(* This file was automatically generated: do not edit *********************)
-include "Basic-1/drop/defs.ma".
+include "basic_1/drop/defs.ma".
+
+include "basic_1/lift/fwd.ma".
+
+include "basic_1/r/props.ma".
+
+include "basic_1/C/fwd.ma".
+
+let rec drop_ind (P: (nat \to (nat \to (C \to (C \to Prop))))) (f: (\forall
+(c: C).(P O O c c))) (f0: (\forall (k: K).(\forall (h: nat).(\forall (c:
+C).(\forall (e: C).((drop (r k h) O c e) \to ((P (r k h) O c e) \to (\forall
+(u: T).(P (S h) O (CHead c k u) e))))))))) (f1: (\forall (k: K).(\forall (h:
+nat).(\forall (d: nat).(\forall (c: C).(\forall (e: C).((drop h (r k d) c e)
+\to ((P h (r k d) c e) \to (\forall (u: T).(P h (S d) (CHead c k (lift h (r k
+d) u)) (CHead e k u))))))))))) (n: nat) (n0: nat) (c: C) (c0: C) (d: drop n
+n0 c c0) on d: P n n0 c c0 \def match d with [(drop_refl c1) \Rightarrow (f
+c1) | (drop_drop k h c1 e d0 u) \Rightarrow (let TMP_3 \def (r k h) in (let
+TMP_4 \def ((drop_ind P f f0 f1) TMP_3 O c1 e d0) in (f0 k h c1 e d0 TMP_4
+u))) | (drop_skip k h d0 c1 e d1 u) \Rightarrow (let TMP_1 \def (r k d0) in
+(let TMP_2 \def ((drop_ind P f f0 f1) h TMP_1 c1 e d1) in (f1 k h d0 c1 e d1
+TMP_2 u)))].
theorem drop_gen_sort:
\forall (n: nat).(\forall (h: nat).(\forall (d: nat).(\forall (x: C).((drop
h d (CSort n) x) \to (and3 (eq C x (CSort n)) (eq nat h O) (eq nat d O))))))
\def
\lambda (n: nat).(\lambda (h: nat).(\lambda (d: nat).(\lambda (x:
-C).(\lambda (H: (drop h d (CSort n) x)).(insert_eq C (CSort n) (\lambda (c:
-C).(drop h d c x)) (\lambda (c: C).(and3 (eq C x c) (eq nat h O) (eq nat d
-O))) (\lambda (y: C).(\lambda (H0: (drop h d y x)).(drop_ind (\lambda (n0:
+C).(\lambda (H: (drop h d (CSort n) x)).(let TMP_1 \def (CSort n) in (let
+TMP_2 \def (\lambda (c: C).(drop h d c x)) in (let TMP_6 \def (\lambda (c:
+C).(let TMP_3 \def (eq C x c) in (let TMP_4 \def (eq nat h O) in (let TMP_5
+\def (eq nat d O) in (and3 TMP_3 TMP_4 TMP_5))))) in (let TMP_54 \def
+(\lambda (y: C).(\lambda (H0: (drop h d y x)).(let TMP_10 \def (\lambda (n0:
nat).(\lambda (n1: nat).(\lambda (c: C).(\lambda (c0: C).((eq C c (CSort n))
-\to (and3 (eq C c0 c) (eq nat n0 O) (eq nat n1 O))))))) (\lambda (c:
-C).(\lambda (H1: (eq C c (CSort n))).(let H2 \def (f_equal C C (\lambda (e:
-C).e) c (CSort n) H1) in (eq_ind_r C (CSort n) (\lambda (c0: C).(and3 (eq C
-c0 c0) (eq nat O O) (eq nat O O))) (and3_intro (eq C (CSort n) (CSort n)) (eq
-nat O O) (eq nat O O) (refl_equal C (CSort n)) (refl_equal nat O) (refl_equal
-nat O)) c H2)))) (\lambda (k: K).(\lambda (h0: nat).(\lambda (c: C).(\lambda
-(e: C).(\lambda (_: (drop (r k h0) O c e)).(\lambda (_: (((eq C c (CSort n))
-\to (and3 (eq C e c) (eq nat (r k h0) O) (eq nat O O))))).(\lambda (u:
-T).(\lambda (H3: (eq C (CHead c k u) (CSort n))).(let H4 \def (eq_ind C
-(CHead c k u) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop)
-with [(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow True])) I
-(CSort n) H3) in (False_ind (and3 (eq C e (CHead c k u)) (eq nat (S h0) O)
-(eq nat O O)) H4)))))))))) (\lambda (k: K).(\lambda (h0: nat).(\lambda (d0:
-nat).(\lambda (c: C).(\lambda (e: C).(\lambda (_: (drop h0 (r k d0) c
-e)).(\lambda (_: (((eq C c (CSort n)) \to (and3 (eq C e c) (eq nat h0 O) (eq
-nat (r k d0) O))))).(\lambda (u: T).(\lambda (H3: (eq C (CHead c k (lift h0
-(r k d0) u)) (CSort n))).(let H4 \def (eq_ind C (CHead c k (lift h0 (r k d0)
-u)) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with [(CSort
-_) \Rightarrow False | (CHead _ _ _) \Rightarrow True])) I (CSort n) H3) in
-(False_ind (and3 (eq C (CHead e k u) (CHead c k (lift h0 (r k d0) u))) (eq
-nat h0 O) (eq nat (S d0) O)) H4))))))))))) h d y x H0))) H))))).
