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stlc_small1k.idr
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Ty : Type
Ty = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty : Ty
empty = \ _, empty, _ => empty
arr : Ty -> Ty -> Ty
arr = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con : Type
Con = (Con : Type)
->(nil : Con)
->(snoc : Con -> Ty -> Con)
-> Con
nil : Con
nil = \ con, nil, snoc => nil
snoc : Con -> Ty -> Con
snoc = \ g, a, con, nil, snoc => snoc (g con nil snoc) a
Var : Con -> Ty -> Type
Var = \ g, a =>
(Var : Con -> Ty -> Type)
-> (vz : (g : _)-> (a : _) -> Var (snoc g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var g a -> Var (snoc g b) a)
-> Var g a
vz : {g : _}-> {a : _} -> Var (snoc g a) a
vz = \ var, vz, vs => vz _ _
vs : {g : _} -> {B : _} -> {a : _} -> Var g a -> Var (snoc g B) a
vs = \ x, var, vz, vs => vs _ _ _ (x var vz vs)
Tm : Con -> Ty -> Type
Tm = \ g, a =>
(Tm : Con -> Ty -> Type)
-> (var : (g : _) -> (a : _) -> Var g a -> Tm g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm (snoc g a) B -> Tm g (arr a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm g (arr a B) -> Tm g a -> Tm g B)
-> Tm g a
var : {g : _} -> {a : _} -> Var g a -> Tm g a
var = \ x, tm, var, lam, app => var _ _ x
lam : {g : _} -> {a : _} -> {B : _} -> Tm (snoc g a) B -> Tm g (arr a B)
lam = \ t, tm, var, lam, app => lam _ _ _ (t tm var lam app)
app : {g:_}->{a:_}->{B:_} -> Tm g (arr a B) -> Tm g a -> Tm g B
app = \ t, u, tm, var, lam, app => app _ _ _ (t tm var lam app) (u tm var lam app)
v0 : {g:_}->{a:_} -> Tm (snoc g a) a
v0 = var vz
v1 : {g:_}->{a:_}-> {B:_}-> Tm (snoc (snoc g a) B) a
v1 = var (vs vz)
v2 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm (snoc (snoc (snoc g a) B) C) a
v2 = var (vs (vs vz))
v3 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm (snoc (snoc (snoc (snoc g a) B) C) D) a
v3 = var (vs (vs (vs vz)))
v4 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm (snoc (snoc (snoc (snoc (snoc g a) B) C) D) E) a
v4 = var (vs (vs (vs (vs vz))))
test : {g:_}-> {a:_} -> Tm g (arr (arr a a) (arr a a))
test = lam (lam (app v1 (app v1 (app v1 (app v1 (app v1 (app v1 v0)))))))
Ty1 : Type
Ty1 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty1 : Ty1
empty1 = \ _, empty, _ => empty
arr1 : Ty1 -> Ty1 -> Ty1
arr1 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con1 : Type
Con1 = (Con1 : Type)
->(nil : Con1)
->(snoc : Con1 -> Ty1 -> Con1)
-> Con1
nil1 : Con1
nil1 = \ con, nil1, snoc => nil1
snoc1 : Con1 -> Ty1 -> Con1
snoc1 = \ g, a, con, nil1, snoc1 => snoc1 (g con nil1 snoc1) a
Var1 : Con1 -> Ty1 -> Type
Var1 = \ g, a =>
(Var1 : Con1 -> Ty1 -> Type)
-> (vz : (g : _)-> (a : _) -> Var1 (snoc1 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var1 g a -> Var1 (snoc1 g b) a)
-> Var1 g a
vz1 : {g : _}-> {a : _} -> Var1 (snoc1 g a) a
vz1 = \ var, vz1, vs => vz1 _ _
vs1 : {g : _} -> {B : _} -> {a : _} -> Var1 g a -> Var1 (snoc1 g B) a
vs1 = \ x, var, vz1, vs1 => vs1 _ _ _ (x var vz1 vs1)
Tm1 : Con1 -> Ty1 -> Type
Tm1 = \ g, a =>
(Tm1 : Con1 -> Ty1 -> Type)
-> (var : (g : _) -> (a : _) -> Var1 g a -> Tm1 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm1 (snoc1 g a) B -> Tm1 g (arr1 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm1 g (arr1 a B) -> Tm1 g a -> Tm1 g B)
-> Tm1 g a
var1 : {g : _} -> {a : _} -> Var1 g a -> Tm1 g a
var1 = \ x, tm, var1, lam, app => var1 _ _ x
lam1 : {g : _} -> {a : _} -> {B : _} -> Tm1 (snoc1 g a) B -> Tm1 g (arr1 a B)
lam1 = \ t, tm, var1, lam1, app => lam1 _ _ _ (t tm var1 lam1 app)
app1 : {g:_}->{a:_}->{B:_} -> Tm1 g (arr1 a B) -> Tm1 g a -> Tm1 g B
app1 = \ t, u, tm, var1, lam1, app1 => app1 _ _ _ (t tm var1 lam1 app1) (u tm var1 lam1 app1)
v01 : {g:_}->{a:_} -> Tm1 (snoc1 g a) a
v01 = var1 vz1
v11 : {g:_}->{a:_}-> {B:_}-> Tm1 (snoc1 (snoc1 g a) B) a
v11 = var1 (vs1 vz1)
v21 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm1 (snoc1 (snoc1 (snoc1 g a) B) C) a
v21 = var1 (vs1 (vs1 vz1))
