ A} : Var7 Γ A → Tm7 Γ A
:= λ x Tm7 var7 lam app =>
var7 _ _ x
def lam7 {Γ A B} : Tm7 (snoc7 Γ A) B → Tm7 Γ (arr7 A B)
:= λ t Tm7 var7 lam7 app =>
lam7 _ _ _ (t Tm7 var7 lam7 app)
def app7 {Γ A B} : Tm7 Γ (arr7 A B) → Tm7 Γ A → Tm7 Γ B
:= λ t u Tm7 var7 lam7 app7 =>
app7 _ _ _
(t Tm7 var7 lam7 app7)
(u Tm7 var7 lam7 app7)
def v07 {Γ A} : Tm7 (snoc7 Γ A) A
:= var7 vz7
def v17 {Γ A B} : Tm7 (snoc7 (snoc7 Γ A) B) A
:= var7 (vs7 vz7)
def v27 {Γ A B C} : Tm7 (snoc7 (snoc7 (snoc7 Γ A) B) C) A
:= var7 (vs7 (vs7 vz7))
def v37 {Γ A B C D} : Tm7 (snoc7 (snoc7 (snoc7 (snoc7 Γ A) B) C) D) A
:= var7 (vs7 (vs7 (vs7 vz7)))
def v47 {Γ A B C D E} : Tm7 (snoc7 (snoc7 (snoc7 (snoc7 (snoc7 Γ A) B) C) D) E) A
:= var7 (vs7 (vs7 (vs7 (vs7 vz7))))
def test7 {Γ A} : Tm7 Γ (arr7 (arr7 A A) (arr7 A A))
:= lam7 (lam7 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 v07)))))))
def Ty8 : Type 1
:= ∀ (Ty8 : Type)
(ι : Ty8)
(arr : Ty8 → Ty8 → Ty8)
, Ty8
def ι8 : Ty8 := λ _ ι8 _ => ι8
def arr8 : Ty8 → Ty8 → Ty8
:= λ A B Ty8 ι8 arr8 =>
arr8 (A Ty8 ι8 arr8) (B Ty8 ι8 arr8)
def Con8 : Type 1
:= ∀ (Con8 : Type)
(nil : Con8)
(snoc : Con8 → Ty8 → Con8)
, Con8
def nil8 : Con8
:= λ Con8 nil8 snoc => nil8
def snoc8 : Con8 → Ty8 → Con8
:= λ Γ A Con8 nil8 snoc8 => snoc8 (Γ Con8 nil8 snoc8) A
def Var8 : Con8 → Ty8 → Type 1
:= λ Γ A =>
∀ (Var8 : Con8 → Ty8 → Type)
(vz : ∀ Γ A, Var8 (snoc8 Γ A) A)
(vs : ∀ Γ B A, Var8 Γ A → Var8 (snoc8 Γ B) A)
, Var8 Γ A
def vz8 {Γ A} : Var8 (snoc8 Γ A) A
:= λ Var8 vz8 vs => vz8 _ _
def vs8 {Γ B A} : Var8 Γ A → Var8 (snoc8 Γ B) A
:= λ x Var8 vz8 vs8 => vs8 _ _ _ (x Var8 vz8 vs8)
def Tm8 : Con8 → Ty8 → Type 1
:= λ Γ A =>
∀ (Tm8 : Con8 → Ty8 → Type)
(var : ∀ Γ A , Var8 Γ A → Tm8 Γ A)
(lam : ∀ Γ A B , Tm8 (snoc8 Γ A) B → Tm8 Γ (arr8 A B))
(app : ∀ Γ A B , Tm8 Γ (arr8 A B) → Tm8 Γ A → Tm8 Γ B)
, Tm8 Γ A
def var8 {Γ A} : Var8 Γ A → Tm8 Γ A
:= λ x Tm8 var8 lam app =>
var8 _ _ x
def lam8 {Γ A B} : Tm8 (snoc8 Γ A) B → Tm8 Γ (arr8 A B)
:= λ t Tm8 var8 lam8 app =>
lam8 _ _ _ (t Tm8 var8 lam8 app)
