-x (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1:
-T).(subst0 i v v1 v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1
-c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C x (CHead c1 (Bind b) v1))))))))
-(\lambda (y0: nat).(\lambda (H1: (csubst0 y0 v x y)).(csubst0_ind (\lambda
-(n: nat).(\lambda (t: T).(\lambda (c: C).(\lambda (c0: C).((eq nat n (S i))
-\to ((eq C c0 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1:
-T).(subst0 i t v1 v2)) (\lambda (v1: T).(eq C c (CHead c2 (Bind b) v1))))
-(ex2 C (\lambda (c1: C).(csubst0 i t c1 c2)) (\lambda (c1: C).(eq C c (CHead
-c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i t v1
-v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i t c1 c2))) (\lambda (c1:
-C).(\lambda (v1: T).(eq C c (CHead c1 (Bind b) v1)))))))))))) (\lambda (k:
-K).(\lambda (i0: nat).(\lambda (v0: T).(\lambda (u1: T).(\lambda (u2:
-T).(\lambda (H2: (subst0 i0 v0 u1 u2)).(\lambda (c: C).(\lambda (H3: (eq nat
-(s k i0) (S i))).(\lambda (H4: (eq C (CHead c k u2) (CHead c2 (Bind b)
-v2))).(let H5 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c | (CHead c0 _ _) \Rightarrow c0]))
-(CHead c k u2) (CHead c2 (Bind b) v2) H4) in ((let H6 \def (f_equal C K
-(\lambda (e: C).(match e in C return (\lambda (_: C).K) with [(CSort _)
-\Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c k u2) (CHead c2
-(Bind b) v2) H4) in ((let H7 \def (f_equal C T (\lambda (e: C).(match e in C
-return (\lambda (_: C).T) with [(CSort _) \Rightarrow u2 | (CHead _ _ t)
-\Rightarrow t])) (CHead c k u2) (CHead c2 (Bind b) v2) H4) in (\lambda (H8:
-(eq K k (Bind b))).(\lambda (H9: (eq C c c2)).(eq_ind_r C c2 (\lambda (c0:
-C).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C
-(CHead c0 k u1) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i
-v0 c1 c2)) (\lambda (c1: C).(eq C (CHead c0 k u1) (CHead c1 (Bind b) v2))))
-(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda
-(c1: C).(\lambda (_: T).(csubst0 i v0 c1 c2))) (\lambda (c1: C).(\lambda (v1:
-T).(eq C (CHead c0 k u1) (CHead c1 (Bind b) v1))))))) (let H10 \def (eq_ind T
-u2 (\lambda (t: T).(subst0 i0 v0 u1 t)) H2 v2 H7) in (let H11 \def (eq_ind K
-k (\lambda (k0: K).(eq nat (s k0 i0) (S i))) H3 (Bind b) H8) in (eq_ind_r K
-(Bind b) (\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2))
-(\lambda (v1: T).(eq C (CHead c2 k0 u1) (CHead c2 (Bind b) v1)))) (ex2 C
-(\lambda (c1: C).(csubst0 i v0 c1 c2)) (\lambda (c1: C).(eq C (CHead c2 k0
-u1) (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1:
-T).(subst0 i v0 v1 v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v0 c1
-c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C (CHead c2 k0 u1) (CHead c1
-(Bind b) v1))))))) (let H12 \def (f_equal nat nat (\lambda (e: nat).(match e
-in nat return (\lambda (_: nat).nat) with [O \Rightarrow i0 | (S n)
-\Rightarrow n])) (S i0) (S i) H11) in (let H13 \def (eq_ind nat i0 (\lambda
-(n: nat).(subst0 n v0 u1 v2)) H10 i H12) in (or3_intro0 (ex2 T (\lambda (v1:
-T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c2 (Bind b) u1) (CHead
-c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v0 c1 c2)) (\lambda
-(c1: C).(eq C (CHead c2 (Bind b) u1) (CHead c1 (Bind b) v2)))) (ex3_2 C T
-(\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c1:
-C).(\lambda (_: T).(csubst0 i v0 c1 c2))) (\lambda (c1: C).(\lambda (v1:
-T).(eq C (CHead c2 (Bind b) u1) (CHead c1 (Bind b) v1))))) (ex_intro2 T
-(\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c2 (Bind
-b) u1) (CHead c2 (Bind b) v1))) u1 H13 (refl_equal C (CHead c2 (Bind b)
-u1)))))) k H8))) c H9)))) H6)) H5))))))))))) (\lambda (k: K).(\lambda (i0:
-nat).(\lambda (c1: C).(\lambda (c0: C).(\lambda (v0: T).(\lambda (H2:
-(csubst0 i0 v0 c1 c0)).(\lambda (H3: (((eq nat i0 (S i)) \to ((eq C c0 (CHead
-c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2))
-(\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3:
-C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2))))