v31 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm1 (snoc1 (snoc1 (snoc1 (snoc1 g a) B) C) D) a
v31 = var1 (vs1 (vs1 (vs1 vz1)))
v41 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm1 (snoc1 (snoc1 (snoc1 (snoc1 (snoc1 g a) B) C) D) E) a
v41 = var1 (vs1 (vs1 (vs1 (vs1 vz1))))
test1 : {g:_}-> {a:_} -> Tm1 g (arr1 (arr1 a a) (arr1 a a))
test1 = lam1 (lam1 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 (app1 v11 v01)))))))
Ty2 : Type
Ty2 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty2 : Ty2
empty2 = \ _, empty, _ => empty
arr2 : Ty2 -> Ty2 -> Ty2
arr2 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con2 : Type
Con2 = (Con2 : Type)
->(nil : Con2)
->(snoc : Con2 -> Ty2 -> Con2)
-> Con2
nil2 : Con2
nil2 = \ con, nil2, snoc => nil2
snoc2 : Con2 -> Ty2 -> Con2
snoc2 = \ g, a, con, nil2, snoc2 => snoc2 (g con nil2 snoc2) a
Var2 : Con2 -> Ty2 -> Type
Var2 = \ g, a =>
(Var2 : Con2 -> Ty2 -> Type)
-> (vz : (g : _)-> (a : _) -> Var2 (snoc2 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var2 g a -> Var2 (snoc2 g b) a)
-> Var2 g a
vz2 : {g : _}-> {a : _} -> Var2 (snoc2 g a) a
vz2 = \ var, vz2, vs => vz2 _ _
vs2 : {g : _} -> {B : _} -> {a : _} -> Var2 g a -> Var2 (snoc2 g B) a
vs2 = \ x, var, vz2, vs2 => vs2 _ _ _ (x var vz2 vs2)
Tm2 : Con2 -> Ty2 -> Type
Tm2 = \ g, a =>
(Tm2 : Con2 -> Ty2 -> Type)
-> (var : (g : _) -> (a : _) -> Var2 g a -> Tm2 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm2 (snoc2 g a) B -> Tm2 g (arr2 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm2 g (arr2 a B) -> Tm2 g a -> Tm2 g B)
-> Tm2 g a
var2 : {g : _} -> {a : _} -> Var2 g a -> Tm2 g a
var2 = \ x, tm, var2, lam, app => var2 _ _ x
lam2 : {g : _} -> {a : _} -> {B : _} -> Tm2 (snoc2 g a) B -> Tm2 g (arr2 a B)
lam2 = \ t, tm, var2, lam2, app => lam2 _ _ _ (t tm var2 lam2 app)
app2 : {g:_}->{a:_}->{B:_} -> Tm2 g (arr2 a B) -> Tm2 g a -> Tm2 g B
app2 = \ t, u, tm, var2, lam2, app2 => app2 _ _ _ (t tm var2 lam2 app2) (u tm var2 lam2 app2)
v02 : {g:_}->{a:_} -> Tm2 (snoc2 g a) a
v02 = var2 vz2
v12 : {g:_}->{a:_}-> {B:_}-> Tm2 (snoc2 (snoc2 g a) B) a
v12 = var2 (vs2 vz2)
v22 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm2 (snoc2 (snoc2 (snoc2 g a) B) C) a
v22 = var2 (vs2 (vs2 vz2))
v32 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm2 (snoc2 (snoc2 (snoc2 (snoc2 g a) B) C) D) a
v32 = var2 (vs2 (vs2 (vs2 vz2)))
v42 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm2 (snoc2 (snoc2 (snoc2 (snoc2 (snoc2 g a) B) C) D) E) a
v42 = var2 (vs2 (vs2 (vs2 (vs2 vz2))))
test2 : {g:_}-> {a:_} -> Tm2 g (arr2 (arr2 a a) (arr2 a a))
test2 = lam2 (lam2 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 (app2 v12 v02)))))))
Ty3 : Type
Ty3 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty3 : Ty3
empty3 = \ _, empty, _ => empty
arr3 : Ty3 -> Ty3 -> Ty3
arr3 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con3 : Type
Con3 = (Con3 : Type)
->(nil : Con3)
->(snoc : Con3 -> Ty3 -> Con3)
-> Con3
nil3 : Con3
nil3 = \ con, nil3, snoc => nil3
snoc3 : Con3 -> Ty3 -> Con3
snoc3 = \ g, a, con, nil3, snoc3 => snoc3 (g con nil3 snoc3) a
Var3 : Con3 -> Ty3 -> Type
Var3 = \ g, a =>
(Var3 : Con3 -> Ty3 -> Type)
-> (vz : (g : _)-> (a : _) -> Var3 (snoc3 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var3 g a -> Var3 (snoc3 g b) a)
-> Var3 g a
vz3 : {g : _}-> {a : _} -> Var3 (snoc3 g a) a
vz3 = \ var, vz3, vs => vz3 _ _
vs3 : {g : _} -> {B : _} -> {a : _} -> Var3 g a -> Var3 (snoc3 g B) a
vs3 = \ x, var, vz3, vs3 => vs3 _ _ _ (x var vz3 vs3)
Tm3 : Con3 -> Ty3 -> Type
Tm3 = \ g, a =>
(Tm3 : Con3 -> Ty3 -> Type)
-> (var : (g : _) -> (a : _) -> Var3 g a -> Tm3 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm3 (snoc3 g a) B -> Tm3 g (arr3 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm3 g (arr3 a B) -> Tm3 g a -> Tm3 g B)
-> Tm3 g a
var3 : {g : _} -> {a : _} -> Var3 g a -> Tm3 g a
var3 = \ x, tm, var3, lam, app => var3 _ _ x
lam3 : {g : _} -> {a : _} -> {B : _} -> Tm3 (snoc3 g a) B -> Tm3 g (arr3 a B)
lam3 = \ t, tm, var3, lam3, app => lam3 _ _ _ (t tm var3 lam3 app)