def app8 {Γ A B} : Tm8 Γ (arr8 A B) → Tm8 Γ A → Tm8 Γ B
:= λ t u Tm8 var8 lam8 app8 =>
app8 _ _ _
(t Tm8 var8 lam8 app8)
(u Tm8 var8 lam8 app8)
def v08 {Γ A} : Tm8 (snoc8 Γ A) A
:= var8 vz8
def v18 {Γ A B} : Tm8 (snoc8 (snoc8 Γ A) B) A
:= var8 (vs8 vz8)
def v28 {Γ A B C} : Tm8 (snoc8 (snoc8 (snoc8 Γ A) B) C) A
:= var8 (vs8 (vs8 vz8))
def v38 {Γ A B C D} : Tm8 (snoc8 (snoc8 (snoc8 (snoc8 Γ A) B) C) D) A
:= var8 (vs8 (vs8 (vs8 vz8)))
def v48 {Γ A B C D E} : Tm8 (snoc8 (snoc8 (snoc8 (snoc8 (snoc8 Γ A) B) C) D) E) A
:= var8 (vs8 (vs8 (vs8 (vs8 vz8))))
def test8 {Γ A} : Tm8 Γ (arr8 (arr8 A A) (arr8 A A))
:= lam8 (lam8 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 v08)))))))
def Ty9 : Type 1
:= ∀ (Ty9 : Type)
(ι : Ty9)
(arr : Ty9 → Ty9 → Ty9)
, Ty9
def ι9 : Ty9 := λ _ ι9 _ => ι9
def arr9 : Ty9 → Ty9 → Ty9
:= λ A B Ty9 ι9 arr9 =>
arr9 (A Ty9 ι9 arr9) (B Ty9 ι9 arr9)
def Con9 : Type 1
:= ∀ (Con9 : Type)
(nil : Con9)
(snoc : Con9 → Ty9 → Con9)
, Con9
def nil9 : Con9
:= λ Con9 nil9 snoc => nil9
def snoc9 : Con9 → Ty9 → Con9
:= λ Γ A Con9 nil9 snoc9 => snoc9 (Γ Con9 nil9 snoc9) A
def Var9 : Con9 → Ty9 → Type 1
:= λ Γ A =>
∀ (Var9 : Con9 → Ty9 → Type)
(vz : ∀ Γ A, Var9 (snoc9 Γ A) A)
(vs : ∀ Γ B A, Var9 Γ A → Var9 (snoc9 Γ B) A)
, Var9 Γ A
def vz9 {Γ A} : Var9 (snoc9 Γ A) A
:= λ Var9 vz9 vs => vz9 _ _
def vs9 {Γ B A} : Var9 Γ A → Var9 (snoc9 Γ B) A
:= λ x Var9 vz9 vs9 => vs9 _ _ _ (x Var9 vz9 vs9)
def Tm9 : Con9 → Ty9 → Type 1
:= λ Γ A =>
∀ (Tm9 : Con9 → Ty9 → Type)
(var : ∀ Γ A , Var9 Γ A → Tm9 Γ A)
(lam : ∀ Γ A B , Tm9 (snoc9 Γ A) B → Tm9 Γ (arr9 A B))
(app : ∀ Γ A B , Tm9 Γ (arr9 A B) → Tm9 Γ A → Tm9 Γ B)
, Tm9 Γ A
def var9 {Γ A} : Var9 Γ A → Tm9 Γ A
:= λ x Tm9 var9 lam app =>
var9 _ _ x
def lam9 {Γ A B} : Tm9 (snoc9 Γ A) B → Tm9 Γ (arr9 A B)
:= λ t Tm9 var9 lam9 app =>
lam9 _ _ _ (t Tm9 var9 lam9 app)
def app9 {Γ A B} : Tm9 Γ (arr9 A B) → Tm9 Γ A → Tm9 Γ B
:= λ t u Tm9 var9 lam9 app9 =>
app9 _ _ _
(t Tm9 var9 lam9 app9)
(u Tm9 var9 lam9 app9)
def v09 {Γ A} : Tm9 (snoc9 Γ A) A
:= var9 vz9
