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stlc_small10k.agda
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{-# OPTIONS --type-in-type #-}
Ty : Set; Ty
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι : Ty; ι = λ _ ι _ → ι
arr : Ty → Ty → Ty; arr = λ A B Ty ι arr → arr (A Ty ι arr) (B Ty ι arr)
Con : Set;Con
= (Con : Set)
(nil : Con)
(snoc : Con → Ty → Con)
→ Con
nil : Con;nil
= λ Con nil snoc → nil
snoc : Con → Ty → Con;snoc
= λ Γ A Con nil snoc → snoc (Γ Con nil snoc) A
Var : Con → Ty → Set;Var
= λ Γ A →
(Var : Con → Ty → Set)
(vz : (Γ : _)(A : _) → Var (snoc Γ A) A)
(vs : (Γ : _)(B A : _) → Var Γ A → Var (snoc Γ B) A)
→ Var Γ A
vz : ∀{Γ A} → Var (snoc Γ A) A;vz
= λ Var vz vs → vz _ _
vs : ∀{Γ B A} → Var Γ A → Var (snoc Γ B) A;vs
= λ x Var vz vs → vs _ _ _ (x Var vz vs)
Tm : Con → Ty → Set;Tm
= λ Γ A →
(Tm : Con → Ty → Set)
(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
var : ∀{Γ A} → Var Γ A → Tm Γ A;var
= λ x Tm var lam app → var _ _ x
lam : ∀{Γ A B} → Tm (snoc Γ A) B → Tm Γ (arr A B);lam
= λ t Tm var lam app → lam _ _ _ (t Tm var lam app)
app : ∀{Γ A B} → Tm Γ (arr A B) → Tm Γ A → Tm Γ B;app
= λ t u Tm var lam app →
app _ _ _ (t Tm var lam app) (u Tm var lam app)
v0 : ∀{Γ A} → Tm (snoc Γ A) A;v0
= var vz
v1 : ∀{Γ A B} → Tm (snoc (snoc Γ A) B) A;v1
= var (vs vz)
v2 : ∀{Γ A B C} → Tm (snoc (snoc (snoc Γ A) B) C) A;v2
= var (vs (vs vz))
v3 : ∀{Γ A B C D} → Tm (snoc (snoc (snoc (snoc Γ A) B) C) D) A;v3
= var (vs (vs (vs vz)))
v4 : ∀{Γ A B C D E} → Tm (snoc (snoc (snoc (snoc (snoc Γ A) B) C) D) E) A;v4
= var (vs (vs (vs (vs vz))))
test : ∀{Γ A} → Tm Γ (arr (arr A A) (arr A A));test
= lam (lam (app v1 (app v1 (app v1 (app v1 (app v1 (app v1 v0)))))))
{-# OPTIONS --type-in-type #-}
Ty1 : Set; Ty1
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι1 : Ty1; ι1 = λ _ ι1 _ → ι1
arr1 : Ty1 → Ty1 → Ty1; arr1 = λ A B Ty1 ι1 arr1 → arr1 (A Ty1 ι1 arr1) (B Ty1 ι1 arr1)
Con1 : Set;Con1
= (Con1 : Set)
(nil : Con1)
(snoc : Con1 → Ty1 → Con1)
→ Con1
nil1 : Con1;nil1
= λ Con1 nil1 snoc → nil1
snoc1 : Con1 → Ty1 → Con1;snoc1
= λ Γ A Con1 nil1 snoc1 → snoc1 (Γ Con1 nil1 snoc1) A
Var1 : Con1 → Ty1 → Set;Var1
= λ Γ A →
(Var1 : Con1 → Ty1 → Set)
(vz : (Γ : _)(A : _) → Var1 (snoc1 Γ A) A)
(vs : (Γ : _)(B A : _) → Var1 Γ A → Var1 (snoc1 Γ B) A)
→ Var1 Γ A
vz1 : ∀{Γ A} → Var1 (snoc1 Γ A) A;vz1
= λ Var1 vz1 vs → vz1 _ _
vs1 : ∀{Γ B A} → Var1 Γ A → Var1 (snoc1 Γ B) A;vs1
= λ x Var1 vz1 vs1 → vs1 _ _ _ (x Var1 vz1 vs1)
Tm1 : Con1 → Ty1 → Set;Tm1
= λ Γ A →
(Tm1 : Con1 → Ty1 → Set)
(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
var1 : ∀{Γ A} → Var1 Γ A → Tm1 Γ A;var1
= λ x Tm1 var1 lam app → var1 _ _ x
lam1 : ∀{Γ A B} → Tm1 (snoc1 Γ A) B → Tm1 Γ (arr1 A B);lam1
= λ t Tm1 var1 lam1 app → lam1 _ _ _ (t Tm1 var1 lam1 app)
app1 : ∀{Γ A B} → Tm1 Γ (arr1 A B) → Tm1 Γ A → Tm1 Γ B;app1
= λ t u Tm1 var1 lam1 app1 →
app1 _ _ _ (t Tm1 var1 lam1 app1) (u Tm1 var1 lam1 app1)
v01 : ∀{Γ A} → Tm1 (snoc1 Γ A) A;v01
= var1 vz1
v11 : ∀{Γ A B} → Tm1 (snoc1 (snoc1 Γ A) B) A;v11
= var1 (vs1 vz1)
v21 : ∀{Γ A B C} → Tm1 (snoc1 (snoc1 (snoc1 Γ A) B) C) A;v21
= var1 (vs1 (vs1 vz1))
v31 : ∀{Γ A B C D} → Tm1 (snoc1 (snoc1 (snoc1 (snoc1 Γ A) B) C) D) A;v31
= var1 (vs1 (vs1 (vs1 vz1)))