-(* COMMENTS
-Initial nodes: 595
-END *)
+\to (let TMP_7 \def (eq C c0 c) in (let TMP_8 \def (eq nat n0 O) in (let
+TMP_9 \def (eq nat n1 O) in (and3 TMP_7 TMP_8 TMP_9))))))))) in (let TMP_28
+\def (\lambda (c: C).(\lambda (H1: (eq C c (CSort n))).(let TMP_11 \def
+(\lambda (e: C).e) in (let TMP_12 \def (CSort n) in (let H2 \def (f_equal C C
+TMP_11 c TMP_12 H1) in (let TMP_13 \def (CSort n) in (let TMP_17 \def
+(\lambda (c0: C).(let TMP_14 \def (eq C c0 c0) in (let TMP_15 \def (eq nat O
+O) in (let TMP_16 \def (eq nat O O) in (and3 TMP_14 TMP_15 TMP_16))))) in
+(let TMP_18 \def (CSort n) in (let TMP_19 \def (CSort n) in (let TMP_20 \def
+(eq C TMP_18 TMP_19) in (let TMP_21 \def (eq nat O O) in (let TMP_22 \def (eq
+nat O O) in (let TMP_23 \def (CSort n) in (let TMP_24 \def (refl_equal C
+TMP_23) in (let TMP_25 \def (refl_equal nat O) in (let TMP_26 \def
+(refl_equal nat O) in (let TMP_27 \def (and3_intro TMP_20 TMP_21 TMP_22
+TMP_24 TMP_25 TMP_26) in (eq_ind_r C TMP_13 TMP_17 TMP_27 c
+H2)))))))))))))))))) in (let TMP_38 \def (\lambda (k: K).(\lambda (h0:
+nat).(\lambda (c: C).(\lambda (e: C).(\lambda (_: (drop (r k h0) O c
+e)).(\lambda (_: (((eq C c (CSort n)) \to (and3 (eq C e c) (eq nat (r k h0)
+O) (eq nat O O))))).(\lambda (u: T).(\lambda (H3: (eq C (CHead c k u) (CSort
+n))).(let TMP_29 \def (CHead c k u) in (let TMP_30 \def (\lambda (ee:
+C).(match ee with [(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow
+True])) in (let TMP_31 \def (CSort n) in (let H4 \def (eq_ind C TMP_29 TMP_30
+I TMP_31 H3) in (let TMP_32 \def (CHead c k u) in (let TMP_33 \def (eq C e
+TMP_32) in (let TMP_34 \def (S h0) in (let TMP_35 \def (eq nat TMP_34 O) in
+(let TMP_36 \def (eq nat O O) in (let TMP_37 \def (and3 TMP_33 TMP_35 TMP_36)
+in (False_ind TMP_37 H4))))))))))))))))))) in (let TMP_53 \def (\lambda (k:
+K).(\lambda (h0: nat).(\lambda (d0: nat).(\lambda (c: C).(\lambda (e:
+C).(\lambda (_: (drop h0 (r k d0) c e)).(\lambda (_: (((eq C c (CSort n)) \to
+(and3 (eq C e c) (eq nat h0 O) (eq nat (r k d0) O))))).(\lambda (u:
+T).(\lambda (H3: (eq C (CHead c k (lift h0 (r k d0) u)) (CSort n))).(let
+TMP_39 \def (r k d0) in (let TMP_40 \def (lift h0 TMP_39 u) in (let TMP_41
+\def (CHead c k TMP_40) in (let TMP_42 \def (\lambda (ee: C).(match ee with
+[(CSort _) \Rightarrow False | (CHead _ _ _) \Rightarrow True])) in (let
+TMP_43 \def (CSort n) in (let H4 \def (eq_ind C TMP_41 TMP_42 I TMP_43 H3) in
+(let TMP_44 \def (CHead e k u) in (let TMP_45 \def (r k d0) in (let TMP_46
+\def (lift h0 TMP_45 u) in (let TMP_47 \def (CHead c k TMP_46) in (let TMP_48
+\def (eq C TMP_44 TMP_47) in (let TMP_49 \def (eq nat h0 O) in (let TMP_50
+\def (S d0) in (let TMP_51 \def (eq nat TMP_50 O) in (let TMP_52 \def (and3
+TMP_48 TMP_49 TMP_51) in (False_ind TMP_52 H4))))))))))))))))))))))))) in
+(drop_ind TMP_10 TMP_28 TMP_38 TMP_53 h d y x H0))))))) in (insert_eq C TMP_1
+TMP_2 TMP_6 TMP_54 H))))))))).