def v19 {Γ A B} : Tm9 (snoc9 (snoc9 Γ A) B) A
:= var9 (vs9 vz9)
def v29 {Γ A B C} : Tm9 (snoc9 (snoc9 (snoc9 Γ A) B) C) A
:= var9 (vs9 (vs9 vz9))
def v39 {Γ A B C D} : Tm9 (snoc9 (snoc9 (snoc9 (snoc9 Γ A) B) C) D) A
:= var9 (vs9 (vs9 (vs9 vz9)))
def v49 {Γ A B C D E} : Tm9 (snoc9 (snoc9 (snoc9 (snoc9 (snoc9 Γ A) B) C) D) E) A
:= var9 (vs9 (vs9 (vs9 (vs9 vz9))))
def test9 {Γ A} : Tm9 Γ (arr9 (arr9 A A) (arr9 A A))
:= lam9 (lam9 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 v09)))))))
def Ty10 : Type 1
:= ∀ (Ty10 : Type)
(ι : Ty10)
(arr : Ty10 → Ty10 → Ty10)
, Ty10
def ι10 : Ty10 := λ _ ι10 _ => ι10
def arr10 : Ty10 → Ty10 → Ty10
:= λ A B Ty10 ι10 arr10 =>
arr10 (A Ty10 ι10 arr10) (B Ty10 ι10 arr10)
def Con10 : Type 1
:= ∀ (Con10 : Type)
(nil : Con10)
(snoc : Con10 → Ty10 → Con10)
, Con10
def nil10 : Con10
:= λ Con10 nil10 snoc => nil10
def snoc10 : Con10 → Ty10 → Con10
:= λ Γ A Con10 nil10 snoc10 => snoc10 (Γ Con10 nil10 snoc10) A
def Var10 : Con10 → Ty10 → Type 1
:= λ Γ A =>
∀ (Var10 : Con10 → Ty10 → Type)
(vz : ∀ Γ A, Var10 (snoc10 Γ A) A)
(vs : ∀ Γ B A, Var10 Γ A → Var10 (snoc10 Γ B) A)
, Var10 Γ A
def vz10 {Γ A} : Var10 (snoc10 Γ A) A
:= λ Var10 vz10 vs => vz10 _ _
def vs10 {Γ B A} : Var10 Γ A → Var10 (snoc10 Γ B) A
:= λ x Var10 vz10 vs10 => vs10 _ _ _ (x Var10 vz10 vs10)
def Tm10 : Con10 → Ty10 → Type 1
:= λ Γ A =>
∀ (Tm10 : Con10 → Ty10 → Type)
(var : ∀ Γ A , Var10 Γ A → Tm10 Γ A)
(lam : ∀ Γ A B , Tm10 (snoc10 Γ A) B → Tm10 Γ (arr10 A B))
(app : ∀ Γ A B , Tm10 Γ (arr10 A B) → Tm10 Γ A → Tm10 Γ B)
, Tm10 Γ A
def var10 {Γ A} : Var10 Γ A → Tm10 Γ A
:= λ x Tm10 var10 lam app =>
var10 _ _ x
def lam10 {Γ A B} : Tm10 (snoc10 Γ A) B → Tm10 Γ (arr10 A B)
:= λ t Tm10 var10 lam10 app =>
lam10 _ _ _ (t Tm10 var10 lam10 app)
def app10 {Γ A B} : Tm10 Γ (arr10 A B) → Tm10 Γ A → Tm10 Γ B
:= λ t u Tm10 var10 lam10 app10 =>
app10 _ _ _
(t Tm10 var10 lam10 app10)
(u Tm10 var10 lam10 app10)
def v010 {Γ A} : Tm10 (snoc10 Γ A) A
:= var10 vz10
def v110 {Γ A B} : Tm10 (snoc10 (snoc10 Γ A) B) A