v41 : ∀{Γ A B C D E} → Tm1 (snoc1 (snoc1 (snoc1 (snoc1 (snoc1 Γ A) B) C) D) E) A;v41
= var1 (vs1 (vs1 (vs1 (vs1 vz1))))
test1 : ∀{Γ A} → Tm1 Γ (arr1 (arr1 A A) (arr1 A A));test1
= lam1 (lam1 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 v01)))))))
{-# OPTIONS --type-in-type #-}
Ty2 : Set; Ty2
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι2 : Ty2; ι2 = λ _ ι2 _ → ι2
arr2 : Ty2 → Ty2 → Ty2; arr2 = λ A B Ty2 ι2 arr2 → arr2 (A Ty2 ι2 arr2) (B Ty2 ι2 arr2)
Con2 : Set;Con2
= (Con2 : Set)
(nil : Con2)
(snoc : Con2 → Ty2 → Con2)
→ Con2
nil2 : Con2;nil2
= λ Con2 nil2 snoc → nil2
snoc2 : Con2 → Ty2 → Con2;snoc2
= λ Γ A Con2 nil2 snoc2 → snoc2 (Γ Con2 nil2 snoc2) A
Var2 : Con2 → Ty2 → Set;Var2
= λ Γ A →
(Var2 : Con2 → Ty2 → Set)
(vz : (Γ : _)(A : _) → Var2 (snoc2 Γ A) A)
(vs : (Γ : _)(B A : _) → Var2 Γ A → Var2 (snoc2 Γ B) A)
→ Var2 Γ A
vz2 : ∀{Γ A} → Var2 (snoc2 Γ A) A;vz2
= λ Var2 vz2 vs → vz2 _ _
vs2 : ∀{Γ B A} → Var2 Γ A → Var2 (snoc2 Γ B) A;vs2
= λ x Var2 vz2 vs2 → vs2 _ _ _ (x Var2 vz2 vs2)
Tm2 : Con2 → Ty2 → Set;Tm2
= λ Γ A →
(Tm2 : Con2 → Ty2 → Set)
(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
var2 : ∀{Γ A} → Var2 Γ A → Tm2 Γ A;var2
= λ x Tm2 var2 lam app → var2 _ _ x
lam2 : ∀{Γ A B} → Tm2 (snoc2 Γ A) B → Tm2 Γ (arr2 A B);lam2
= λ t Tm2 var2 lam2 app → lam2 _ _ _ (t Tm2 var2 lam2 app)
app2 : ∀{Γ A B} → Tm2 Γ (arr2 A B) → Tm2 Γ A → Tm2 Γ B;app2
= λ t u Tm2 var2 lam2 app2 →
app2 _ _ _ (t Tm2 var2 lam2 app2) (u Tm2 var2 lam2 app2)
v02 : ∀{Γ A} → Tm2 (snoc2 Γ A) A;v02
= var2 vz2
v12 : ∀{Γ A B} → Tm2 (snoc2 (snoc2 Γ A) B) A;v12
= var2 (vs2 vz2)
v22 : ∀{Γ A B C} → Tm2 (snoc2 (snoc2 (snoc2 Γ A) B) C) A;v22
= var2 (vs2 (vs2 vz2))
v32 : ∀{Γ A B C D} → Tm2 (snoc2 (snoc2 (snoc2 (snoc2 Γ A) B) C) D) A;v32
= var2 (vs2 (vs2 (vs2 vz2)))
v42 : ∀{Γ A B C D E} → Tm2 (snoc2 (snoc2 (snoc2 (snoc2 (snoc2 Γ A) B) C) D) E) A;v42
= var2 (vs2 (vs2 (vs2 (vs2 vz2))))
test2 : ∀{Γ A} → Tm2 Γ (arr2 (arr2 A A) (arr2 A A));test2
= lam2 (lam2 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 v02)))))))
{-# OPTIONS --type-in-type #-}
Ty3 : Set; Ty3
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι3 : Ty3; ι3 = λ _ ι3 _ → ι3
arr3 : Ty3 → Ty3 → Ty3; arr3 = λ A B Ty3 ι3 arr3 → arr3 (A Ty3 ι3 arr3) (B Ty3 ι3 arr3)
Con3 : Set;Con3
= (Con3 : Set)
(nil : Con3)
(snoc : Con3 → Ty3 → Con3)
→ Con3
nil3 : Con3;nil3
= λ Con3 nil3 snoc → nil3
snoc3 : Con3 → Ty3 → Con3;snoc3
= λ Γ A Con3 nil3 snoc3 → snoc3 (Γ Con3 nil3 snoc3) A
Var3 : Con3 → Ty3 → Set;Var3
= λ Γ A →
(Var3 : Con3 → Ty3 → Set)
(vz : (Γ : _)(A : _) → Var3 (snoc3 Γ A) A)
(vs : (Γ : _)(B A : _) → Var3 Γ A → Var3 (snoc3 Γ B) A)
→ Var3 Γ A
vz3 : ∀{Γ A} → Var3 (snoc3 Γ A) A;vz3
= λ Var3 vz3 vs → vz3 _ _
vs3 : ∀{Γ B A} → Var3 Γ A → Var3 (snoc3 Γ B) A;vs3
= λ x Var3 vz3 vs3 → vs3 _ _ _ (x Var3 vz3 vs3)
Tm3 : Con3 → Ty3 → Set;Tm3
= λ Γ A →
(Tm3 : Con3 → Ty3 → Set)
(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
var3 : ∀{Γ A} → Var3 Γ A → Tm3 Γ A;var3
= λ x Tm3 var3 lam app → var3 _ _ x
lam3 : ∀{Γ A B} → Tm3 (snoc3 Γ A) B → Tm3 Γ (arr3 A B);lam3
= λ t Tm3 var3 lam3 app → lam3 _ _ _ (t Tm3 var3 lam3 app)
app3 : ∀{Γ A B} → Tm3 Γ (arr3 A B) → Tm3 Γ A → Tm3 Γ B;app3
= λ t u Tm3 var3 lam3 app3 →
app3 _ _ _ (t Tm3 var3 lam3 app3) (u Tm3 var3 lam3 app3)