theorem drop_gen_refl:
\forall (x: C).(\forall (e: C).((drop O O x e) \to (eq C x e)))
\def
- \lambda (x: C).(\lambda (e: C).(\lambda (H: (drop O O x e)).(insert_eq nat O
-(\lambda (n: nat).(drop n O x e)) (\lambda (_: nat).(eq C x e)) (\lambda (y:
-nat).(\lambda (H0: (drop y O x e)).(insert_eq nat O (\lambda (n: nat).(drop y
-n x e)) (\lambda (n: nat).((eq nat y n) \to (eq C x e))) (\lambda (y0:
-nat).(\lambda (H1: (drop y y0 x e)).(drop_ind (\lambda (n: nat).(\lambda (n0:
-nat).(\lambda (c: C).(\lambda (c0: C).((eq nat n0 O) \to ((eq nat n n0) \to
-(eq C c c0))))))) (\lambda (c: C).(\lambda (_: (eq nat O O)).(\lambda (_: (eq
-nat O O)).(refl_equal C c)))) (\lambda (k: K).(\lambda (h: nat).(\lambda (c:
+ \lambda (x: C).(\lambda (e: C).(\lambda (H: (drop O O x e)).(let TMP_1 \def
+(\lambda (n: nat).(drop n O x e)) in (let TMP_2 \def (\lambda (_: nat).(eq C
+x e)) in (let TMP_36 \def (\lambda (y: nat).(\lambda (H0: (drop y O x
+e)).(let TMP_3 \def (\lambda (n: nat).(drop y n x e)) in (let TMP_4 \def
+(\lambda (n: nat).((eq nat y n) \to (eq C x e))) in (let TMP_35 \def (\lambda
+(y0: nat).(\lambda (H1: (drop y y0 x e)).(let TMP_5 \def (\lambda (n:
+nat).(\lambda (n0: nat).(\lambda (c: C).(\lambda (c0: C).((eq nat n0 O) \to
+((eq nat n n0) \to (eq C c c0))))))) in (let TMP_6 \def (\lambda (c:
+C).(\lambda (_: (eq nat O O)).(\lambda (_: (eq nat O O)).(refl_equal C c))))
+in (let TMP_11 \def (\lambda (k: K).(\lambda (h: nat).(\lambda (c:
C).(\lambda (e0: C).(\lambda (_: (drop (r k h) O c e0)).(\lambda (_: (((eq
nat O O) \to ((eq nat (r k h) O) \to (eq C c e0))))).(\lambda (u: T).(\lambda
-(_: (eq nat O O)).(\lambda (H5: (eq nat (S h) O)).(let H6 \def (eq_ind nat (S
-h) (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H5) in (False_ind (eq C
-(CHead c k u) e0) H6))))))))))) (\lambda (k: K).(\lambda (h: nat).(\lambda
-(d: nat).(\lambda (c: C).(\lambda (e0: C).(\lambda (H2: (drop h (r k d) c
-e0)).(\lambda (H3: (((eq nat (r k d) O) \to ((eq nat h (r k d)) \to (eq C c
-e0))))).(\lambda (u: T).(\lambda (H4: (eq nat (S d) O)).(\lambda (H5: (eq nat
-h (S d))).(let H6 \def (f_equal nat nat (\lambda (e1: nat).e1) h (S d) H5) in
-(let H7 \def (eq_ind nat h (\lambda (n: nat).((eq nat (r k d) O) \to ((eq nat
-n (r k d)) \to (eq C c e0)))) H3 (S d) H6) in (let H8 \def (eq_ind nat h
-(\lambda (n: nat).(drop n (r k d) c e0)) H2 (S d) H6) in (eq_ind_r nat (S d)
-(\lambda (n: nat).(eq C (CHead c k (lift n (r k d) u)) (CHead e0 k u))) (let
-H9 \def (eq_ind nat (S d) (\lambda (ee: nat).(match ee in nat return (\lambda
-(_: nat).Prop) with [O \Rightarrow False | (S _) \Rightarrow True])) I O H4)
-in (False_ind (eq C (CHead c k (lift (S d) (r k d) u)) (CHead e0 k u)) H9)) h
-H6)))))))))))))) y y0 x e H1))) H0))) H))).