app3 : {g:_}->{a:_}->{B:_} -> Tm3 g (arr3 a B) -> Tm3 g a -> Tm3 g B
app3 = \ t, u, tm, var3, lam3, app3 => app3 _ _ _ (t tm var3 lam3 app3) (u tm var3 lam3 app3)
v03 : {g:_}->{a:_} -> Tm3 (snoc3 g a) a
v03 = var3 vz3
v13 : {g:_}->{a:_}-> {B:_}-> Tm3 (snoc3 (snoc3 g a) B) a
v13 = var3 (vs3 vz3)
v23 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm3 (snoc3 (snoc3 (snoc3 g a) B) C) a
v23 = var3 (vs3 (vs3 vz3))
v33 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm3 (snoc3 (snoc3 (snoc3 (snoc3 g a) B) C) D) a
v33 = var3 (vs3 (vs3 (vs3 vz3)))
v43 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm3 (snoc3 (snoc3 (snoc3 (snoc3 (snoc3 g a) B) C) D) E) a
v43 = var3 (vs3 (vs3 (vs3 (vs3 vz3))))
test3 : {g:_}-> {a:_} -> Tm3 g (arr3 (arr3 a a) (arr3 a a))
test3 = lam3 (lam3 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 (app3 v13 v03)))))))
Ty4 : Type
Ty4 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty4 : Ty4
empty4 = \ _, empty, _ => empty
arr4 : Ty4 -> Ty4 -> Ty4
arr4 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con4 : Type
Con4 = (Con4 : Type)
->(nil : Con4)
->(snoc : Con4 -> Ty4 -> Con4)
-> Con4
nil4 : Con4
nil4 = \ con, nil4, snoc => nil4
snoc4 : Con4 -> Ty4 -> Con4
snoc4 = \ g, a, con, nil4, snoc4 => snoc4 (g con nil4 snoc4) a
Var4 : Con4 -> Ty4 -> Type
Var4 = \ g, a =>
(Var4 : Con4 -> Ty4 -> Type)
-> (vz : (g : _)-> (a : _) -> Var4 (snoc4 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var4 g a -> Var4 (snoc4 g b) a)
-> Var4 g a
vz4 : {g : _}-> {a : _} -> Var4 (snoc4 g a) a
vz4 = \ var, vz4, vs => vz4 _ _
vs4 : {g : _} -> {B : _} -> {a : _} -> Var4 g a -> Var4 (snoc4 g B) a
vs4 = \ x, var, vz4, vs4 => vs4 _ _ _ (x var vz4 vs4)
Tm4 : Con4 -> Ty4 -> Type
Tm4 = \ g, a =>
(Tm4 : Con4 -> Ty4 -> Type)
-> (var : (g : _) -> (a : _) -> Var4 g a -> Tm4 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm4 (snoc4 g a) B -> Tm4 g (arr4 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm4 g (arr4 a B) -> Tm4 g a -> Tm4 g B)
-> Tm4 g a
var4 : {g : _} -> {a : _} -> Var4 g a -> Tm4 g a
var4 = \ x, tm, var4, lam, app => var4 _ _ x
lam4 : {g : _} -> {a : _} -> {B : _} -> Tm4 (snoc4 g a) B -> Tm4 g (arr4 a B)
lam4 = \ t, tm, var4, lam4, app => lam4 _ _ _ (t tm var4 lam4 app)
app4 : {g:_}->{a:_}->{B:_} -> Tm4 g (arr4 a B) -> Tm4 g a -> Tm4 g B
app4 = \ t, u, tm, var4, lam4, app4 => app4 _ _ _ (t tm var4 lam4 app4) (u tm var4 lam4 app4)
v04 : {g:_}->{a:_} -> Tm4 (snoc4 g a) a
v04 = var4 vz4
v14 : {g:_}->{a:_}-> {B:_}-> Tm4 (snoc4 (snoc4 g a) B) a
v14 = var4 (vs4 vz4)
v24 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm4 (snoc4 (snoc4 (snoc4 g a) B) C) a
v24 = var4 (vs4 (vs4 vz4))
v34 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm4 (snoc4 (snoc4 (snoc4 (snoc4 g a) B) C) D) a
v34 = var4 (vs4 (vs4 (vs4 vz4)))
v44 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm4 (snoc4 (snoc4 (snoc4 (snoc4 (snoc4 g a) B) C) D) E) a
v44 = var4 (vs4 (vs4 (vs4 (vs4 vz4))))
test4 : {g:_}-> {a:_} -> Tm4 g (arr4 (arr4 a a) (arr4 a a))
test4 = lam4 (lam4 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 (app4 v14 v04)))))))
Ty5 : Type
Ty5 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty5 : Ty5
empty5 = \ _, empty, _ => empty
arr5 : Ty5 -> Ty5 -> Ty5
arr5 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con5 : Type
Con5 = (Con5 : Type)
->(nil : Con5)
->(snoc : Con5 -> Ty5 -> Con5)
-> Con5
nil5 : Con5
nil5 = \ con, nil5, snoc => nil5
snoc5 : Con5 -> Ty5 -> Con5
snoc5 = \ g, a, con, nil5, snoc5 => snoc5 (g con nil5 snoc5) a
Var5 : Con5 -> Ty5 -> Type
Var5 = \ g, a =>
(Var5 : Con5 -> Ty5 -> Type)
-> (vz : (g : _)-> (a : _) -> Var5 (snoc5 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var5 g a -> Var5 (snoc5 g b) a)
-> Var5 g a
vz5 : {g : _}-> {a : _} -> Var5 (snoc5 g a) a
vz5 = \ var, vz5, vs => vz5 _ _
vs5 : {g : _} -> {B : _} -> {a : _} -> Var5 g a -> Var5 (snoc5 g B) a
vs5 = \ x, var, vz5, vs5 => vs5 _ _ _ (x var vz5 vs5)
Tm5 : Con5 -> Ty5 -> Type
Tm5 = \ g, a =>
(Tm5 : Con5 -> Ty5 -> Type)