-(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda
-(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1:
-T).(eq C c1 (CHead c3 (Bind b) v1)))))))))).(\lambda (u: T).(\lambda (H4: (eq
-nat (s k i0) (S i))).(\lambda (H5: (eq C (CHead c0 k u) (CHead c2 (Bind b)
-v2))).(let H6 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda
-(_: C).C) with [(CSort _) \Rightarrow c0 | (CHead c _ _) \Rightarrow c]))
-(CHead c0 k u) (CHead c2 (Bind b) v2) H5) in ((let H7 \def (f_equal C K
-(\lambda (e: C).(match e in C return (\lambda (_: C).K) with [(CSort _)
-\Rightarrow k | (CHead _ k0 _) \Rightarrow k0])) (CHead c0 k u) (CHead c2
-(Bind b) v2) H5) in ((let H8 \def (f_equal C T (\lambda (e: C).(match e in C
-return (\lambda (_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t)
-\Rightarrow t])) (CHead c0 k u) (CHead c2 (Bind b) v2) H5) in (\lambda (H9:
-(eq K k (Bind b))).(\lambda (H10: (eq C c0 c2)).(eq_ind_r T v2 (\lambda (t:
-T).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C
-(CHead c1 k t) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i
-v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 k t) (CHead c3 (Bind b) v2))))
-(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda
-(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1:
-T).(eq C (CHead c1 k t) (CHead c3 (Bind b) v1))))))) (let H11 \def (eq_ind C
-c0 (\lambda (c: C).((eq nat i0 (S i)) \to ((eq C c (CHead c2 (Bind b) v2))
-\to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C
-c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2))
-(\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_:
-C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_:
-T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead
-c3 (Bind b) v1))))))))) H3 c2 H10) in (let H12 \def (eq_ind C c0 (\lambda (c:
-C).(csubst0 i0 v0 c1 c)) H2 c2 H10) in (let H13 \def (eq_ind K k (\lambda
-(k0: K).(eq nat (s k0 i0) (S i))) H4 (Bind b) H9) in (eq_ind_r K (Bind b)
-(\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda
-(v1: T).(eq C (CHead c1 k0 v2) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3:
-C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 k0 v2) (CHead c3
-(Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1
-v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3:
-C).(\lambda (v1: T).(eq C (CHead c1 k0 v2) (CHead c3 (Bind b) v1))))))) (let
-H14 \def (f_equal nat nat (\lambda (e: nat).(match e in nat return (\lambda
-(_: nat).nat) with [O \Rightarrow i0 | (S n) \Rightarrow n])) (S i0) (S i)
-H13) in (let H15 \def (eq_ind nat i0 (\lambda (n: nat).((eq nat n (S i)) \to
-((eq C c2 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i
-v0 v1 v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C
-(\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3
-(Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1
-v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3:
-C).(\lambda (v1: T).(eq C c1 (CHead c3 (Bind b) v1))))))))) H11 i H14) in
-(let H16 \def (eq_ind nat i0 (\lambda (n: nat).(csubst0 n v0 c1 c2)) H12 i
-H14) in (or3_intro1 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda
-(v1: T).(eq C (CHead c1 (Bind b) v2) (CHead c2 (Bind b) v1)))) (ex2 C
-(\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C (CHead c1 (Bind
-b) v2) (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1:
-T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3
-c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C (CHead c1 (Bind b) v2) (CHead
-c3 (Bind b) v1))))) (ex_intro2 C (\lambda (c3: C).(csubst0 i v0 c3 c2))
-(\lambda (c3: C).(eq C (CHead c1 (Bind b) v2) (CHead c3 (Bind b) v2))) c1 H16
-(refl_equal C (CHead c1 (Bind b) v2))))))) k H9)))) u H8)))) H7))
-H6)))))))))))) (\lambda (k: K).(\lambda (i0: nat).(\lambda (v0: T).(\lambda
-(u1: T).(\lambda (u2: T).(\lambda (H2: (subst0 i0 v0 u1 u2)).(\lambda (c1:
-C).(\lambda (c0: C).(\lambda (H3: (csubst0 i0 v0 c1 c0)).(\lambda (H4: (((eq