-(* COMMENTS
-Initial nodes: 561
-END *)
+(_: (eq nat O O)).(\lambda (H5: (eq nat (S h) O)).(let TMP_7 \def (S h) in
+(let TMP_8 \def (\lambda (ee: nat).(match ee with [O \Rightarrow False | (S
+_) \Rightarrow True])) in (let H6 \def (eq_ind nat TMP_7 TMP_8 I O H5) in
+(let TMP_9 \def (CHead c k u) in (let TMP_10 \def (eq C TMP_9 e0) in
+(False_ind TMP_10 H6))))))))))))))) in (let TMP_34 \def (\lambda (k:
+K).(\lambda (h: nat).(\lambda (d: nat).(\lambda (c: C).(\lambda (e0:
+C).(\lambda (H2: (drop h (r k d) c e0)).(\lambda (H3: (((eq nat (r k d) O)
+\to ((eq nat h (r k d)) \to (eq C c e0))))).(\lambda (u: T).(\lambda (H4: (eq
+nat (S d) O)).(\lambda (H5: (eq nat h (S d))).(let TMP_12 \def (\lambda (e1:
+nat).e1) in (let TMP_13 \def (S d) in (let H6 \def (f_equal nat nat TMP_12 h
+TMP_13 H5) in (let TMP_14 \def (\lambda (n: nat).((eq nat (r k d) O) \to ((eq
+nat n (r k d)) \to (eq C c e0)))) in (let TMP_15 \def (S d) in (let H7 \def
+(eq_ind nat h TMP_14 H3 TMP_15 H6) in (let TMP_17 \def (\lambda (n: nat).(let
+TMP_16 \def (r k d) in (drop n TMP_16 c e0))) in (let TMP_18 \def (S d) in
+(let H8 \def (eq_ind nat h TMP_17 H2 TMP_18 H6) in (let TMP_19 \def (S d) in
+(let TMP_24 \def (\lambda (n: nat).(let TMP_20 \def (r k d) in (let TMP_21
+\def (lift n TMP_20 u) in (let TMP_22 \def (CHead c k TMP_21) in (let TMP_23
+\def (CHead e0 k u) in (eq C TMP_22 TMP_23)))))) in (let TMP_25 \def (S d) in
+(let TMP_26 \def (\lambda (ee: nat).(match ee with [O \Rightarrow False | (S
+_) \Rightarrow True])) in (let H9 \def (eq_ind nat TMP_25 TMP_26 I O H4) in
+(let TMP_27 \def (S d) in (let TMP_28 \def (r k d) in (let TMP_29 \def (lift
+TMP_27 TMP_28 u) in (let TMP_30 \def (CHead c k TMP_29) in (let TMP_31 \def
+(CHead e0 k u) in (let TMP_32 \def (eq C TMP_30 TMP_31) in (let TMP_33 \def
+(False_ind TMP_32 H9) in (eq_ind_r nat TMP_19 TMP_24 TMP_33 h
+H6)))))))))))))))))))))))))))))))) in (drop_ind TMP_5 TMP_6 TMP_11 TMP_34 y
+y0 x e H1))))))) in (insert_eq nat O TMP_3 TMP_4 TMP_35 H0)))))) in
+(insert_eq nat O TMP_1 TMP_2 TMP_36 H)))))).
theorem drop_gen_drop:
\forall (k: K).(\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h:
nat).((drop (S h) O (CHead c k u) x) \to (drop (r k h) O c x))))))
\def
\lambda (k: K).(\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h:
-nat).(\lambda (H: (drop (S h) O (CHead c k u) x)).(insert_eq C (CHead c k u)
-(\lambda (c0: C).(drop (S h) O c0 x)) (\lambda (_: C).(drop (r k h) O c x))
-(\lambda (y: C).(\lambda (H0: (drop (S h) O y x)).(insert_eq nat O (\lambda
-(n: nat).(drop (S h) n y x)) (\lambda (n: nat).((eq C y (CHead c k u)) \to
-(drop (r k h) n c x))) (\lambda (y0: nat).(\lambda (H1: (drop (S h) y0 y
-x)).(insert_eq nat (S h) (\lambda (n: nat).(drop n y0 y x)) (\lambda (_:
-nat).((eq nat y0 O) \to ((eq C y (CHead c k u)) \to (drop (r k h) y0 c x))))
-(\lambda (y1: nat).(\lambda (H2: (drop y1 y0 y x)).(drop_ind (\lambda (n:
+nat).(\lambda (H: (drop (S h) O (CHead c k u) x)).(let TMP_1 \def (CHead c k
+u) in (let TMP_3 \def (\lambda (c0: C).(let TMP_2 \def (S h) in (drop TMP_2 O
+c0 x))) in (let TMP_5 \def (\lambda (_: C).(let TMP_4 \def (r k h) in (drop
+TMP_4 O c x))) in (let TMP_130 \def (\lambda (y: C).(\lambda (H0: (drop (S h)
+O y x)).(let TMP_7 \def (\lambda (n: nat).(let TMP_6 \def (S h) in (drop
+TMP_6 n y x))) in (let TMP_9 \def (\lambda (n: nat).((eq C y (CHead c k u))
+\to (let TMP_8 \def (r k h) in (drop TMP_8 n c x)))) in (let TMP_129 \def
