(* This file was automatically generated: do not edit *********************)
-include "Basic-1/csubst1/props.ma".
+include "basic_1/csubst1/props.ma".
-include "Basic-1/csubst0/getl.ma".
+include "basic_1/csubst0/getl.ma".
-include "Basic-1/subst1/props.ma".
+include "basic_1/subst1/props.ma".
-include "Basic-1/drop/props.ma".
+include "basic_1/drop/props.ma".
-theorem csubst1_getl_ge:
+lemma csubst1_getl_ge:
\forall (i: nat).(\forall (n: nat).((le i n) \to (\forall (c1: C).(\forall
(c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e: C).((getl n c1
e) \to (getl n c2 e)))))))))
(getl n c e)))) (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) (\lambda
(c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: C).(\lambda (H2:
(getl n c1 e)).(csubst0_getl_ge i n H c1 c3 v H1 e H2))))) c2 H0))))))).
-(* COMMENTS
-Initial nodes: 111
-END *)
-theorem csubst1_getl_lt:
+lemma csubst1_getl_lt:
\forall (i: nat).(\forall (n: nat).((lt n i) \to (\forall (c1: C).(\forall
(c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e1: C).((getl n c1
e1) \to (ex2 C (\lambda (e2: C).(csubst1 (minus i n) v e1 e2)) (\lambda (e2:
(csubst1_sing (S (minus i (S n))) v (CHead x1 (Bind x0) x3) (CHead x2 (Bind
x0) x4) (csubst0_both_bind x0 (minus i (S n)) v x3 x4 H7 x1 x2 H8)) H6) e1
H5)))))))))) H4)) H3)) (minus i n) (minus_x_Sy i n H)))))) c2 H0))))))).
-(* COMMENTS
-Initial nodes: 2035
-END *)
-theorem csubst1_getl_ge_back:
+lemma csubst1_getl_ge_back:
\forall (i: nat).(\forall (n: nat).((le i n) \to (\forall (c1: C).(\forall
(c2: C).(\forall (v: T).((csubst1 i v c1 c2) \to (\forall (e: C).((getl n c2
e) \to (getl n c1 e)))))))))
(getl n c1 e)))) (\lambda (e: C).(\lambda (H1: (getl n c1 e)).H1)) (\lambda
(c3: C).(\lambda (H1: (csubst0 i v c1 c3)).(\lambda (e: C).(\lambda (H2:
(getl n c3 e)).(csubst0_getl_ge_back i n H c1 c3 v H1 e H2))))) c2 H0))))))).
-(* COMMENTS
-Initial nodes: 111
-END *)
-theorem getl_csubst1:
+lemma getl_csubst1:
\forall (d: nat).(\forall (c: C).(\forall (e: C).(\forall (u: T).((getl d c
(CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_:
C).(csubst1 d u c a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) d a0
C).(\lambda (a: C).(drop (S O) O a0 a))))))))) (\lambda (b: B).(\lambda (t:
T).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl O (CHead c0 (Bind b)
t) (CHead e (Bind Abbr) u))).(let H1 \def (f_equal C C (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow e |
-(CHead c1 _ _) \Rightarrow c1])) (CHead e (Bind Abbr) u) (CHead c0 (Bind b)
-t) (clear_gen_bind b c0 (CHead e (Bind Abbr) u) t (getl_gen_O (CHead c0 (Bind
-b) t) (CHead e (Bind Abbr) u) H0))) in ((let H2 \def (f_equal C B (\lambda
-(e0: C).(match e0 in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow
-Abbr | (CHead _ k0 _) \Rightarrow (match k0 in K return (\lambda (_: K).B)
-with [(Bind b0) \Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead e
-(Bind Abbr) u) (CHead c0 (Bind b) t) (clear_gen_bind b c0 (CHead e (Bind
-Abbr) u) t (getl_gen_O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u) H0))) in
-((let H3 \def (f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda
-(_: C).T) with [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0]))