-nat i0 (S i)) \to ((eq C c0 (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda
-(v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b)
-v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C
-c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1:
-T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_: T).(csubst0 i v0 c3
-c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead c3 (Bind b)
-v1)))))))))).(\lambda (H5: (eq nat (s k i0) (S i))).(\lambda (H6: (eq C
-(CHead c0 k u2) (CHead c2 (Bind b) v2))).(let H7 \def (f_equal C C (\lambda
-(e: C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c0
-| (CHead c _ _) \Rightarrow c])) (CHead c0 k u2) (CHead c2 (Bind b) v2) H6)
-in ((let H8 \def (f_equal C K (\lambda (e: C).(match e in C return (\lambda
-(_: C).K) with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
-(CHead c0 k u2) (CHead c2 (Bind b) v2) H6) in ((let H9 \def (f_equal C T
-(\lambda (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _)
-\Rightarrow u2 | (CHead _ _ t) \Rightarrow t])) (CHead c0 k u2) (CHead c2
-(Bind b) v2) H6) in (\lambda (H10: (eq K k (Bind b))).(\lambda (H11: (eq C c0
-c2)).(let H12 \def (eq_ind C c0 (\lambda (c: C).((eq nat i0 (S i)) \to ((eq C
-c (CHead c2 (Bind b) v2)) \to (or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1
-v2)) (\lambda (v1: T).(eq C c1 (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3:
-C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2))))
-(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda
-(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1:
-T).(eq C c1 (CHead c3 (Bind b) v1))))))))) H4 c2 H11) in (let H13 \def
-(eq_ind C c0 (\lambda (c: C).(csubst0 i0 v0 c1 c)) H3 c2 H11) in (let H14
-\def (eq_ind T u2 (\lambda (t: T).(subst0 i0 v0 u1 t)) H2 v2 H9) in (let H15
-\def (eq_ind K k (\lambda (k0: K).(eq nat (s k0 i0) (S i))) H5 (Bind b) H10)
-in (eq_ind_r K (Bind b) (\lambda (k0: K).(or3 (ex2 T (\lambda (v1: T).(subst0
-i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c1 k0 u1) (CHead c2 (Bind b)
-v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2)) (\lambda (c3: C).(eq C
-(CHead c1 k0 u1) (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_:
-C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_:
-T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C (CHead c1
-k0 u1) (CHead c3 (Bind b) v1))))))) (let H16 \def (f_equal nat nat (\lambda
-(e: nat).(match e in nat return (\lambda (_: nat).nat) with [O \Rightarrow i0
-| (S n) \Rightarrow n])) (S i0) (S i) H15) in (let H17 \def (eq_ind nat i0
-(\lambda (n: nat).((eq nat n (S i)) \to ((eq C c2 (CHead c2 (Bind b) v2)) \to
-(or3 (ex2 T (\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C c1
-(CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3 c2))
-(\lambda (c3: C).(eq C c1 (CHead c3 (Bind b) v2)))) (ex3_2 C T (\lambda (_:
-C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3: C).(\lambda (_:
-T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1: T).(eq C c1 (CHead
-c3 (Bind b) v1))))))))) H12 i H16) in (let H18 \def (eq_ind nat i0 (\lambda
-(n: nat).(csubst0 n v0 c1 c2)) H13 i H16) in (let H19 \def (eq_ind nat i0
-(\lambda (n: nat).(subst0 n v0 u1 v2)) H14 i H16) in (or3_intro2 (ex2 T
-(\lambda (v1: T).(subst0 i v0 v1 v2)) (\lambda (v1: T).(eq C (CHead c1 (Bind
-b) u1) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c3: C).(csubst0 i v0 c3
-c2)) (\lambda (c3: C).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v2))))
-(ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda
-(c3: C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1:
-T).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v1))))) (ex3_2_intro C T
-(\lambda (_: C).(\lambda (v1: T).(subst0 i v0 v1 v2))) (\lambda (c3:
-C).(\lambda (_: T).(csubst0 i v0 c3 c2))) (\lambda (c3: C).(\lambda (v1:
-T).(eq C (CHead c1 (Bind b) u1) (CHead c3 (Bind b) v1)))) c1 u1 H19 H18
-(refl_equal C (CHead c1 (Bind b) u1)))))))) k H10)))))))) H8))
-H7)))))))))))))) y0 v x y H1))) H0))) H))))))).