+(\lambda (y0: nat).(\lambda (H1: (drop (S h) y0 y x)).(let TMP_10 \def (S h)
+in (let TMP_11 \def (\lambda (n: nat).(drop n y0 y x)) in (let TMP_13 \def
+(\lambda (_: nat).((eq nat y0 O) \to ((eq C y (CHead c k u)) \to (let TMP_12
+\def (r k h) in (drop TMP_12 y0 c x))))) in (let TMP_128 \def (\lambda (y1:
+nat).(\lambda (H2: (drop y1 y0 y x)).(let TMP_15 \def (\lambda (n:
nat).(\lambda (n0: nat).(\lambda (c0: C).(\lambda (c1: C).((eq nat n (S h))
-\to ((eq nat n0 O) \to ((eq C c0 (CHead c k u)) \to (drop (r k h) n0 c
-c1)))))))) (\lambda (c0: C).(\lambda (H3: (eq nat O (S h))).(\lambda (_: (eq
-nat O O)).(\lambda (H5: (eq C c0 (CHead c k u))).(eq_ind_r C (CHead c k u)
-(\lambda (c1: C).(drop (r k h) O c c1)) (let H6 \def (eq_ind nat O (\lambda
-(ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O \Rightarrow
-True | (S _) \Rightarrow False])) I (S h) H3) in (False_ind (drop (r k h) O c
-(CHead c k u)) H6)) c0 H5))))) (\lambda (k0: K).(\lambda (h0: nat).(\lambda
-(c0: C).(\lambda (e: C).(\lambda (H3: (drop (r k0 h0) O c0 e)).(\lambda (H4:
-(((eq nat (r k0 h0) (S h)) \to ((eq nat O O) \to ((eq C c0 (CHead c k u)) \to
-(drop (r k h) O c e)))))).(\lambda (u0: T).(\lambda (H5: (eq nat (S h0) (S
+\to ((eq nat n0 O) \to ((eq C c0 (CHead c k u)) \to (let TMP_14 \def (r k h)
+in (drop TMP_14 n0 c c1))))))))) in (let TMP_25 \def (\lambda (c0:
+C).(\lambda (H3: (eq nat O (S h))).(\lambda (_: (eq nat O O)).(\lambda (H5:
+(eq C c0 (CHead c k u))).(let TMP_16 \def (CHead c k u) in (let TMP_18 \def
+(\lambda (c1: C).(let TMP_17 \def (r k h) in (drop TMP_17 O c c1))) in (let
+TMP_19 \def (\lambda (ee: nat).(match ee with [O \Rightarrow True | (S _)
+\Rightarrow False])) in (let TMP_20 \def (S h) in (let H6 \def (eq_ind nat O
+TMP_19 I TMP_20 H3) in (let TMP_21 \def (r k h) in (let TMP_22 \def (CHead c
+k u) in (let TMP_23 \def (drop TMP_21 O c TMP_22) in (let TMP_24 \def
+(False_ind TMP_23 H6) in (eq_ind_r C TMP_16 TMP_18 TMP_24 c0 H5))))))))))))))
+in (let TMP_52 \def (\lambda (k0: K).(\lambda (h0: nat).(\lambda (c0:
+C).(\lambda (e: C).(\lambda (H3: (drop (r k0 h0) O c0 e)).(\lambda (H4: (((eq
+nat (r k0 h0) (S h)) \to ((eq nat O O) \to ((eq C c0 (CHead c k u)) \to (drop
+(r k h) O c e)))))).(\lambda (u0: T).(\lambda (H5: (eq nat (S h0) (S
h))).(\lambda (_: (eq nat O O)).(\lambda (H7: (eq C (CHead c0 k0 u0) (CHead c
-k u))).(let H8 \def (f_equal C C (\lambda (e0: C).(match e0 in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow c0 | (CHead c1 _ _)
-\Rightarrow c1])) (CHead c0 k0 u0) (CHead c k u) H7) in ((let H9 \def
-(f_equal C K (\lambda (e0: C).(match e0 in C return (\lambda (_: C).K) with
-[(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) (CHead c0 k0 u0)
-(CHead c k u) H7) in ((let H10 \def (f_equal C T (\lambda (e0: C).(match e0
-in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t)
-\Rightarrow t])) (CHead c0 k0 u0) (CHead c k u) H7) in (\lambda (H11: (eq K
-k0 k)).(\lambda (H12: (eq C c0 c)).(let H13 \def (eq_ind C c0 (\lambda (c1:
-C).((eq nat (r k0 h0) (S h)) \to ((eq nat O O) \to ((eq C c1 (CHead c k u))
-\to (drop (r k h) O c e))))) H4 c H12) in (let H14 \def (eq_ind C c0 (\lambda
-(c1: C).(drop (r k0 h0) O c1 e)) H3 c H12) in (let H15 \def (eq_ind K k0
-(\lambda (k1: K).((eq nat (r k1 h0) (S h)) \to ((eq nat O O) \to ((eq C c
-(CHead c k u)) \to (drop (r k h) O c e))))) H13 k H11) in (let H16 \def
-(eq_ind K k0 (\lambda (k1: K).(drop (r k1 h0) O c e)) H14 k H11) in (let H17