-> (var : (g : _) -> (a : _) -> Var5 g a -> Tm5 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm5 (snoc5 g a) B -> Tm5 g (arr5 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm5 g (arr5 a B) -> Tm5 g a -> Tm5 g B)
-> Tm5 g a
var5 : {g : _} -> {a : _} -> Var5 g a -> Tm5 g a
var5 = \ x, tm, var5, lam, app => var5 _ _ x
lam5 : {g : _} -> {a : _} -> {B : _} -> Tm5 (snoc5 g a) B -> Tm5 g (arr5 a B)
lam5 = \ t, tm, var5, lam5, app => lam5 _ _ _ (t tm var5 lam5 app)
app5 : {g:_}->{a:_}->{B:_} -> Tm5 g (arr5 a B) -> Tm5 g a -> Tm5 g B
app5 = \ t, u, tm, var5, lam5, app5 => app5 _ _ _ (t tm var5 lam5 app5) (u tm var5 lam5 app5)
v05 : {g:_}->{a:_} -> Tm5 (snoc5 g a) a
v05 = var5 vz5
v15 : {g:_}->{a:_}-> {B:_}-> Tm5 (snoc5 (snoc5 g a) B) a
v15 = var5 (vs5 vz5)
v25 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm5 (snoc5 (snoc5 (snoc5 g a) B) C) a
v25 = var5 (vs5 (vs5 vz5))
v35 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm5 (snoc5 (snoc5 (snoc5 (snoc5 g a) B) C) D) a
v35 = var5 (vs5 (vs5 (vs5 vz5)))
v45 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm5 (snoc5 (snoc5 (snoc5 (snoc5 (snoc5 g a) B) C) D) E) a
v45 = var5 (vs5 (vs5 (vs5 (vs5 vz5))))
test5 : {g:_}-> {a:_} -> Tm5 g (arr5 (arr5 a a) (arr5 a a))
test5 = lam5 (lam5 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 (app5 v15 v05)))))))
Ty6 : Type
Ty6 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty6 : Ty6
empty6 = \ _, empty, _ => empty
arr6 : Ty6 -> Ty6 -> Ty6
arr6 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con6 : Type
Con6 = (Con6 : Type)
->(nil : Con6)
->(snoc : Con6 -> Ty6 -> Con6)
-> Con6
nil6 : Con6
nil6 = \ con, nil6, snoc => nil6
snoc6 : Con6 -> Ty6 -> Con6
snoc6 = \ g, a, con, nil6, snoc6 => snoc6 (g con nil6 snoc6) a
Var6 : Con6 -> Ty6 -> Type
Var6 = \ g, a =>
(Var6 : Con6 -> Ty6 -> Type)
-> (vz : (g : _)-> (a : _) -> Var6 (snoc6 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var6 g a -> Var6 (snoc6 g b) a)
-> Var6 g a
vz6 : {g : _}-> {a : _} -> Var6 (snoc6 g a) a
vz6 = \ var, vz6, vs => vz6 _ _
vs6 : {g : _} -> {B : _} -> {a : _} -> Var6 g a -> Var6 (snoc6 g B) a
vs6 = \ x, var, vz6, vs6 => vs6 _ _ _ (x var vz6 vs6)
Tm6 : Con6 -> Ty6 -> Type
Tm6 = \ g, a =>
(Tm6 : Con6 -> Ty6 -> Type)
-> (var : (g : _) -> (a : _) -> Var6 g a -> Tm6 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm6 (snoc6 g a) B -> Tm6 g (arr6 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm6 g (arr6 a B) -> Tm6 g a -> Tm6 g B)
-> Tm6 g a
var6 : {g : _} -> {a : _} -> Var6 g a -> Tm6 g a
var6 = \ x, tm, var6, lam, app => var6 _ _ x
lam6 : {g : _} -> {a : _} -> {B : _} -> Tm6 (snoc6 g a) B -> Tm6 g (arr6 a B)
lam6 = \ t, tm, var6, lam6, app => lam6 _ _ _ (t tm var6 lam6 app)
app6 : {g:_}->{a:_}->{B:_} -> Tm6 g (arr6 a B) -> Tm6 g a -> Tm6 g B
app6 = \ t, u, tm, var6, lam6, app6 => app6 _ _ _ (t tm var6 lam6 app6) (u tm var6 lam6 app6)
v06 : {g:_}->{a:_} -> Tm6 (snoc6 g a) a
v06 = var6 vz6
v16 : {g:_}->{a:_}-> {B:_}-> Tm6 (snoc6 (snoc6 g a) B) a
v16 = var6 (vs6 vz6)
v26 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm6 (snoc6 (snoc6 (snoc6 g a) B) C) a
v26 = var6 (vs6 (vs6 vz6))
v36 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm6 (snoc6 (snoc6 (snoc6 (snoc6 g a) B) C) D) a
v36 = var6 (vs6 (vs6 (vs6 vz6)))
v46 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm6 (snoc6 (snoc6 (snoc6 (snoc6 (snoc6 g a) B) C) D) E) a
v46 = var6 (vs6 (vs6 (vs6 (vs6 vz6))))
test6 : {g:_}-> {a:_} -> Tm6 g (arr6 (arr6 a a) (arr6 a a))
test6 = lam6 (lam6 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 (app6 v16 v06)))))))
Ty7 : Type
Ty7 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty7 : Ty7
empty7 = \ _, empty, _ => empty
arr7 : Ty7 -> Ty7 -> Ty7
arr7 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con7 : Type
Con7 = (Con7 : Type)
->(nil : Con7)
->(snoc : Con7 -> Ty7 -> Con7)
-> Con7
nil7 : Con7
nil7 = \ con, nil7, snoc => nil7
snoc7 : Con7 -> Ty7 -> Con7
snoc7 = \ g, a, con, nil7, snoc7 => snoc7 (g con nil7 snoc7) a