:= var10 (vs10 vz10)
def v210 {Γ A B C} : Tm10 (snoc10 (snoc10 (snoc10 Γ A) B) C) A
:= var10 (vs10 (vs10 vz10))
def v310 {Γ A B C D} : Tm10 (snoc10 (snoc10 (snoc10 (snoc10 Γ A) B) C) D) A
:= var10 (vs10 (vs10 (vs10 vz10)))
def v410 {Γ A B C D E} : Tm10 (snoc10 (snoc10 (snoc10 (snoc10 (snoc10 Γ A) B) C) D) E) A
:= var10 (vs10 (vs10 (vs10 (vs10 vz10))))
def test10 {Γ A} : Tm10 Γ (arr10 (arr10 A A) (arr10 A A))
:= lam10 (lam10 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 v010)))))))
def Ty11 : Type 1
:= ∀ (Ty11 : Type)
(ι : Ty11)
(arr : Ty11 → Ty11 → Ty11)
, Ty11
def ι11 : Ty11 := λ _ ι11 _ => ι11
def arr11 : Ty11 → Ty11 → Ty11
:= λ A B Ty11 ι11 arr11 =>
arr11 (A Ty11 ι11 arr11) (B Ty11 ι11 arr11)
def Con11 : Type 1
:= ∀ (Con11 : Type)
(nil : Con11)
(snoc : Con11 → Ty11 → Con11)
, Con11
def nil11 : Con11
:= λ Con11 nil11 snoc => nil11
def snoc11 : Con11 → Ty11 → Con11
:= λ Γ A Con11 nil11 snoc11 => snoc11 (Γ Con11 nil11 snoc11) A
def Var11 : Con11 → Ty11 → Type 1
:= λ Γ A =>
∀ (Var11 : Con11 → Ty11 → Type)
(vz : ∀ Γ A, Var11 (snoc11 Γ A) A)
(vs : ∀ Γ B A, Var11 Γ A → Var11 (snoc11 Γ B) A)
, Var11 Γ A
def vz11 {Γ A} : Var11 (snoc11 Γ A) A
:= λ Var11 vz11 vs => vz11 _ _
def vs11 {Γ B A} : Var11 Γ A → Var11 (snoc11 Γ B) A
:= λ x Var11 vz11 vs11 => vs11 _ _ _ (x Var11 vz11 vs11)
def Tm11 : Con11 → Ty11 → Type 1
:= λ Γ A =>
∀ (Tm11 : Con11 → Ty11 → Type)
(var : ∀ Γ A , Var11 Γ A → Tm11 Γ A)
(lam : ∀ Γ A B , Tm11 (snoc11 Γ A) B → Tm11 Γ (arr11 A B))
(app : ∀ Γ A B , Tm11 Γ (arr11 A B) → Tm11 Γ A → Tm11 Γ B)
, Tm11 Γ A
def var11 {Γ A} : Var11 Γ A → Tm11 Γ A
:= λ x Tm11 var11 lam app =>
var11 _ _ x
def lam11 {Γ A B} : Tm11 (snoc11 Γ A) B → Tm11 Γ (arr11 A B)
:= λ t Tm11 var11 lam11 app =>
lam11 _ _ _ (t Tm11 var11 lam11 app)
def app11 {Γ A B} : Tm11 Γ (arr11 A B) → Tm11 Γ A → Tm11 Γ B
:= λ t u Tm11 var11 lam11 app11 =>
app11 _ _ _
(t Tm11 var11 lam11 app11)
(u Tm11 var11 lam11 app11)
def v011 {Γ A} : Tm11 (snoc11 Γ A) A
:= var11 vz11
def v111 {Γ A B} : Tm11 (snoc11 (snoc11 Γ A) B) A