+C).(match e0 with [(CSort _) \Rightarrow e | (CHead c1 _ _) \Rightarrow c1]))
(CHead e (Bind Abbr) u) (CHead c0 (Bind b) t) (clear_gen_bind b c0 (CHead e
(Bind Abbr) u) t (getl_gen_O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u)
-H0))) in (\lambda (H4: (eq B Abbr b)).(\lambda (_: (eq C e c0)).(eq_ind_r T t
-(\lambda (t0: T).(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O t0
-(CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0
-a))))) (eq_ind B Abbr (\lambda (b0: B).(ex2_2 C C (\lambda (a0: C).(\lambda
-(_: C).(csubst1 O t (CHead c0 (Bind b0) t) a0))) (\lambda (a0: C).(\lambda
-(a: C).(drop (S O) O a0 a))))) (ex2_2_intro C C (\lambda (a0: C).(\lambda (_:
-C).(csubst1 O t (CHead c0 (Bind Abbr) t) a0))) (\lambda (a0: C).(\lambda (a:
-C).(drop (S O) O a0 a))) (CHead c0 (Bind Abbr) t) c0 (csubst1_refl O t (CHead
-c0 (Bind Abbr) t)) (drop_drop (Bind Abbr) O c0 c0 (drop_refl c0) t)) b H4) u
-H3)))) H2)) H1))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (e:
-C).(\lambda (u: T).(\lambda (H0: (getl O (CHead c0 (Flat f) t) (CHead e (Bind
-Abbr) u))).(let H_x \def (subst1_ex u t O) in (let H1 \def H_x in (ex_ind T
-(\lambda (t2: T).(subst1 O u t (lift (S O) O t2))) (ex2_2 C C (\lambda (a0:
-C).(\lambda (_: C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda (a0:
-C).(\lambda (a: C).(drop (S O) O a0 a)))) (\lambda (x: T).(\lambda (H2:
-(subst1 O u t (lift (S O) O x))).(let H3 \def (H e u (getl_intro O c0 (CHead
-e (Bind Abbr) u) c0 (drop_refl c0) (clear_gen_flat f c0 (CHead e (Bind Abbr)
-u) t (getl_gen_O (CHead c0 (Flat f) t) (CHead e (Bind Abbr) u) H0)))) in
-(ex2_2_ind C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O u c0 a0)))
-(\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a))) (ex2_2 C C (\lambda
-(a0: C).(\lambda (_: C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda
-(a0: C).(\lambda (a: C).(drop (S O) O a0 a)))) (\lambda (x0: C).(\lambda (x1:
-C).(\lambda (H4: (csubst1 O u c0 x0)).(\lambda (H5: (drop (S O) O x0
-x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O u (CHead c0
-(Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a)))
-(CHead x0 (Flat f) (lift (S O) O x)) x1 (csubst1_flat f O u t (lift (S O) O
-x) H2 c0 x0 H4) (drop_drop (Flat f) O x0 x1 H5 (lift (S O) O x))))))) H3))))
-H1)))))))) k)))) c)) (\lambda (n: nat).(\lambda (H: ((\forall (c: C).(\forall
-(e: C).(\forall (u: T).((getl n c (CHead e (Bind Abbr) u)) \to (ex2_2 C C
-(\lambda (a0: C).(\lambda (_: C).(csubst1 n u c a0))) (\lambda (a0:
-C).(\lambda (a: C).(drop (S O) n a0 a)))))))))).(\lambda (c: C).(C_ind
-(\lambda (c0: C).(\forall (e: C).(\forall (u: T).((getl (S n) c0 (CHead e
-(Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S
-n) u c0 a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))))))))
-(\lambda (n0: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl (S n)
-(CSort n0) (CHead e (Bind Abbr) u))).(getl_gen_sort n0 (S n) (CHead e (Bind
-Abbr) u) H0 (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u
-(CSort n0) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0
-a))))))))) (\lambda (c0: C).(\lambda (H0: ((\forall (e: C).(\forall (u:
-T).((getl (S n) c0 (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0:
-C).(\lambda (_: C).(csubst1 (S n) u c0 a0))) (\lambda (a0: C).(\lambda (a:
-C).(drop (S O) (S n) a0 a))))))))).(\lambda (k: K).(K_ind (\lambda (k0:
-K).(\forall (t: T).(\forall (e: C).(\forall (u: T).((getl (S n) (CHead c0 k0
-t) (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_:
-C).(csubst1 (S n) u (CHead c0 k0 t) a0))) (\lambda (a0: C).(\lambda (a:
-C).(drop (S O) (S n) a0 a))))))))) (\lambda (b: B).(\lambda (t: T).(\lambda
-(e: C).(\lambda (u: T).(\lambda (H1: (getl (S n) (CHead c0 (Bind b) t) (CHead
-e (Bind Abbr) u))).(let H_x \def (subst1_ex u t n) in (let H2 \def H_x in
-(ex_ind T (\lambda (t2: T).(subst1 n u t (lift (S O) n t2))) (ex2_2 C C
+H0))) in ((let H2 \def (f_equal C B (\lambda (e0: C).(match e0 with [(CSort
+_) \Rightarrow Abbr | (CHead _ k0 _) \Rightarrow (match k0 with [(Bind b0)
+\Rightarrow b0 | (Flat _) \Rightarrow Abbr])])) (CHead e (Bind Abbr) u)
+(CHead c0 (Bind b) t) (clear_gen_bind b c0 (CHead e (Bind Abbr) u) t
+(getl_gen_O (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u) H0))) in ((let H3
+\def (f_equal C T (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u |
+(CHead _ _ t0) \Rightarrow t0])) (CHead e (Bind Abbr) u) (CHead c0 (Bind b)
+t) (clear_gen_bind b c0 (CHead e (Bind Abbr) u) t (getl_gen_O (CHead c0 (Bind
+b) t) (CHead e (Bind Abbr) u) H0))) in (\lambda (H4: (eq B Abbr b)).(\lambda
+(_: (eq C e c0)).(eq_ind_r T t (\lambda (t0: T).(ex2_2 C C (\lambda (a0:
+C).(\lambda (_: C).(csubst1 O t0 (CHead c0 (Bind b) t) a0))) (\lambda (a0:
+C).(\lambda (a: C).(drop (S O) O a0 a))))) (eq_ind B Abbr (\lambda (b0:
+B).(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O t (CHead c0 (Bind
+b0) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a)))))
+(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 O t (CHead c0
+(Bind Abbr) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a)))
+(CHead c0 (Bind Abbr) t) c0 (csubst1_refl O t (CHead c0 (Bind Abbr) t))
+(drop_drop (Bind Abbr) O c0 c0 (drop_refl c0) t)) b H4) u H3)))) H2))
+H1))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (e: C).(\lambda (u:
+T).(\lambda (H0: (getl O (CHead c0 (Flat f) t) (CHead e (Bind Abbr) u))).(let
+H_x \def (subst1_ex u t O) in (let H1 \def H_x in (ex_ind T (\lambda (t2:
+T).(subst1 O u t (lift (S O) O t2))) (ex2_2 C C (\lambda (a0: C).(\lambda (_:
+C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a:
+C).(drop (S O) O a0 a)))) (\lambda (x: T).(\lambda (H2: (subst1 O u t (lift
+(S O) O x))).(let H3 \def (H e u (getl_intro O c0 (CHead e (Bind Abbr) u) c0
+(drop_refl c0) (clear_gen_flat f c0 (CHead e (Bind Abbr) u) t (getl_gen_O
+(CHead c0 (Flat f) t) (CHead e (Bind Abbr) u) H0)))) in (ex2_2_ind C C
+(\lambda (a0: C).(\lambda (_: C).(csubst1 O u c0 a0))) (\lambda (a0:
+C).(\lambda (a: C).(drop (S O) O a0 a))) (ex2_2 C C (\lambda (a0: C).(\lambda
+(_: C).(csubst1 O u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a:
+C).(drop (S O) O a0 a)))) (\lambda (x0: C).(\lambda (x1: C).(\lambda (H4:
+(csubst1 O u c0 x0)).(\lambda (H5: (drop (S O) O x0 x1)).(ex2_2_intro C C
+(\lambda (a0: C).(\lambda (_: C).(csubst1 O u (CHead c0 (Flat f) t) a0)))