Var7 : Con7 -> Ty7 -> Type
Var7 = \ g, a =>
(Var7 : Con7 -> Ty7 -> Type)
-> (vz : (g : _)-> (a : _) -> Var7 (snoc7 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var7 g a -> Var7 (snoc7 g b) a)
-> Var7 g a
vz7 : {g : _}-> {a : _} -> Var7 (snoc7 g a) a
vz7 = \ var, vz7, vs => vz7 _ _
vs7 : {g : _} -> {B : _} -> {a : _} -> Var7 g a -> Var7 (snoc7 g B) a
vs7 = \ x, var, vz7, vs7 => vs7 _ _ _ (x var vz7 vs7)
Tm7 : Con7 -> Ty7 -> Type
Tm7 = \ g, a =>
(Tm7 : Con7 -> Ty7 -> Type)
-> (var : (g : _) -> (a : _) -> Var7 g a -> Tm7 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm7 (snoc7 g a) B -> Tm7 g (arr7 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm7 g (arr7 a B) -> Tm7 g a -> Tm7 g B)
-> Tm7 g a
var7 : {g : _} -> {a : _} -> Var7 g a -> Tm7 g a
var7 = \ x, tm, var7, lam, app => var7 _ _ x
lam7 : {g : _} -> {a : _} -> {B : _} -> Tm7 (snoc7 g a) B -> Tm7 g (arr7 a B)
lam7 = \ t, tm, var7, lam7, app => lam7 _ _ _ (t tm var7 lam7 app)
app7 : {g:_}->{a:_}->{B:_} -> Tm7 g (arr7 a B) -> Tm7 g a -> Tm7 g B
app7 = \ t, u, tm, var7, lam7, app7 => app7 _ _ _ (t tm var7 lam7 app7) (u tm var7 lam7 app7)
v07 : {g:_}->{a:_} -> Tm7 (snoc7 g a) a
v07 = var7 vz7
v17 : {g:_}->{a:_}-> {B:_}-> Tm7 (snoc7 (snoc7 g a) B) a
v17 = var7 (vs7 vz7)
v27 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm7 (snoc7 (snoc7 (snoc7 g a) B) C) a
v27 = var7 (vs7 (vs7 vz7))
v37 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm7 (snoc7 (snoc7 (snoc7 (snoc7 g a) B) C) D) a
v37 = var7 (vs7 (vs7 (vs7 vz7)))
v47 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm7 (snoc7 (snoc7 (snoc7 (snoc7 (snoc7 g a) B) C) D) E) a
v47 = var7 (vs7 (vs7 (vs7 (vs7 vz7))))
test7 : {g:_}-> {a:_} -> Tm7 g (arr7 (arr7 a a) (arr7 a a))
test7 = lam7 (lam7 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 (app7 v17 v07)))))))
Ty8 : Type
Ty8 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty8 : Ty8
empty8 = \ _, empty, _ => empty
arr8 : Ty8 -> Ty8 -> Ty8
arr8 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con8 : Type
Con8 = (Con8 : Type)
->(nil : Con8)
->(snoc : Con8 -> Ty8 -> Con8)
-> Con8
nil8 : Con8
nil8 = \ con, nil8, snoc => nil8
snoc8 : Con8 -> Ty8 -> Con8
snoc8 = \ g, a, con, nil8, snoc8 => snoc8 (g con nil8 snoc8) a
Var8 : Con8 -> Ty8 -> Type
Var8 = \ g, a =>
(Var8 : Con8 -> Ty8 -> Type)
-> (vz : (g : _)-> (a : _) -> Var8 (snoc8 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var8 g a -> Var8 (snoc8 g b) a)
-> Var8 g a
vz8 : {g : _}-> {a : _} -> Var8 (snoc8 g a) a
vz8 = \ var, vz8, vs => vz8 _ _
vs8 : {g : _} -> {B : _} -> {a : _} -> Var8 g a -> Var8 (snoc8 g B) a
vs8 = \ x, var, vz8, vs8 => vs8 _ _ _ (x var vz8 vs8)
Tm8 : Con8 -> Ty8 -> Type
Tm8 = \ g, a =>
(Tm8 : Con8 -> Ty8 -> Type)
-> (var : (g : _) -> (a : _) -> Var8 g a -> Tm8 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm8 (snoc8 g a) B -> Tm8 g (arr8 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm8 g (arr8 a B) -> Tm8 g a -> Tm8 g B)
-> Tm8 g a
var8 : {g : _} -> {a : _} -> Var8 g a -> Tm8 g a
var8 = \ x, tm, var8, lam, app => var8 _ _ x
lam8 : {g : _} -> {a : _} -> {B : _} -> Tm8 (snoc8 g a) B -> Tm8 g (arr8 a B)
lam8 = \ t, tm, var8, lam8, app => lam8 _ _ _ (t tm var8 lam8 app)
app8 : {g:_}->{a:_}->{B:_} -> Tm8 g (arr8 a B) -> Tm8 g a -> Tm8 g B
app8 = \ t, u, tm, var8, lam8, app8 => app8 _ _ _ (t tm var8 lam8 app8) (u tm var8 lam8 app8)
v08 : {g:_}->{a:_} -> Tm8 (snoc8 g a) a
v08 = var8 vz8
v18 : {g:_}->{a:_}-> {B:_}-> Tm8 (snoc8 (snoc8 g a) B) a
v18 = var8 (vs8 vz8)
v28 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm8 (snoc8 (snoc8 (snoc8 g a) B) C) a
v28 = var8 (vs8 (vs8 vz8))
v38 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm8 (snoc8 (snoc8 (snoc8 (snoc8 g a) B) C) D) a
v38 = var8 (vs8 (vs8 (vs8 vz8)))
v48 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm8 (snoc8 (snoc8 (snoc8 (snoc8 (snoc8 g a) B) C) D) E) a
v48 = var8 (vs8 (vs8 (vs8 (vs8 vz8))))
test8 : {g:_}-> {a:_} -> Tm8 g (arr8 (arr8 a a) (arr8 a a))