-(* COMMENTS
-Initial nodes: 3878
-END *)
+(CHead c k t) (CHead c1 (Bind b) v2)))) (ex3_2 C T (\lambda (_: C).(\lambda
+(v1: T).(subst0 i v v1 v2))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1
+c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C (CHead c k t) (CHead c1 (Bind
+b) v1)))))) (\lambda (x0: C).(\lambda (x1: nat).(\lambda (H3: (eq nat (S i)
+(s k x1))).(\lambda (H4: (eq C (CHead c2 (Bind b) v2) (CHead x0 k
+t))).(\lambda (H5: (csubst0 x1 v c x0)).(let H6 \def (f_equal C C (\lambda
+(e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _) \Rightarrow
+c0])) (CHead c2 (Bind b) v2) (CHead x0 k t) H4) in ((let H7 \def (f_equal C K
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow (Bind b) | (CHead _ k0
+_) \Rightarrow k0])) (CHead c2 (Bind b) v2) (CHead x0 k t) H4) in ((let H8
+\def (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow v2 |
+(CHead _ _ t0) \Rightarrow t0])) (CHead c2 (Bind b) v2) (CHead x0 k t) H4) in
+(\lambda (H9: (eq K (Bind b) k)).(\lambda (H10: (eq C c2 x0)).(let H11 \def
+(eq_ind_r C x0 (\lambda (c0: C).(csubst0 x1 v c c0)) H5 c2 H10) in (eq_ind_r
+T t (\lambda (t0: T).(or3 (ex2 T (\lambda (v1: T).(subst0 i v v1 t0))
+(\lambda (v1: T).(eq C (CHead c k t) (CHead c2 (Bind b) v1)))) (ex2 C
+(\lambda (c1: C).(csubst0 i v c1 c2)) (\lambda (c1: C).(eq C (CHead c k t)
+(CHead c1 (Bind b) t0)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0
+i v v1 t0))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda
+(c1: C).(\lambda (v1: T).(eq C (CHead c k t) (CHead c1 (Bind b) v1)))))))
+(let H12 \def (eq_ind_r K k (\lambda (k0: K).(eq nat (S i) (s k0 x1))) H3
+(Bind b) H9) in (eq_ind K (Bind b) (\lambda (k0: K).(or3 (ex2 T (\lambda (v1:
+T).(subst0 i v v1 t)) (\lambda (v1: T).(eq C (CHead c k0 t) (CHead c2 (Bind
+b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2)) (\lambda (c1: C).(eq C
+(CHead c k0 t) (CHead c1 (Bind b) t)))) (ex3_2 C T (\lambda (_: C).(\lambda
+(v1: T).(subst0 i v v1 t))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1
+c2))) (\lambda (c1: C).(\lambda (v1: T).(eq C (CHead c k0 t) (CHead c1 (Bind
+b) v1))))))) (let H13 \def (f_equal nat nat (\lambda (e: nat).(match e with
+[O \Rightarrow i | (S n) \Rightarrow n])) (S i) (S x1) H12) in (let H14 \def
+(eq_ind_r nat x1 (\lambda (n: nat).(csubst0 n v c c2)) H11 i H13) in
+(or3_intro1 (ex2 T (\lambda (v1: T).(subst0 i v v1 t)) (\lambda (v1: T).(eq C
+(CHead c (Bind b) t) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1:
+C).(csubst0 i v c1 c2)) (\lambda (c1: C).(eq C (CHead c (Bind b) t) (CHead c1
+(Bind b) t)))) (ex3_2 C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v v1
+t))) (\lambda (c1: C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1:
+C).(\lambda (v1: T).(eq C (CHead c (Bind b) t) (CHead c1 (Bind b) v1)))))
+(ex_intro2 C (\lambda (c1: C).(csubst0 i v c1 c2)) (\lambda (c1: C).(eq C
+(CHead c (Bind b) t) (CHead c1 (Bind b) t))) c H14 (refl_equal C (CHead c
+(Bind b) t)))))) k H9)) v2 H8))))) H7)) H6))))))) H2)) (\lambda (H2: (ex4_3 T
+C nat (\lambda (_: T).(\lambda (_: C).(\lambda (j: nat).(eq nat (S i) (s k
+j))))) (\lambda (u2: T).(\lambda (c3: C).(\lambda (_: nat).(eq C (CHead c2
+(Bind b) v2) (CHead c3 k u2))))) (\lambda (u2: T).(\lambda (_: C).(\lambda
+(j: nat).(subst0 j v t u2)))) (\lambda (_: T).(\lambda (c3: C).(\lambda (j:
+nat).(csubst0 j v c c3)))))).(ex4_3_ind T C nat (\lambda (_: T).(\lambda (_:
+C).(\lambda (j: nat).(eq nat (S i) (s k j))))) (\lambda (u2: T).(\lambda (c3:
+C).(\lambda (_: nat).(eq C (CHead c2 (Bind b) v2) (CHead c3 k u2)))))
+(\lambda (u2: T).(\lambda (_: C).(\lambda (j: nat).(subst0 j v t u2))))
+(\lambda (_: T).(\lambda (c3: C).(\lambda (j: nat).(csubst0 j v c c3)))) (or3
+(ex2 T (\lambda (v1: T).(subst0 i v v1 v2)) (\lambda (v1: T).(eq C (CHead c k
+t) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2))
+(\lambda (c1: C).(eq C (CHead c k t) (CHead c1 (Bind b) v2)))) (ex3_2 C T
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1:
+C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1:
+T).(eq C (CHead c k t) (CHead c1 (Bind b) v1)))))) (\lambda (x0: T).(\lambda
+(x1: C).(\lambda (x2: nat).(\lambda (H3: (eq nat (S i) (s k x2))).(\lambda
+(H4: (eq C (CHead c2 (Bind b) v2) (CHead x1 k x0))).(\lambda (H5: (subst0 x2
+v t x0)).(\lambda (H6: (csubst0 x2 v c x1)).(let H7 \def (f_equal C C
+(\lambda (e: C).(match e with [(CSort _) \Rightarrow c2 | (CHead c0 _ _)
+\Rightarrow c0])) (CHead c2 (Bind b) v2) (CHead x1 k x0) H4) in ((let H8 \def
+(f_equal C K (\lambda (e: C).(match e with [(CSort _) \Rightarrow (Bind b) |
+(CHead _ k0 _) \Rightarrow k0])) (CHead c2 (Bind b) v2) (CHead x1 k x0) H4)
+in ((let H9 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow v2 | (CHead _ _ t0) \Rightarrow t0])) (CHead c2 (Bind b) v2)
+(CHead x1 k x0) H4) in (\lambda (H10: (eq K (Bind b) k)).(\lambda (H11: (eq C
+c2 x1)).(let H12 \def (eq_ind_r C x1 (\lambda (c0: C).(csubst0 x2 v c c0)) H6
+c2 H11) in (let H13 \def (eq_ind_r T x0 (\lambda (t0: T).(subst0 x2 v t t0))
+H5 v2 H9) in (let H14 \def (eq_ind_r K k (\lambda (k0: K).(eq nat (S i) (s k0
+x2))) H3 (Bind b) H10) in (eq_ind K (Bind b) (\lambda (k0: K).(or3 (ex2 T
+(\lambda (v1: T).(subst0 i v v1 v2)) (\lambda (v1: T).(eq C (CHead c k0 t)
+(CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2))
+(\lambda (c1: C).(eq C (CHead c k0 t) (CHead c1 (Bind b) v2)))) (ex3_2 C T
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1:
+C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1:
+T).(eq C (CHead c k0 t) (CHead c1 (Bind b) v1))))))) (let H15 \def (f_equal
+nat nat (\lambda (e: nat).(match e with [O \Rightarrow i | (S n) \Rightarrow
+n])) (S i) (S x2) H14) in (let H16 \def (eq_ind_r nat x2 (\lambda (n:
+nat).(csubst0 n v c c2)) H12 i H15) in (let H17 \def (eq_ind_r nat x2
+(\lambda (n: nat).(subst0 n v t v2)) H13 i H15) in (or3_intro2 (ex2 T
+(\lambda (v1: T).(subst0 i v v1 v2)) (\lambda (v1: T).(eq C (CHead c (Bind b)
+t) (CHead c2 (Bind b) v1)))) (ex2 C (\lambda (c1: C).(csubst0 i v c1 c2))
+(\lambda (c1: C).(eq C (CHead c (Bind b) t) (CHead c1 (Bind b) v2)))) (ex3_2
+C T (\lambda (_: C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1:
+C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1:
+T).(eq C (CHead c (Bind b) t) (CHead c1 (Bind b) v1))))) (ex3_2_intro C T
+(\lambda (_: C).(\lambda (v1: T).(subst0 i v v1 v2))) (\lambda (c1:
+C).(\lambda (_: T).(csubst0 i v c1 c2))) (\lambda (c1: C).(\lambda (v1:
+T).(eq C (CHead c (Bind b) t) (CHead c1 (Bind b) v1)))) c t H17 H16
+(refl_equal C (CHead c (Bind b) t))))))) k H10))))))) H8)) H7))))))))) H2))
+H1))))))))))) x)).