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) O a0 a))) (CHead x0 (Flat f)
+(lift (S O) O x)) x1 (csubst1_flat f O u t (lift (S O) O x) H2 c0 x0 H4)
+(drop_drop (Flat f) O x0 x1 H5 (lift (S O) O x))))))) H3)))) H1)))))))) k))))
+c)) (\lambda (n: nat).(\lambda (H: ((\forall (c: C).(\forall (e: C).(\forall
+(u: T).((getl n c (CHead e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0:
+C).(\lambda (_: C).(csubst1 n u c a0))) (\lambda (a0: C).(\lambda (a:
+C).(drop (S O) n a0 a)))))))))).(\lambda (c: C).(C_ind (\lambda (c0:
+C).(\forall (e: C).(\forall (u: T).((getl (S n) c0 (CHead e (Bind Abbr) u))
+\to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u c0 a0)))
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))))))) (\lambda (n0:
+nat).(\lambda (e: C).(\lambda (u: T).(\lambda (H0: (getl (S n) (CSort n0)
+(CHead e (Bind Abbr) u))).(getl_gen_sort n0 (S n) (CHead e (Bind Abbr) u) H0
+(ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CSort n0) a0)))
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))))))))) (\lambda
+(c0: C).(\lambda (H0: ((\forall (e: C).(\forall (u: T).((getl (S n) c0 (CHead
+e (Bind Abbr) u)) \to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S
+n) u c0 a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0
+a))))))))).(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t: T).(\forall
+(e: C).(\forall (u: T).((getl (S n) (CHead c0 k0 t) (CHead e (Bind Abbr) u))
+\to (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 k0
+t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))))))))
+(\lambda (b: B).(\lambda (t: T).(\lambda (e: C).(\lambda (u: T).(\lambda (H1:
+(getl (S n) (CHead c0 (Bind b) t) (CHead e (Bind Abbr) u))).(let H_x \def
+(subst1_ex u t n) in (let H2 \def H_x in (ex_ind T (\lambda (t2: T).(subst1 n
+u t (lift (S O) n t2))) (ex2_2 C C (\lambda (a0: C).(\lambda (_: C).(csubst1
+(S n) u (CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S
+O) (S n) a0 a)))) (\lambda (x: T).(\lambda (H3: (subst1 n u t (lift (S O) n
+x))).(let H4 \def (H c0 e u (getl_gen_S (Bind b) c0 (CHead e (Bind Abbr) u) t
+n H1)) in (ex2_2_ind C C (\lambda (a0: C).(\lambda (_: C).(csubst1 n u c0
+a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) n a0 a))) (ex2_2 C C
(\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Bind b) t) a0)))
-(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x:
-T).(\lambda (H3: (subst1 n u t (lift (S O) n x))).(let H4 \def (H c0 e u
-(getl_gen_S (Bind b) c0 (CHead e (Bind Abbr) u) t n H1)) in (ex2_2_ind C C
-(\lambda (a0: C).(\lambda (_: C).(csubst1 n u c0 a0))) (\lambda (a0:
-C).(\lambda (a: C).(drop (S O) n a0 a))) (ex2_2 C C (\lambda (a0: C).(\lambda
-(_: C).(csubst1 (S n) u (CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda
-(a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0: C).(\lambda (x1: C).(\lambda
-(H5: (csubst1 n u c0 x0)).(\lambda (H6: (drop (S O) n x0 x1)).(ex2_2_intro C
-C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Bind b) t)
-a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))) (CHead x0
-(Bind b) (lift (S O) n x)) (CHead x1 (Bind b) x) (csubst1_bind b n u t (lift