-\def (f_equal nat nat (\lambda (e0: nat).(match e0 in nat return (\lambda (_:
-nat).nat) with [O \Rightarrow h0 | (S n) \Rightarrow n])) (S h0) (S h) H5) in
-(let H18 \def (eq_ind nat h0 (\lambda (n: nat).((eq nat (r k n) (S h)) \to
-((eq nat O O) \to ((eq C c (CHead c k u)) \to (drop (r k h) O c e))))) H15 h
-H17) in (let H19 \def (eq_ind nat h0 (\lambda (n: nat).(drop (r k n) O c e))
-H16 h H17) in H19)))))))))) H9)) H8)))))))))))) (\lambda (k0: K).(\lambda
-(h0: nat).(\lambda (d: nat).(\lambda (c0: C).(\lambda (e: C).(\lambda (H3:
-(drop h0 (r k0 d) c0 e)).(\lambda (H4: (((eq nat h0 (S h)) \to ((eq nat (r k0
-d) O) \to ((eq C c0 (CHead c k u)) \to (drop (r k h) (r k0 d) c
-e)))))).(\lambda (u0: T).(\lambda (H5: (eq nat h0 (S h))).(\lambda (H6: (eq
-nat (S d) O)).(\lambda (H7: (eq C (CHead c0 k0 (lift h0 (r k0 d) u0)) (CHead
-c k u))).(let H8 \def (eq_ind nat h0 (\lambda (n: nat).(eq C (CHead c0 k0
-(lift n (r k0 d) u0)) (CHead c k u))) H7 (S h) H5) in (let H9 \def (eq_ind
-nat h0 (\lambda (n: nat).((eq nat n (S h)) \to ((eq nat (r k0 d) O) \to ((eq
-C c0 (CHead c k u)) \to (drop (r k h) (r k0 d) c e))))) H4 (S h) H5) in (let
-H10 \def (eq_ind nat h0 (\lambda (n: nat).(drop n (r k0 d) c0 e)) H3 (S h)
-H5) in (let H11 \def (f_equal C C (\lambda (e0: C).(match e0 in C return
-(\lambda (_: C).C) with [(CSort _) \Rightarrow c0 | (CHead c1 _ _)
-\Rightarrow c1])) (CHead c0 k0 (lift (S h) (r k0 d) u0)) (CHead c k u) H8) in
-((let H12 \def (f_equal C K (\lambda (e0: C).(match e0 in C return (\lambda
-(_: C).K) with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1]))
-(CHead c0 k0 (lift (S h) (r k0 d) u0)) (CHead c k u) H8) in ((let H13 \def
-(f_equal C T (\lambda (e0: C).(match e0 in C return (\lambda (_: C).T) with
-[(CSort _) \Rightarrow ((let rec lref_map (f: ((nat \to nat))) (d0: nat) (t:
-T) on t: T \def (match t with [(TSort n) \Rightarrow (TSort n) | (TLRef i)
-\Rightarrow (TLRef (match (blt i d0) with [true \Rightarrow i | false
-\Rightarrow (f i)])) | (THead k1 u1 t0) \Rightarrow (THead k1 (lref_map f d0
-u1) (lref_map f (s k1 d0) t0))]) in lref_map) (\lambda (x0: nat).(plus x0 (S
-h))) (r k0 d) u0) | (CHead _ _ t) \Rightarrow t])) (CHead c0 k0 (lift (S h)
-(r k0 d) u0)) (CHead c k u) H8) in (\lambda (H14: (eq K k0 k)).(\lambda (H15:
-(eq C c0 c)).(let H16 \def (eq_ind C c0 (\lambda (c1: C).((eq nat (S h) (S
-h)) \to ((eq nat (r k0 d) O) \to ((eq C c1 (CHead c k u)) \to (drop (r k h)
-(r k0 d) c e))))) H9 c H15) in (let H17 \def (eq_ind C c0 (\lambda (c1:
-C).(drop (S h) (r k0 d) c1 e)) H10 c H15) in (let H18 \def (eq_ind K k0
-(\lambda (k1: K).(eq T (lift (S h) (r k1 d) u0) u)) H13 k H14) in (let H19
-\def (eq_ind K k0 (\lambda (k1: K).((eq nat (S h) (S h)) \to ((eq nat (r k1
-d) O) \to ((eq C c (CHead c k u)) \to (drop (r k h) (r k1 d) c e))))) H16 k
-H14) in (let H20 \def (eq_ind K k0 (\lambda (k1: K).(drop (S h) (r k1 d) c
-e)) H17 k H14) in (eq_ind_r K k (\lambda (k1: K).(drop (r k h) (S d) c (CHead
-e k1 u0))) (let H21 \def (eq_ind_r T u (\lambda (t: T).((eq nat (S h) (S h))
-\to ((eq nat (r k d) O) \to ((eq C c (CHead c k t)) \to (drop (r k h) (r k d)
-c e))))) H19 (lift (S h) (r k d) u0) H18) in (let H22 \def (eq_ind nat (S d)
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow False | (S _) \Rightarrow True])) I O H6) in (False_ind (drop (r
-k h) (S d) c (CHead e k u0)) H22))) k0 H14))))))))) H12)) H11))))))))))))))))
-y1 y0 y x H2))) H1))) H0))) H)))))).