test8 = lam8 (lam8 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 (app8 v18 v08)))))))
Ty9 : Type
Ty9 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty9 : Ty9
empty9 = \ _, empty, _ => empty
arr9 : Ty9 -> Ty9 -> Ty9
arr9 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con9 : Type
Con9 = (Con9 : Type)
->(nil : Con9)
->(snoc : Con9 -> Ty9 -> Con9)
-> Con9
nil9 : Con9
nil9 = \ con, nil9, snoc => nil9
snoc9 : Con9 -> Ty9 -> Con9
snoc9 = \ g, a, con, nil9, snoc9 => snoc9 (g con nil9 snoc9) a
Var9 : Con9 -> Ty9 -> Type
Var9 = \ g, a =>
(Var9 : Con9 -> Ty9 -> Type)
-> (vz : (g : _)-> (a : _) -> Var9 (snoc9 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var9 g a -> Var9 (snoc9 g b) a)
-> Var9 g a
vz9 : {g : _}-> {a : _} -> Var9 (snoc9 g a) a
vz9 = \ var, vz9, vs => vz9 _ _
vs9 : {g : _} -> {B : _} -> {a : _} -> Var9 g a -> Var9 (snoc9 g B) a
vs9 = \ x, var, vz9, vs9 => vs9 _ _ _ (x var vz9 vs9)
Tm9 : Con9 -> Ty9 -> Type
Tm9 = \ g, a =>
(Tm9 : Con9 -> Ty9 -> Type)
-> (var : (g : _) -> (a : _) -> Var9 g a -> Tm9 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm9 (snoc9 g a) B -> Tm9 g (arr9 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm9 g (arr9 a B) -> Tm9 g a -> Tm9 g B)
-> Tm9 g a
var9 : {g : _} -> {a : _} -> Var9 g a -> Tm9 g a
var9 = \ x, tm, var9, lam, app => var9 _ _ x
lam9 : {g : _} -> {a : _} -> {B : _} -> Tm9 (snoc9 g a) B -> Tm9 g (arr9 a B)
lam9 = \ t, tm, var9, lam9, app => lam9 _ _ _ (t tm var9 lam9 app)
app9 : {g:_}->{a:_}->{B:_} -> Tm9 g (arr9 a B) -> Tm9 g a -> Tm9 g B
app9 = \ t, u, tm, var9, lam9, app9 => app9 _ _ _ (t tm var9 lam9 app9) (u tm var9 lam9 app9)
v09 : {g:_}->{a:_} -> Tm9 (snoc9 g a) a
v09 = var9 vz9
v19 : {g:_}->{a:_}-> {B:_}-> Tm9 (snoc9 (snoc9 g a) B) a
v19 = var9 (vs9 vz9)
v29 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm9 (snoc9 (snoc9 (snoc9 g a) B) C) a
v29 = var9 (vs9 (vs9 vz9))
v39 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm9 (snoc9 (snoc9 (snoc9 (snoc9 g a) B) C) D) a
v39 = var9 (vs9 (vs9 (vs9 vz9)))
v49 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm9 (snoc9 (snoc9 (snoc9 (snoc9 (snoc9 g a) B) C) D) E) a
v49 = var9 (vs9 (vs9 (vs9 (vs9 vz9))))
test9 : {g:_}-> {a:_} -> Tm9 g (arr9 (arr9 a a) (arr9 a a))
test9 = lam9 (lam9 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 (app9 v19 v09)))))))
Ty10 : Type
Ty10 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty10 : Ty10
empty10 = \ _, empty, _ => empty
arr10 : Ty10 -> Ty10 -> Ty10
arr10 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con10 : Type
Con10 = (Con10 : Type)
->(nil : Con10)
->(snoc : Con10 -> Ty10 -> Con10)
-> Con10
nil10 : Con10
nil10 = \ con, nil10, snoc => nil10
snoc10 : Con10 -> Ty10 -> Con10
snoc10 = \ g, a, con, nil10, snoc10 => snoc10 (g con nil10 snoc10) a
Var10 : Con10 -> Ty10 -> Type
Var10 = \ g, a =>
(Var10 : Con10 -> Ty10 -> Type)
-> (vz : (g : _)-> (a : _) -> Var10 (snoc10 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var10 g a -> Var10 (snoc10 g b) a)
-> Var10 g a
vz10 : {g : _}-> {a : _} -> Var10 (snoc10 g a) a
vz10 = \ var, vz10, vs => vz10 _ _
vs10 : {g : _} -> {B : _} -> {a : _} -> Var10 g a -> Var10 (snoc10 g B) a
vs10 = \ x, var, vz10, vs10 => vs10 _ _ _ (x var vz10 vs10)
Tm10 : Con10 -> Ty10 -> Type
Tm10 = \ g, a =>
(Tm10 : Con10 -> Ty10 -> Type)
-> (var : (g : _) -> (a : _) -> Var10 g a -> Tm10 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm10 (snoc10 g a) B -> Tm10 g (arr10 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm10 g (arr10 a B) -> Tm10 g a -> Tm10 g B)
-> Tm10 g a
var10 : {g : _} -> {a : _} -> Var10 g a -> Tm10 g a
var10 = \ x, tm, var10, lam, app => var10 _ _ x
lam10 : {g : _} -> {a : _} -> {B : _} -> Tm10 (snoc10 g a) B -> Tm10 g (arr10 a B)
lam10 = \ t, tm, var10, lam10, app => lam10 _ _ _ (t tm var10 lam10 app)
app10 : {g:_}->{a:_}->{B:_} -> Tm10 g (arr10 a B) -> Tm10 g a -> Tm10 g B
app10 = \ t, u, tm, var10, lam10, app10 => app10 _ _ _ (t tm var10 lam10 app10) (u tm var10 lam10 app10)
v010 : {g:_}->{a:_} -> Tm10 (snoc10 g a) a
v010 = var10 vz10