-(S O) n x) H3 c0 x0 H5) (drop_skip_bind (S O) n x0 x1 H6 b x)))))) H4))))
-H2)))))))) (\lambda (f: F).(\lambda (t: T).(\lambda (e: C).(\lambda (u:
-T).(\lambda (H1: (getl (S n) (CHead c0 (Flat f) t) (CHead e (Bind Abbr)
-u))).(let H_x \def (subst1_ex u t (S n)) in (let H2 \def H_x in (ex_ind T
-(\lambda (t2: T).(subst1 (S n) u t (lift (S O) (S n) t2))) (ex2_2 C C
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0:
+C).(\lambda (x1: C).(\lambda (H5: (csubst1 n u c0 x0)).(\lambda (H6: (drop (S
+O) n x0 x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n)
+u (CHead c0 (Bind b) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S
+n) a0 a))) (CHead x0 (Bind b) (lift (S O) n x)) (CHead x1 (Bind b) x)
+(csubst1_bind b n u t (lift (S O) n x) H3 c0 x0 H5) (drop_skip_bind (S O) n
+x0 x1 H6 b x)))))) H4)))) H2)))))))) (\lambda (f: F).(\lambda (t: T).(\lambda
+(e: C).(\lambda (u: T).(\lambda (H1: (getl (S n) (CHead c0 (Flat f) t) (CHead
+e (Bind Abbr) u))).(let H_x \def (subst1_ex u t (S n)) in (let H2 \def H_x in
+(ex_ind T (\lambda (t2: T).(subst1 (S n) u t (lift (S O) (S n) t2))) (ex2_2 C
+C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Flat f) t)
+a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda
+(x: T).(\lambda (H3: (subst1 (S n) u t (lift (S O) (S n) x))).(let H4 \def
+(H0 e u (getl_gen_S (Flat f) c0 (CHead e (Bind Abbr) u) t n H1)) in
+(ex2_2_ind C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u c0 a0)))
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a))) (ex2_2 C C
(\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Flat f) t) a0)))
-(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x:
-T).(\lambda (H3: (subst1 (S n) u t (lift (S O) (S n) x))).(let H4 \def (H0 e
-u (getl_gen_S (Flat f) c0 (CHead e (Bind Abbr) u) t n H1)) in (ex2_2_ind C C
-(\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u c0 a0))) (\lambda (a0:
-C).(\lambda (a: C).(drop (S O) (S n) a0 a))) (ex2_2 C C (\lambda (a0:
-C).(\lambda (_: C).(csubst1 (S n) u (CHead c0 (Flat f) t) a0))) (\lambda (a0:
-C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0: C).(\lambda (x1:
-C).(\lambda (H5: (csubst1 (S n) u c0 x0)).(\lambda (H6: (drop (S O) (S n) x0
-x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_: C).(csubst1 (S n) u
-(CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a: C).(drop (S O) (S
-n) a0 a))) (CHead x0 (Flat f) (lift (S O) (S n) x)) (CHead x1 (Flat f) x)
-(csubst1_flat f (S n) u t (lift (S O) (S n) x) H3 c0 x0 H5) (drop_skip_flat
-(S O) n x0 x1 H6 f x)))))) H4)))) H2)))))))) k)))) c)))) d).
-(* COMMENTS
-Initial nodes: 2467
-END *)
+(\lambda (a0: C).(\lambda (a: C).(drop (S O) (S n) a0 a)))) (\lambda (x0:
+C).(\lambda (x1: C).(\lambda (H5: (csubst1 (S n) u c0 x0)).(\lambda (H6:
+(drop (S O) (S n) x0 x1)).(ex2_2_intro C C (\lambda (a0: C).(\lambda (_:
+C).(csubst1 (S n) u (CHead c0 (Flat f) t) a0))) (\lambda (a0: C).(\lambda (a:
+C).(drop (S O) (S n) a0 a))) (CHead x0 (Flat f) (lift (S O) (S n) x)) (CHead
+x1 (Flat f) x) (csubst1_flat f (S n) u t (lift (S O) (S n) x) H3 c0 x0 H5)
+(drop_skip_flat (S O) n x0 x1 H6 f x)))))) H4)))) H2)))))))) k)))) c)))) d).
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