v03 : ∀{Γ A} → Tm3 (snoc3 Γ A) A;v03
= var3 vz3
v13 : ∀{Γ A B} → Tm3 (snoc3 (snoc3 Γ A) B) A;v13
= var3 (vs3 vz3)
v23 : ∀{Γ A B C} → Tm3 (snoc3 (snoc3 (snoc3 Γ A) B) C) A;v23
= var3 (vs3 (vs3 vz3))
v33 : ∀{Γ A B C D} → Tm3 (snoc3 (snoc3 (snoc3 (snoc3 Γ A) B) C) D) A;v33
= var3 (vs3 (vs3 (vs3 vz3)))
v43 : ∀{Γ A B C D E} → Tm3 (snoc3 (snoc3 (snoc3 (snoc3 (snoc3 Γ A) B) C) D) E) A;v43
= var3 (vs3 (vs3 (vs3 (vs3 vz3))))
test3 : ∀{Γ A} → Tm3 Γ (arr3 (arr3 A A) (arr3 A A));test3
= lam3 (lam3 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 v03)))))))
{-# OPTIONS --type-in-type #-}
Ty4 : Set; Ty4
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι4 : Ty4; ι4 = λ _ ι4 _ → ι4
arr4 : Ty4 → Ty4 → Ty4; arr4 = λ A B Ty4 ι4 arr4 → arr4 (A Ty4 ι4 arr4) (B Ty4 ι4 arr4)
Con4 : Set;Con4
= (Con4 : Set)
(nil : Con4)
(snoc : Con4 → Ty4 → Con4)
→ Con4
nil4 : Con4;nil4
= λ Con4 nil4 snoc → nil4
snoc4 : Con4 → Ty4 → Con4;snoc4
= λ Γ A Con4 nil4 snoc4 → snoc4 (Γ Con4 nil4 snoc4) A
Var4 : Con4 → Ty4 → Set;Var4
= λ Γ A →
(Var4 : Con4 → Ty4 → Set)
(vz : (Γ : _)(A : _) → Var4 (snoc4 Γ A) A)
(vs : (Γ : _)(B A : _) → Var4 Γ A → Var4 (snoc4 Γ B) A)
→ Var4 Γ A
vz4 : ∀{Γ A} → Var4 (snoc4 Γ A) A;vz4
= λ Var4 vz4 vs → vz4 _ _
vs4 : ∀{Γ B A} → Var4 Γ A → Var4 (snoc4 Γ B) A;vs4
= λ x Var4 vz4 vs4 → vs4 _ _ _ (x Var4 vz4 vs4)
Tm4 : Con4 → Ty4 → Set;Tm4
= λ Γ A →
(Tm4 : Con4 → Ty4 → Set)
(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
var4 : ∀{Γ A} → Var4 Γ A → Tm4 Γ A;var4
= λ x Tm4 var4 lam app → var4 _ _ x
lam4 : ∀{Γ A B} → Tm4 (snoc4 Γ A) B → Tm4 Γ (arr4 A B);lam4
= λ t Tm4 var4 lam4 app → lam4 _ _ _ (t Tm4 var4 lam4 app)
app4 : ∀{Γ A B} → Tm4 Γ (arr4 A B) → Tm4 Γ A → Tm4 Γ B;app4
= λ t u Tm4 var4 lam4 app4 →
app4 _ _ _ (t Tm4 var4 lam4 app4) (u Tm4 var4 lam4 app4)
v04 : ∀{Γ A} → Tm4 (snoc4 Γ A) A;v04
= var4 vz4
v14 : ∀{Γ A B} → Tm4 (snoc4 (snoc4 Γ A) B) A;v14
= var4 (vs4 vz4)
v24 : ∀{Γ A B C} → Tm4 (snoc4 (snoc4 (snoc4 Γ A) B) C) A;v24
= var4 (vs4 (vs4 vz4))
v34 : ∀{Γ A B C D} → Tm4 (snoc4 (snoc4 (snoc4 (snoc4 Γ A) B) C) D) A;v34
= var4 (vs4 (vs4 (vs4 vz4)))
v44 : ∀{Γ A B C D E} → Tm4 (snoc4 (snoc4 (snoc4 (snoc4 (snoc4 Γ A) B) C) D) E) A;v44
= var4 (vs4 (vs4 (vs4 (vs4 vz4))))
test4 : ∀{Γ A} → Tm4 Γ (arr4 (arr4 A A) (arr4 A A));test4
= lam4 (lam4 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 v04)))))))
{-# OPTIONS --type-in-type #-}
Ty5 : Set; Ty5
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι5 : Ty5; ι5 = λ _ ι5 _ → ι5
arr5 : Ty5 → Ty5 → Ty5; arr5 = λ A B Ty5 ι5 arr5 → arr5 (A Ty5 ι5 arr5) (B Ty5 ι5 arr5)
Con5 : Set;Con5
= (Con5 : Set)
(nil : Con5)
(snoc : Con5 → Ty5 → Con5)
→ Con5
nil5 : Con5;nil5
= λ Con5 nil5 snoc → nil5
snoc5 : Con5 → Ty5 → Con5;snoc5
= λ Γ A Con5 nil5 snoc5 → snoc5 (Γ Con5 nil5 snoc5) A
Var5 : Con5 → Ty5 → Set;Var5
= λ Γ A →
(Var5 : Con5 → Ty5 → Set)
(vz : (Γ : _)(A : _) → Var5 (snoc5 Γ A) A)
(vs : (Γ : _)(B A : _) → Var5 Γ A → Var5 (snoc5 Γ B) A)
→ Var5 Γ A
vz5 : ∀{Γ A} → Var5 (snoc5 Γ A) A;vz5
= λ Var5 vz5 vs → vz5 _ _
vs5 : ∀{Γ B A} → Var5 Γ A → Var5 (snoc5 Γ B) A;vs5
= λ x Var5 vz5 vs5 → vs5 _ _ _ (x Var5 vz5 vs5)
Tm5 : Con5 → Ty5 → Set;Tm5
= λ Γ A →
(Tm5 : Con5 → Ty5 → Set)
(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