:= var11 (vs11 vz11)
def v211 {Γ A B C} : Tm11 (snoc11 (snoc11 (snoc11 Γ A) B) C) A
:= var11 (vs11 (vs11 vz11))
def v311 {Γ A B C D} : Tm11 (snoc11 (snoc11 (snoc11 (snoc11 Γ A) B) C) D) A
:= var11 (vs11 (vs11 (vs11 vz11)))
def v411 {Γ A B C D E} : Tm11 (snoc11 (snoc11 (snoc11 (snoc11 (snoc11 Γ A) B) C) D) E) A
:= var11 (vs11 (vs11 (vs11 (vs11 vz11))))
def test11 {Γ A} : Tm11 Γ (arr11 (arr11 A A) (arr11 A A))
:= lam11 (lam11 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 v011)))))))
def Ty12 : Type 1
:= ∀ (Ty12 : Type)
(ι : Ty12)
(arr : Ty12 → Ty12 → Ty12)
, Ty12
def ι12 : Ty12 := λ _ ι12 _ => ι12
def arr12 : Ty12 → Ty12 → Ty12
:= λ A B Ty12 ι12 arr12 =>
arr12 (A Ty12 ι12 arr12) (B Ty12 ι12 arr12)
def Con12 : Type 1
:= ∀ (Con12 : Type)
(nil : Con12)
(snoc : Con12 → Ty12 → Con12)
, Con12
def nil12 : Con12
:= λ Con12 nil12 snoc => nil12
def snoc12 : Con12 → Ty12 → Con12
:= λ Γ A Con12 nil12 snoc12 => snoc12 (Γ Con12 nil12 snoc12) A
def Var12 : Con12 → Ty12 → Type 1
:= λ Γ A =>
∀ (Var12 : Con12 → Ty12 → Type)
(vz : ∀ Γ A, Var12 (snoc12 Γ A) A)
(vs : ∀ Γ B A, Var12 Γ A → Var12 (snoc12 Γ B) A)
, Var12 Γ A
def vz12 {Γ A} : Var12 (snoc12 Γ A) A
:= λ Var12 vz12 vs => vz12 _ _
def vs12 {Γ B A} : Var12 Γ A → Var12 (snoc12 Γ B) A
:= λ x Var12 vz12 vs12 => vs12 _ _ _ (x Var12 vz12 vs12)
def Tm12 : Con12 → Ty12 → Type 1
:= λ Γ A =>
∀ (Tm12 : Con12 → Ty12 → Type)
(var : ∀ Γ A , Var12 Γ A → Tm12 Γ A)
(lam : ∀ Γ A B , Tm12 (snoc12 Γ A) B → Tm12 Γ (arr12 A B))
(app : ∀ Γ A B , Tm12 Γ (arr12 A B) → Tm12 Γ A → Tm12 Γ B)
, Tm12 Γ A
def var12 {Γ A} : Var12 Γ A → Tm12 Γ A
:= λ x Tm12 var12 lam app =>
var12 _ _ x
def lam12 {Γ A B} : Tm12 (snoc12 Γ A) B → Tm12 Γ (arr12 A B)
:= λ t Tm12 var12 lam12 app =>
lam12 _ _ _ (t Tm12 var12 lam12 app)
def app12 {Γ A B} : Tm12 Γ (arr12 A B) → Tm12 Γ A → Tm12 Γ B
:= λ t u Tm12 var12 lam12 app12 =>
app12 _ _ _
(t Tm12 var12 lam12 app12)
(u Tm12 var12 lam12 app12)
def v012 {Γ A} : Tm12 (snoc12 Γ A) A
:= var12 vz12
def v112 {Γ A B} : Tm12 (snoc12 (snoc12 Γ A) B) A