-(* COMMENTS
-Initial nodes: 1856
-END *)
+k u))).(let TMP_26 \def (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_27 \def (CHead
+c0 k0 u0) in (let TMP_28 \def (CHead c k u) in (let H8 \def (f_equal C C
+TMP_26 TMP_27 TMP_28 H7) in (let TMP_29 \def (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) in (let TMP_30
+\def (CHead c0 k0 u0) in (let TMP_31 \def (CHead c k u) in (let H9 \def
+(f_equal C K TMP_29 TMP_30 TMP_31 H7) in (let TMP_32 \def (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t]))
+in (let TMP_33 \def (CHead c0 k0 u0) in (let TMP_34 \def (CHead c k u) in
+(let H10 \def (f_equal C T TMP_32 TMP_33 TMP_34 H7) in (let TMP_50 \def
+(\lambda (H11: (eq K k0 k)).(\lambda (H12: (eq C c0 c)).(let TMP_36 \def
+(\lambda (c1: C).((eq nat (r k0 h0) (S h)) \to ((eq nat O O) \to ((eq C c1
+(CHead c k u)) \to (let TMP_35 \def (r k h) in (drop TMP_35 O c e)))))) in
+(let H13 \def (eq_ind C c0 TMP_36 H4 c H12) in (let TMP_38 \def (\lambda (c1:
+C).(let TMP_37 \def (r k0 h0) in (drop TMP_37 O c1 e))) in (let H14 \def
+(eq_ind C c0 TMP_38 H3 c H12) in (let TMP_40 \def (\lambda (k1: K).((eq nat
+(r k1 h0) (S h)) \to ((eq nat O O) \to ((eq C c (CHead c k u)) \to (let
+TMP_39 \def (r k h) in (drop TMP_39 O c e)))))) in (let H15 \def (eq_ind K k0
+TMP_40 H13 k H11) in (let TMP_42 \def (\lambda (k1: K).(let TMP_41 \def (r k1
+h0) in (drop TMP_41 O c e))) in (let H16 \def (eq_ind K k0 TMP_42 H14 k H11)
+in (let TMP_43 \def (\lambda (e0: nat).(match e0 with [O \Rightarrow h0 | (S
+n) \Rightarrow n])) in (let TMP_44 \def (S h0) in (let TMP_45 \def (S h) in
+(let H17 \def (f_equal nat nat TMP_43 TMP_44 TMP_45 H5) in (let TMP_47 \def
+(\lambda (n: nat).((eq nat (r k n) (S h)) \to ((eq nat O O) \to ((eq C c
+(CHead c k u)) \to (let TMP_46 \def (r k h) in (drop TMP_46 O c e)))))) in
+(let H18 \def (eq_ind nat h0 TMP_47 H15 h H17) in (let TMP_49 \def (\lambda
+(n: nat).(let TMP_48 \def (r k n) in (drop TMP_48 O c e))) in (let H19 \def
+(eq_ind nat h0 TMP_49 H16 h H17) in H19)))))))))))))))))) in (let TMP_51 \def
+(TMP_50 H9) in (TMP_51 H8))))))))))))))))))))))))) in (let TMP_127 \def
+(\lambda (k0: K).(\lambda (h0: nat).(\lambda (d: nat).(\lambda (c0:
+C).(\lambda (e: C).(\lambda (H3: (drop h0 (r k0 d) c0 e)).(\lambda (H4: (((eq
+nat h0 (S h)) \to ((eq nat (r k0 d) O) \to ((eq C c0 (CHead c k u)) \to (drop
+(r k h) (r k0 d) c e)))))).(\lambda (u0: T).(\lambda (H5: (eq nat h0 (S
+h))).(\lambda (H6: (eq nat (S d) O)).(\lambda (H7: (eq C (CHead c0 k0 (lift
+h0 (r k0 d) u0)) (CHead c k u))).(let TMP_57 \def (\lambda (n: nat).(let
+TMP_53 \def (r k0 d) in (let TMP_54 \def (lift n TMP_53 u0) in (let TMP_55
+\def (CHead c0 k0 TMP_54) in (let TMP_56 \def (CHead c k u) in (eq C TMP_55