var5 : ∀{Γ A} → Var5 Γ A → Tm5 Γ A;var5
= λ x Tm5 var5 lam app → var5 _ _ x
lam5 : ∀{Γ A B} → Tm5 (snoc5 Γ A) B → Tm5 Γ (arr5 A B);lam5
= λ t Tm5 var5 lam5 app → lam5 _ _ _ (t Tm5 var5 lam5 app)
app5 : ∀{Γ A B} → Tm5 Γ (arr5 A B) → Tm5 Γ A → Tm5 Γ B;app5
= λ t u Tm5 var5 lam5 app5 →
app5 _ _ _ (t Tm5 var5 lam5 app5) (u Tm5 var5 lam5 app5)
v05 : ∀{Γ A} → Tm5 (snoc5 Γ A) A;v05
= var5 vz5
v15 : ∀{Γ A B} → Tm5 (snoc5 (snoc5 Γ A) B) A;v15
= var5 (vs5 vz5)
v25 : ∀{Γ A B C} → Tm5 (snoc5 (snoc5 (snoc5 Γ A) B) C) A;v25
= var5 (vs5 (vs5 vz5))
v35 : ∀{Γ A B C D} → Tm5 (snoc5 (snoc5 (snoc5 (snoc5 Γ A) B) C) D) A;v35
= var5 (vs5 (vs5 (vs5 vz5)))
v45 : ∀{Γ A B C D E} → Tm5 (snoc5 (snoc5 (snoc5 (snoc5 (snoc5 Γ A) B) C) D) E) A;v45
= var5 (vs5 (vs5 (vs5 (vs5 vz5))))
test5 : ∀{Γ A} → Tm5 Γ (arr5 (arr5 A A) (arr5 A A));test5
= lam5 (lam5 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 v05)))))))
{-# OPTIONS --type-in-type #-}
Ty6 : Set; Ty6
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι6 : Ty6; ι6 = λ _ ι6 _ → ι6
arr6 : Ty6 → Ty6 → Ty6; arr6 = λ A B Ty6 ι6 arr6 → arr6 (A Ty6 ι6 arr6) (B Ty6 ι6 arr6)
Con6 : Set;Con6
= (Con6 : Set)
(nil : Con6)
(snoc : Con6 → Ty6 → Con6)
→ Con6
nil6 : Con6;nil6
= λ Con6 nil6 snoc → nil6
snoc6 : Con6 → Ty6 → Con6;snoc6
= λ Γ A Con6 nil6 snoc6 → snoc6 (Γ Con6 nil6 snoc6) A
Var6 : Con6 → Ty6 → Set;Var6
= λ Γ A →
(Var6 : Con6 → Ty6 → Set)
(vz : (Γ : _)(A : _) → Var6 (snoc6 Γ A) A)
(vs : (Γ : _)(B A : _) → Var6 Γ A → Var6 (snoc6 Γ B) A)
→ Var6 Γ A
vz6 : ∀{Γ A} → Var6 (snoc6 Γ A) A;vz6
= λ Var6 vz6 vs → vz6 _ _
vs6 : ∀{Γ B A} → Var6 Γ A → Var6 (snoc6 Γ B) A;vs6
= λ x Var6 vz6 vs6 → vs6 _ _ _ (x Var6 vz6 vs6)
Tm6 : Con6 → Ty6 → Set;Tm6
= λ Γ A →
(Tm6 : Con6 → Ty6 → Set)
(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
var6 : ∀{Γ A} → Var6 Γ A → Tm6 Γ A;var6
= λ x Tm6 var6 lam app → var6 _ _ x
lam6 : ∀{Γ A B} → Tm6 (snoc6 Γ A) B → Tm6 Γ (arr6 A B);lam6
= λ t Tm6 var6 lam6 app → lam6 _ _ _ (t Tm6 var6 lam6 app)
app6 : ∀{Γ A B} → Tm6 Γ (arr6 A B) → Tm6 Γ A → Tm6 Γ B;app6
= λ t u Tm6 var6 lam6 app6 →
app6 _ _ _ (t Tm6 var6 lam6 app6) (u Tm6 var6 lam6 app6)
v06 : ∀{Γ A} → Tm6 (snoc6 Γ A) A;v06
= var6 vz6
v16 : ∀{Γ A B} → Tm6 (snoc6 (snoc6 Γ A) B) A;v16
= var6 (vs6 vz6)
v26 : ∀{Γ A B C} → Tm6 (snoc6 (snoc6 (snoc6 Γ A) B) C) A;v26
= var6 (vs6 (vs6 vz6))
v36 : ∀{Γ A B C D} → Tm6 (snoc6 (snoc6 (snoc6 (snoc6 Γ A) B) C) D) A;v36
= var6 (vs6 (vs6 (vs6 vz6)))
v46 : ∀{Γ A B C D E} → Tm6 (snoc6 (snoc6 (snoc6 (snoc6 (snoc6 Γ A) B) C) D) E) A;v46
= var6 (vs6 (vs6 (vs6 (vs6 vz6))))
test6 : ∀{Γ A} → Tm6 Γ (arr6 (arr6 A A) (arr6 A A));test6
= lam6 (lam6 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 v06)))))))
{-# OPTIONS --type-in-type #-}
Ty7 : Set; Ty7
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι7 : Ty7; ι7 = λ _ ι7 _ → ι7
arr7 : Ty7 → Ty7 → Ty7; arr7 = λ A B Ty7 ι7 arr7 → arr7 (A Ty7 ι7 arr7) (B Ty7 ι7 arr7)
Con7 : Set;Con7
= (Con7 : Set)
(nil : Con7)
(snoc : Con7 → Ty7 → Con7)
→ Con7
nil7 : Con7;nil7
= λ Con7 nil7 snoc → nil7
snoc7 : Con7 → Ty7 → Con7;snoc7
= λ Γ A Con7 nil7 snoc7 → snoc7 (Γ Con7 nil7 snoc7) A
Var7 : Con7 → Ty7 → Set;Var7
= λ Γ A →
(Var7 : Con7 → Ty7 → Set)
(vz : (Γ : _)(A : _) → Var7 (snoc7 Γ A) A)