v110 : {g:_}->{a:_}-> {B:_}-> Tm10 (snoc10 (snoc10 g a) B) a
v110 = var10 (vs10 vz10)
v210 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm10 (snoc10 (snoc10 (snoc10 g a) B) C) a
v210 = var10 (vs10 (vs10 vz10))
v310 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm10 (snoc10 (snoc10 (snoc10 (snoc10 g a) B) C) D) a
v310 = var10 (vs10 (vs10 (vs10 vz10)))
v410 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm10 (snoc10 (snoc10 (snoc10 (snoc10 (snoc10 g a) B) C) D) E) a
v410 = var10 (vs10 (vs10 (vs10 (vs10 vz10))))
test10 : {g:_}-> {a:_} -> Tm10 g (arr10 (arr10 a a) (arr10 a a))
test10 = lam10 (lam10 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 (app10 v110 v010)))))))
Ty11 : Type
Ty11 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty11 : Ty11
empty11 = \ _, empty, _ => empty
arr11 : Ty11 -> Ty11 -> Ty11
arr11 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con11 : Type
Con11 = (Con11 : Type)
->(nil : Con11)
->(snoc : Con11 -> Ty11 -> Con11)
-> Con11
nil11 : Con11
nil11 = \ con, nil11, snoc => nil11
snoc11 : Con11 -> Ty11 -> Con11
snoc11 = \ g, a, con, nil11, snoc11 => snoc11 (g con nil11 snoc11) a
Var11 : Con11 -> Ty11 -> Type
Var11 = \ g, a =>
(Var11 : Con11 -> Ty11 -> Type)
-> (vz : (g : _)-> (a : _) -> Var11 (snoc11 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var11 g a -> Var11 (snoc11 g b) a)
-> Var11 g a
vz11 : {g : _}-> {a : _} -> Var11 (snoc11 g a) a
vz11 = \ var, vz11, vs => vz11 _ _
vs11 : {g : _} -> {B : _} -> {a : _} -> Var11 g a -> Var11 (snoc11 g B) a
vs11 = \ x, var, vz11, vs11 => vs11 _ _ _ (x var vz11 vs11)
Tm11 : Con11 -> Ty11 -> Type
Tm11 = \ g, a =>
(Tm11 : Con11 -> Ty11 -> Type)
-> (var : (g : _) -> (a : _) -> Var11 g a -> Tm11 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm11 (snoc11 g a) B -> Tm11 g (arr11 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm11 g (arr11 a B) -> Tm11 g a -> Tm11 g B)
-> Tm11 g a
var11 : {g : _} -> {a : _} -> Var11 g a -> Tm11 g a
var11 = \ x, tm, var11, lam, app => var11 _ _ x
lam11 : {g : _} -> {a : _} -> {B : _} -> Tm11 (snoc11 g a) B -> Tm11 g (arr11 a B)
lam11 = \ t, tm, var11, lam11, app => lam11 _ _ _ (t tm var11 lam11 app)
app11 : {g:_}->{a:_}->{B:_} -> Tm11 g (arr11 a B) -> Tm11 g a -> Tm11 g B
app11 = \ t, u, tm, var11, lam11, app11 => app11 _ _ _ (t tm var11 lam11 app11) (u tm var11 lam11 app11)
v011 : {g:_}->{a:_} -> Tm11 (snoc11 g a) a
v011 = var11 vz11
v111 : {g:_}->{a:_}-> {B:_}-> Tm11 (snoc11 (snoc11 g a) B) a
v111 = var11 (vs11 vz11)
v211 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm11 (snoc11 (snoc11 (snoc11 g a) B) C) a
v211 = var11 (vs11 (vs11 vz11))
v311 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm11 (snoc11 (snoc11 (snoc11 (snoc11 g a) B) C) D) a
v311 = var11 (vs11 (vs11 (vs11 vz11)))
v411 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm11 (snoc11 (snoc11 (snoc11 (snoc11 (snoc11 g a) B) C) D) E) a
v411 = var11 (vs11 (vs11 (vs11 (vs11 vz11))))
test11 : {g:_}-> {a:_} -> Tm11 g (arr11 (arr11 a a) (arr11 a a))
test11 = lam11 (lam11 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 (app11 v111 v011)))))))
Ty12 : Type
Ty12 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty12 : Ty12
empty12 = \ _, empty, _ => empty
arr12 : Ty12 -> Ty12 -> Ty12
arr12 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con12 : Type
Con12 = (Con12 : Type)
->(nil : Con12)
->(snoc : Con12 -> Ty12 -> Con12)
-> Con12
nil12 : Con12
nil12 = \ con, nil12, snoc => nil12
snoc12 : Con12 -> Ty12 -> Con12
snoc12 = \ g, a, con, nil12, snoc12 => snoc12 (g con nil12 snoc12) a
Var12 : Con12 -> Ty12 -> Type
Var12 = \ g, a =>
(Var12 : Con12 -> Ty12 -> Type)
-> (vz : (g : _)-> (a : _) -> Var12 (snoc12 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var12 g a -> Var12 (snoc12 g b) a)
-> Var12 g a
vz12 : {g : _}-> {a : _} -> Var12 (snoc12 g a) a
vz12 = \ var, vz12, vs => vz12 _ _
vs12 : {g : _} -> {B : _} -> {a : _} -> Var12 g a -> Var12 (snoc12 g B) a
vs12 = \ x, var, vz12, vs12 => vs12 _ _ _ (x var vz12 vs12)