(vs : (Γ : _)(B A : _) → Var7 Γ A → Var7 (snoc7 Γ B) A)
→ Var7 Γ A
vz7 : ∀{Γ A} → Var7 (snoc7 Γ A) A;vz7
= λ Var7 vz7 vs → vz7 _ _
vs7 : ∀{Γ B A} → Var7 Γ A → Var7 (snoc7 Γ B) A;vs7
= λ x Var7 vz7 vs7 → vs7 _ _ _ (x Var7 vz7 vs7)
Tm7 : Con7 → Ty7 → Set;Tm7
= λ Γ A →
(Tm7 : Con7 → Ty7 → Set)
(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
var7 : ∀{Γ A} → Var7 Γ A → Tm7 Γ A;var7
= λ x Tm7 var7 lam app → var7 _ _ x
lam7 : ∀{Γ A B} → Tm7 (snoc7 Γ A) B → Tm7 Γ (arr7 A B);lam7
= λ t Tm7 var7 lam7 app → lam7 _ _ _ (t Tm7 var7 lam7 app)
app7 : ∀{Γ A B} → Tm7 Γ (arr7 A B) → Tm7 Γ A → Tm7 Γ B;app7
= λ t u Tm7 var7 lam7 app7 →
app7 _ _ _ (t Tm7 var7 lam7 app7) (u Tm7 var7 lam7 app7)
v07 : ∀{Γ A} → Tm7 (snoc7 Γ A) A;v07
= var7 vz7
v17 : ∀{Γ A B} → Tm7 (snoc7 (snoc7 Γ A) B) A;v17
= var7 (vs7 vz7)
v27 : ∀{Γ A B C} → Tm7 (snoc7 (snoc7 (snoc7 Γ A) B) C) A;v27
= var7 (vs7 (vs7 vz7))
v37 : ∀{Γ A B C D} → Tm7 (snoc7 (snoc7 (snoc7 (snoc7 Γ A) B) C) D) A;v37
= var7 (vs7 (vs7 (vs7 vz7)))
v47 : ∀{Γ A B C D E} → Tm7 (snoc7 (snoc7 (snoc7 (snoc7 (snoc7 Γ A) B) C) D) E) A;v47
= var7 (vs7 (vs7 (vs7 (vs7 vz7))))
test7 : ∀{Γ A} → Tm7 Γ (arr7 (arr7 A A) (arr7 A A));test7
= lam7 (lam7 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 v07)))))))
{-# OPTIONS --type-in-type #-}
Ty8 : Set; Ty8
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι8 : Ty8; ι8 = λ _ ι8 _ → ι8
arr8 : Ty8 → Ty8 → Ty8; arr8 = λ A B Ty8 ι8 arr8 → arr8 (A Ty8 ι8 arr8) (B Ty8 ι8 arr8)
Con8 : Set;Con8
= (Con8 : Set)
(nil : Con8)
(snoc : Con8 → Ty8 → Con8)
→ Con8
nil8 : Con8;nil8
= λ Con8 nil8 snoc → nil8
snoc8 : Con8 → Ty8 → Con8;snoc8
= λ Γ A Con8 nil8 snoc8 → snoc8 (Γ Con8 nil8 snoc8) A
Var8 : Con8 → Ty8 → Set;Var8
= λ Γ A →
(Var8 : Con8 → Ty8 → Set)
(vz : (Γ : _)(A : _) → Var8 (snoc8 Γ A) A)
(vs : (Γ : _)(B A : _) → Var8 Γ A → Var8 (snoc8 Γ B) A)
→ Var8 Γ A
vz8 : ∀{Γ A} → Var8 (snoc8 Γ A) A;vz8
= λ Var8 vz8 vs → vz8 _ _
vs8 : ∀{Γ B A} → Var8 Γ A → Var8 (snoc8 Γ B) A;vs8
= λ x Var8 vz8 vs8 → vs8 _ _ _ (x Var8 vz8 vs8)
Tm8 : Con8 → Ty8 → Set;Tm8
= λ Γ A →
(Tm8 : Con8 → Ty8 → Set)
(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
var8 : ∀{Γ A} → Var8 Γ A → Tm8 Γ A;var8
= λ x Tm8 var8 lam app → var8 _ _ x
lam8 : ∀{Γ A B} → Tm8 (snoc8 Γ A) B → Tm8 Γ (arr8 A B);lam8
= λ t Tm8 var8 lam8 app → lam8 _ _ _ (t Tm8 var8 lam8 app)
app8 : ∀{Γ A B} → Tm8 Γ (arr8 A B) → Tm8 Γ A → Tm8 Γ B;app8
= λ t u Tm8 var8 lam8 app8 →
app8 _ _ _ (t Tm8 var8 lam8 app8) (u Tm8 var8 lam8 app8)
v08 : ∀{Γ A} → Tm8 (snoc8 Γ A) A;v08
= var8 vz8
v18 : ∀{Γ A B} → Tm8 (snoc8 (snoc8 Γ A) B) A;v18
= var8 (vs8 vz8)
v28 : ∀{Γ A B C} → Tm8 (snoc8 (snoc8 (snoc8 Γ A) B) C) A;v28
= var8 (vs8 (vs8 vz8))
v38 : ∀{Γ A B C D} → Tm8 (snoc8 (snoc8 (snoc8 (snoc8 Γ A) B) C) D) A;v38
= var8 (vs8 (vs8 (vs8 vz8)))
v48 : ∀{Γ A B C D E} → Tm8 (snoc8 (snoc8 (snoc8 (snoc8 (snoc8 Γ A) B) C) D) E) A;v48
= var8 (vs8 (vs8 (vs8 (vs8 vz8))))
test8 : ∀{Γ A} → Tm8 Γ (arr8 (arr8 A A) (arr8 A A));test8
= lam8 (lam8 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 v08)))))))
{-# OPTIONS --type-in-type #-}
Ty9 : Set; Ty9
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι9 : Ty9; ι9 = λ _ ι9 _ → ι9
arr9 : Ty9 → Ty9 → Ty9; arr9 = λ A B Ty9 ι9 arr9 → arr9 (A Ty9 ι9 arr9) (B Ty9 ι9 arr9)
Con9 : Set;Con9
= (Con9 : Set)
(nil : Con9)
(snoc : Con9 → Ty9 → Con9)
→ Con9
nil9 : Con9;nil9
= λ Con9 nil9 snoc → nil9
snoc9 : Con9 → Ty9 → Con9;snoc9
= λ Γ A Con9 nil9 snoc9 → snoc9 (Γ Con9 nil9 snoc9) A
Var9 : Con9 → Ty9 → Set;Var9
= λ Γ A →
(Var9 : Con9 → Ty9 → Set)
(vz : (Γ : _)(A : _) → Var9 (snoc9 Γ A) A)
(vs : (Γ : _)(B A : _) → Var9 Γ A → Var9 (snoc9 Γ B) A)
→ Var9 Γ A
vz9 : ∀{Γ A} → Var9 (snoc9 Γ A) A;vz9
= λ Var9 vz9 vs → vz9 _ _
vs9 : ∀{Γ B A} → Var9 Γ A → Var9 (snoc9 Γ B) A;vs9
= λ x Var9 vz9 vs9 → vs9 _ _ _ (x Var9 vz9 vs9)
Tm9 : Con9 → Ty9 → Set;Tm9
= λ Γ A →
(Tm9 : Con9 → Ty9 → Set)
(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
var9 : ∀{Γ A} → Var9 Γ A → Tm9 Γ A;var9
= λ x Tm9 var9 lam app → var9 _ _ x
lam9 : ∀{Γ A B} → Tm9 (snoc9 Γ A) B → Tm9 Γ (arr9 A B);lam9
= λ t Tm9 var9 lam9 app → lam9 _ _ _ (t Tm9 var9 lam9 app)
app9 : ∀{Γ A B} → Tm9 Γ (arr9 A B) → Tm9 Γ A → Tm9 Γ B;app9
= λ t u Tm9 var9 lam9 app9 →
app9 _ _ _ (t Tm9 var9 lam9 app9) (u Tm9 var9 lam9 app9)
v09 : ∀{Γ A} → Tm9 (snoc9 Γ A) A;v09
= var9 vz9
v19 : ∀{Γ A B} → Tm9 (snoc9 (snoc9 Γ A) B) A;v19
= var9 (vs9 vz9)
v29 : ∀{Γ A B C} → Tm9 (snoc9 (snoc9 (snoc9 Γ A) B) C) A;v29
= var9 (vs9 (vs9 vz9))
v39 : ∀{Γ A B C D} → Tm9 (snoc9 (snoc9 (snoc9 (snoc9 Γ A) B) C) D) A;v39
= var9 (vs9 (vs9 (vs9 vz9)))
v49 : ∀{Γ A B C D E} → Tm9 (snoc9 (snoc9 (snoc9 (snoc9 (snoc9 Γ A) B) C) D) E) A;v49
= var9 (vs9 (vs9 (vs9 (vs9 vz9))))
test9 : ∀{Γ A} → Tm9 Γ (arr9 (arr9 A A) (arr9 A A));test9
= lam9 (lam9 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 v09)))))))
{-# OPTIONS --type-in-type #-}
Ty10 : Set; Ty10
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι10 : Ty10; ι10 = λ _ ι10 _ → ι10
arr10 : Ty10 → Ty10 → Ty10; arr10 = λ A B Ty10 ι10 arr10 → arr10 (A Ty10 ι10 arr10) (B Ty10 ι10 arr10)
Con10 : Set;Con10
= (Con10 : Set)
(nil : Con10)
(snoc : Con10 → Ty10 → Con10)
→ Con10
nil10 : Con10;nil10
= λ Con10 nil10 snoc → nil10
snoc10 : Con10 → Ty10 → Con10;snoc10
= λ Γ A Con10 nil10 snoc10 → snoc10 (Γ Con10 nil10 snoc10) A
Var10 : Con10 → Ty10 → Set;Var10
= λ Γ A →
(Var10 : Con10 → Ty10 → Set)
(vz : (Γ : _)(A : _) → Var10 (snoc10 Γ A) A)
(vs : (Γ : _)(B A : _) → Var10 Γ A → Var10 (snoc10 Γ B) A)
→ Var10 Γ A
vz10 : ∀{Γ A} → Var10 (snoc10 Γ A) A;vz10
= λ Var10 vz10 vs → vz10 _ _
vs10 : ∀{Γ B A} → Var10 Γ A → Var10 (snoc10 Γ B) A;vs10
= λ x Var10 vz10 vs10 → vs10 _ _ _ (x Var10 vz10 vs10)
Tm10 : Con10 → Ty10 → Set;Tm10
= λ Γ A →
(Tm10 : Con10 → Ty10 → Set)
(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
var10 : ∀{Γ A} → Var10 Γ A → Tm10 Γ A;var10
= λ x Tm10 var10 lam app → var10 _ _ x
lam10 : ∀{Γ A B} → Tm10 (snoc10 Γ A) B → Tm10 Γ (arr10 A B);lam10
= λ t Tm10 var10 lam10 app → lam10 _ _ _ (t Tm10 var10 lam10 app)
app10 : ∀{Γ A B} → Tm10 Γ (arr10 A B) → Tm10 Γ A → Tm10 Γ B;app10
= λ t u Tm10 var10 lam10 app10 →
app10 _ _ _ (t Tm10 var10 lam10 app10) (u Tm10 var10 lam10 app10)
v010 : ∀{Γ A} → Tm10 (snoc10 Γ A) A;v010
= var10 vz10
v110 : ∀{Γ A B} → Tm10 (snoc10 (snoc10 Γ A) B) A;v110
= var10 (vs10 vz10)
v210 : ∀{Γ A B C} → Tm10 (snoc10 (snoc10 (snoc10 Γ A) B) C) A;v210
= var10 (vs10 (vs10 vz10))
v310 : ∀{Γ A B C D} → Tm10 (snoc10 (snoc10 (snoc10 (snoc10 Γ A) B) C) D) A;v310
= var10 (vs10 (vs10 (vs10 vz10)))