Tm12 : Con12 -> Ty12 -> Type
Tm12 = \ g, a =>
(Tm12 : Con12 -> Ty12 -> Type)
-> (var : (g : _) -> (a : _) -> Var12 g a -> Tm12 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm12 (snoc12 g a) B -> Tm12 g (arr12 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm12 g (arr12 a B) -> Tm12 g a -> Tm12 g B)
-> Tm12 g a
var12 : {g : _} -> {a : _} -> Var12 g a -> Tm12 g a
var12 = \ x, tm, var12, lam, app => var12 _ _ x
lam12 : {g : _} -> {a : _} -> {B : _} -> Tm12 (snoc12 g a) B -> Tm12 g (arr12 a B)
lam12 = \ t, tm, var12, lam12, app => lam12 _ _ _ (t tm var12 lam12 app)
app12 : {g:_}->{a:_}->{B:_} -> Tm12 g (arr12 a B) -> Tm12 g a -> Tm12 g B
app12 = \ t, u, tm, var12, lam12, app12 => app12 _ _ _ (t tm var12 lam12 app12) (u tm var12 lam12 app12)
v012 : {g:_}->{a:_} -> Tm12 (snoc12 g a) a
v012 = var12 vz12
v112 : {g:_}->{a:_}-> {B:_}-> Tm12 (snoc12 (snoc12 g a) B) a
v112 = var12 (vs12 vz12)
v212 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm12 (snoc12 (snoc12 (snoc12 g a) B) C) a
v212 = var12 (vs12 (vs12 vz12))
v312 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm12 (snoc12 (snoc12 (snoc12 (snoc12 g a) B) C) D) a
v312 = var12 (vs12 (vs12 (vs12 vz12)))
v412 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm12 (snoc12 (snoc12 (snoc12 (snoc12 (snoc12 g a) B) C) D) E) a
v412 = var12 (vs12 (vs12 (vs12 (vs12 vz12))))
test12 : {g:_}-> {a:_} -> Tm12 g (arr12 (arr12 a a) (arr12 a a))
test12 = lam12 (lam12 (app12 v112 (app12 v112 (app12 v112 (app12 v112 (app12 v112 (app12 v112 v012)))))))
Ty13 : Type
Ty13 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty
empty13 : Ty13
empty13 = \ _, empty, _ => empty
arr13 : Ty13 -> Ty13 -> Ty13
arr13 = \ a, b, ty, empty, arr => arr (a ty empty arr) (b ty empty arr)
Con13 : Type
Con13 = (Con13 : Type)
->(nil : Con13)
->(snoc : Con13 -> Ty13 -> Con13)
-> Con13
nil13 : Con13
nil13 = \ con, nil13, snoc => nil13
snoc13 : Con13 -> Ty13 -> Con13
snoc13 = \ g, a, con, nil13, snoc13 => snoc13 (g con nil13 snoc13) a
Var13 : Con13 -> Ty13 -> Type
Var13 = \ g, a =>
(Var13 : Con13 -> Ty13 -> Type)
-> (vz : (g : _)-> (a : _) -> Var13 (snoc13 g a) a)
-> (vs : (g : _)-> (b : _) -> (a : _) -> Var13 g a -> Var13 (snoc13 g b) a)
-> Var13 g a
vz13 : {g : _}-> {a : _} -> Var13 (snoc13 g a) a
vz13 = \ var, vz13, vs => vz13 _ _
vs13 : {g : _} -> {B : _} -> {a : _} -> Var13 g a -> Var13 (snoc13 g B) a
vs13 = \ x, var, vz13, vs13 => vs13 _ _ _ (x var vz13 vs13)
Tm13 : Con13 -> Ty13 -> Type
Tm13 = \ g, a =>
(Tm13 : Con13 -> Ty13 -> Type)
-> (var : (g : _) -> (a : _) -> Var13 g a -> Tm13 g a)
-> (lam : (g : _) -> (a : _) -> (B : _) -> Tm13 (snoc13 g a) B -> Tm13 g (arr13 a B))
-> (app : (g : _) -> (a : _) -> (B : _) -> Tm13 g (arr13 a B) -> Tm13 g a -> Tm13 g B)
-> Tm13 g a
var13 : {g : _} -> {a : _} -> Var13 g a -> Tm13 g a
var13 = \ x, tm, var13, lam, app => var13 _ _ x
lam13 : {g : _} -> {a : _} -> {B : _} -> Tm13 (snoc13 g a) B -> Tm13 g (arr13 a B)
lam13 = \ t, tm, var13, lam13, app => lam13 _ _ _ (t tm var13 lam13 app)
app13 : {g:_}->{a:_}->{B:_} -> Tm13 g (arr13 a B) -> Tm13 g a -> Tm13 g B
app13 = \ t, u, tm, var13, lam13, app13 => app13 _ _ _ (t tm var13 lam13 app13) (u tm var13 lam13 app13)
v013 : {g:_}->{a:_} -> Tm13 (snoc13 g a) a
v013 = var13 vz13
v113 : {g:_}->{a:_}-> {B:_}-> Tm13 (snoc13 (snoc13 g a) B) a
v113 = var13 (vs13 vz13)
v213 : {g:_}-> {a:_}-> {B:_}-> {C:_} -> Tm13 (snoc13 (snoc13 (snoc13 g a) B) C) a
v213 = var13 (vs13 (vs13 vz13))
v313 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_} -> Tm13 (snoc13 (snoc13 (snoc13 (snoc13 g a) B) C) D) a
v313 = var13 (vs13 (vs13 (vs13 vz13)))
v413 : {g:_}-> {a:_}-> {B:_}-> {C:_}-> {D:_}-> {E:_}-> Tm13 (snoc13 (snoc13 (snoc13 (snoc13 (snoc13 g a) B) C) D) E) a
v413 = var13 (vs13 (vs13 (vs13 (vs13 vz13))))
test13 : {g:_}-> {a:_} -> Tm13 g (arr13 (arr13 a a) (arr13 a a))
test13 = lam13 (lam13 (app13 v113 (app13 v113 (app13 v113 (app13 v113 (app13 v113 (app13 v113 v013)))))))
Ty14 : Type
Ty14 = (Ty : Type)
->(empty : Ty)
->(arr : Ty -> Ty -> Ty)
-> Ty