v410 : ∀{Γ A B C D E} → Tm10 (snoc10 (snoc10 (snoc10 (snoc10 (snoc10 Γ A) B) C) D) E) A;v410
= var10 (vs10 (vs10 (vs10 (vs10 vz10))))
test10 : ∀{Γ A} → Tm10 Γ (arr10 (arr10 A A) (arr10 A A));test10
= lam10 (lam10 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 v010)))))))
{-# OPTIONS --type-in-type #-}
Ty11 : Set; Ty11
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι11 : Ty11; ι11 = λ _ ι11 _ → ι11
arr11 : Ty11 → Ty11 → Ty11; arr11 = λ A B Ty11 ι11 arr11 → arr11 (A Ty11 ι11 arr11) (B Ty11 ι11 arr11)
Con11 : Set;Con11
= (Con11 : Set)
(nil : Con11)
(snoc : Con11 → Ty11 → Con11)
→ Con11
nil11 : Con11;nil11
= λ Con11 nil11 snoc → nil11
snoc11 : Con11 → Ty11 → Con11;snoc11
= λ Γ A Con11 nil11 snoc11 → snoc11 (Γ Con11 nil11 snoc11) A
Var11 : Con11 → Ty11 → Set;Var11
= λ Γ A →
(Var11 : Con11 → Ty11 → Set)
(vz : (Γ : _)(A : _) → Var11 (snoc11 Γ A) A)
(vs : (Γ : _)(B A : _) → Var11 Γ A → Var11 (snoc11 Γ B) A)
→ Var11 Γ A
vz11 : ∀{Γ A} → Var11 (snoc11 Γ A) A;vz11
= λ Var11 vz11 vs → vz11 _ _
vs11 : ∀{Γ B A} → Var11 Γ A → Var11 (snoc11 Γ B) A;vs11
= λ x Var11 vz11 vs11 → vs11 _ _ _ (x Var11 vz11 vs11)
Tm11 : Con11 → Ty11 → Set;Tm11
= λ Γ A →
(Tm11 : Con11 → Ty11 → Set)
(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
var11 : ∀{Γ A} → Var11 Γ A → Tm11 Γ A;var11
= λ x Tm11 var11 lam app → var11 _ _ x
lam11 : ∀{Γ A B} → Tm11 (snoc11 Γ A) B → Tm11 Γ (arr11 A B);lam11
= λ t Tm11 var11 lam11 app → lam11 _ _ _ (t Tm11 var11 lam11 app)
app11 : ∀{Γ A B} → Tm11 Γ (arr11 A B) → Tm11 Γ A → Tm11 Γ B;app11
= λ t u Tm11 var11 lam11 app11 →
app11 _ _ _ (t Tm11 var11 lam11 app11) (u Tm11 var11 lam11 app11)
v011 : ∀{Γ A} → Tm11 (snoc11 Γ A) A;v011
= var11 vz11
v111 : ∀{Γ A B} → Tm11 (snoc11 (snoc11 Γ A) B) A;v111
= var11 (vs11 vz11)
v211 : ∀{Γ A B C} → Tm11 (snoc11 (snoc11 (snoc11 Γ A) B) C) A;v211
= var11 (vs11 (vs11 vz11))
v311 : ∀{Γ A B C D} → Tm11 (snoc11 (snoc11 (snoc11 (snoc11 Γ A) B) C) D) A;v311
= var11 (vs11 (vs11 (vs11 vz11)))
v411 : ∀{Γ A B C D E} → Tm11 (snoc11 (snoc11 (snoc11 (snoc11 (snoc11 Γ A) B) C) D) E) A;v411
= var11 (vs11 (vs11 (vs11 (vs11 vz11))))
test11 : ∀{Γ A} → Tm11 Γ (arr11 (arr11 A A) (arr11 A A));test11
= lam11 (lam11 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 v011)))))))
{-# OPTIONS --type-in-type #-}
Ty12 : Set; Ty12
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι12 : Ty12; ι12 = λ _ ι12 _ → ι12
arr12 : Ty12 → Ty12 → Ty12; arr12 = λ A B Ty12 ι12 arr12 → arr12 (A Ty12 ι12 arr12) (B Ty12 ι12 arr12)
Con12 : Set;Con12
= (Con12 : Set)
(nil : Con12)
(snoc : Con12 → Ty12 → Con12)
→ Con12
nil12 : Con12;nil12
= λ Con12 nil12 snoc → nil12
snoc12 : Con12 → Ty12 → Con12;snoc12
= λ Γ A Con12 nil12 snoc12 → snoc12 (Γ Con12 nil12 snoc12) A
Var12 : Con12 → Ty12 → Set;Var12
= λ Γ A →
(Var12 : Con12 → Ty12 → Set)
(vz : (Γ : _)(A : _) → Var12 (snoc12 Γ A) A)
(vs : (Γ : _)(B A : _) → Var12 Γ A → Var12 (snoc12 Γ B) A)
→ Var12 Γ A
vz12 : ∀{Γ A} → Var12 (snoc12 Γ A) A;vz12
= λ Var12 vz12 vs → vz12 _ _
vs12 : ∀{Γ B A} → Var12 Γ A → Var12 (snoc12 Γ B) A;vs12
= λ x Var12 vz12 vs12 → vs12 _ _ _ (x Var12 vz12 vs12)
Tm12 : Con12 → Ty12 → Set;Tm12
= λ Γ A →
(Tm12 : Con12 → Ty12 → Set)
(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
var12 : ∀{Γ A} → Var12 Γ A → Tm12 Γ A;var12
= λ x Tm12 var12 lam app → var12 _ _ x
lam12 : ∀{Γ A B} → Tm12 (snoc12 Γ A) B → Tm12 Γ (arr12 A B);lam12
= λ t Tm12 var12 lam12 app → lam12 _ _ _ (t Tm12 var12 lam12 app)
app12 : ∀{Γ A B} → Tm12 Γ (arr12 A B) → Tm12 Γ A → Tm12 Γ B;app12
= λ t u Tm12 var12 lam12 app12 →
app12 _ _ _ (t Tm12 var12 lam12 app12) (u Tm12 var12 lam12 app12)
v012 : ∀{Γ A} → Tm12 (snoc12 Γ A) A;v012
= var12 vz12
v112 : ∀{Γ A B} → Tm12 (snoc12 (snoc12 Γ A) B) A;v112
= var12 (vs12 vz12)
v212 : ∀{Γ A B C} → Tm12 (snoc12 (snoc12 (snoc12 Γ A) B) C) A;v212
= var12 (vs12 (vs12 vz12))
v312 : ∀{Γ A B C D} → Tm12 (snoc12 (snoc12 (snoc12 (snoc12 Γ A) B) C) D) A;v312
= var12 (vs12 (vs12 (vs12 vz12)))
v412 : ∀{Γ A B C D E} → Tm12 (snoc12 (snoc12 (snoc12 (snoc12 (snoc12 Γ A) B) C) D) E) A;v412
= var12 (vs12 (vs12 (vs12 (vs12 vz12))))
test12 : ∀{Γ A} → Tm12 Γ (arr12 (arr12 A A) (arr12 A A));test12
= lam12 (lam12 (app12 v112 (app12 v112 (app12 v112 (app12 v112 (app12 v112 (app12 v112 v012)))))))
{-# OPTIONS --type-in-type #-}
Ty13 : Set; Ty13
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι13 : Ty13; ι13 = λ _ ι13 _ → ι13
arr13 : Ty13 → Ty13 → Ty13; arr13 = λ A B Ty13 ι13 arr13 → arr13 (A Ty13 ι13 arr13) (B Ty13 ι13 arr13)
Con13 : Set;Con13
= (Con13 : Set)
(nil : Con13)
(snoc : Con13 → Ty13 → Con13)
→ Con13
nil13 : Con13;nil13
= λ Con13 nil13 snoc → nil13
snoc13 : Con13 → Ty13 → Con13;snoc13
= λ Γ A Con13 nil13 snoc13 → snoc13 (Γ Con13 nil13 snoc13) A
Var13 : Con13 → Ty13 → Set;Var13
= λ Γ A →
(Var13 : Con13 → Ty13 → Set)
(vz : (Γ : _)(A : _) → Var13 (snoc13 Γ A) A)
(vs : (Γ : _)(B A : _) → Var13 Γ A → Var13 (snoc13 Γ B) A)
→ Var13 Γ A
vz13 : ∀{Γ A} → Var13 (snoc13 Γ A) A;vz13
= λ Var13 vz13 vs → vz13 _ _
vs13 : ∀{Γ B A} → Var13 Γ A → Var13 (snoc13 Γ B) A;vs13
= λ x Var13 vz13 vs13 → vs13 _ _ _ (x Var13 vz13 vs13)
Tm13 : Con13 → Ty13 → Set;Tm13
= λ Γ A →
(Tm13 : Con13 → Ty13 → Set)
(var : (Γ : _) (A : _) → Var13 Γ A → Tm13 Γ A)
(lam : (Γ : _) (A B : _) → Tm13 (snoc13 Γ A) B → Tm13 Γ (arr13 A B))
(app : (Γ : _) (A B : _) → Tm13 Γ (arr13 A B) → Tm13 Γ A → Tm13 Γ B)
→ Tm13 Γ A
var13 : ∀{Γ A} → Var13 Γ A → Tm13 Γ A;var13
= λ x Tm13 var13 lam app → var13 _ _ x
lam13 : ∀{Γ A B} → Tm13 (snoc13 Γ A) B → Tm13 Γ (arr13 A B);lam13
= λ t Tm13 var13 lam13 app → lam13 _ _ _ (t Tm13 var13 lam13 app)
app13 : ∀{Γ A B} → Tm13 Γ (arr13 A B) → Tm13 Γ A → Tm13 Γ B;app13
= λ t u Tm13 var13 lam13 app13 →
app13 _ _ _ (t Tm13 var13 lam13 app13) (u Tm13 var13 lam13 app13)
v013 : ∀{Γ A} → Tm13 (snoc13 Γ A) A;v013
= var13 vz13
v113 : ∀{Γ A B} → Tm13 (snoc13 (snoc13 Γ A) B) A;v113
= var13 (vs13 vz13)
v213 : ∀{Γ A B C} → Tm13 (snoc13 (snoc13 (snoc13 Γ A) B) C) A;v213
= var13 (vs13 (vs13 vz13))
v313 : ∀{Γ A B C D} → Tm13 (snoc13 (snoc13 (snoc13 (snoc13 Γ A) B) C) D) A;v313
= var13 (vs13 (vs13 (vs13 vz13)))
v413 : ∀{Γ A B C D E} → Tm13 (snoc13 (snoc13 (snoc13 (snoc13 (snoc13 Γ A) B) C) D) E) A;v413
= var13 (vs13 (vs13 (vs13 (vs13 vz13))))
test13 : ∀{Γ A} → Tm13 Γ (arr13 (arr13 A A) (arr13 A A));test13
= lam13 (lam13 (app13 v113 (app13 v113 (app13 v113 (app13 v113 (app13 v113 (app13 v113 v013)))))))
{-# OPTIONS --type-in-type #-}
Ty14 : Set; Ty14
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)