+TMP_56)))))) in (let TMP_58 \def (S h) in (let H8 \def (eq_ind nat h0 TMP_57
+H7 TMP_58 H5) in (let TMP_61 \def (\lambda (n: nat).((eq nat n (S h)) \to
+((eq nat (r k0 d) O) \to ((eq C c0 (CHead c k u)) \to (let TMP_59 \def (r k
+h) in (let TMP_60 \def (r k0 d) in (drop TMP_59 TMP_60 c e))))))) in (let
+TMP_62 \def (S h) in (let H9 \def (eq_ind nat h0 TMP_61 H4 TMP_62 H5) in (let
+TMP_64 \def (\lambda (n: nat).(let TMP_63 \def (r k0 d) in (drop n TMP_63 c0
+e))) in (let TMP_65 \def (S h) in (let H10 \def (eq_ind nat h0 TMP_64 H3
+TMP_65 H5) in (let TMP_66 \def (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_67 \def (S h)
+in (let TMP_68 \def (r k0 d) in (let TMP_69 \def (lift TMP_67 TMP_68 u0) in
+(let TMP_70 \def (CHead c0 k0 TMP_69) in (let TMP_71 \def (CHead c k u) in
+(let H11 \def (f_equal C C TMP_66 TMP_70 TMP_71 H8) in (let TMP_72 \def
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow k0 | (CHead _ k1 _)
+\Rightarrow k1])) in (let TMP_73 \def (S h) in (let TMP_74 \def (r k0 d) in
+(let TMP_75 \def (lift TMP_73 TMP_74 u0) in (let TMP_76 \def (CHead c0 k0
+TMP_75) in (let TMP_77 \def (CHead c k u) in (let H12 \def (f_equal C K
+TMP_72 TMP_76 TMP_77 H8) in (let TMP_86 \def (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow (let TMP_84 \def (\lambda (x0: nat).(let TMP_83 \def
+(S h) in (plus x0 TMP_83))) in (let TMP_85 \def (r k0 d) in (lref_map TMP_84
+TMP_85 u0))) | (CHead _ _ t) \Rightarrow t])) in (let TMP_87 \def (S h) in
+(let TMP_88 \def (r k0 d) in (let TMP_89 \def (lift TMP_87 TMP_88 u0) in (let
+TMP_90 \def (CHead c0 k0 TMP_89) in (let TMP_91 \def (CHead c k u) in (let
+H13 \def (f_equal C T TMP_86 TMP_90 TMP_91 H8) in (let TMP_125 \def (\lambda
+(H14: (eq K k0 k)).(\lambda (H15: (eq C c0 c)).(let TMP_94 \def (\lambda (c1:
+C).((eq nat (S h) (S h)) \to ((eq nat (r k0 d) O) \to ((eq C c1 (CHead c k
+u)) \to (let TMP_92 \def (r k h) in (let TMP_93 \def (r k0 d) in (drop TMP_92
+TMP_93 c e))))))) in (let H16 \def (eq_ind C c0 TMP_94 H9 c H15) in (let
+TMP_97 \def (\lambda (c1: C).(let TMP_95 \def (S h) in (let TMP_96 \def (r k0
+d) in (drop TMP_95 TMP_96 c1 e)))) in (let H17 \def (eq_ind C c0 TMP_97 H10 c
+H15) in (let TMP_101 \def (\lambda (k1: K).(let TMP_98 \def (S h) in (let
+TMP_99 \def (r k1 d) in (let TMP_100 \def (lift TMP_98 TMP_99 u0) in (eq T
+TMP_100 u))))) in (let H18 \def (eq_ind K k0 TMP_101 H13 k H14) in (let
+TMP_104 \def (\lambda (k1: K).((eq nat (S h) (S h)) \to ((eq nat (r k1 d) O)
+\to ((eq C c (CHead c k u)) \to (let TMP_102 \def (r k h) in (let TMP_103
+\def (r k1 d) in (drop TMP_102 TMP_103 c e))))))) in (let H19 \def (eq_ind K
+k0 TMP_104 H16 k H14) in (let TMP_107 \def (\lambda (k1: K).(let TMP_105 \def
+(S h) in (let TMP_106 \def (r k1 d) in (drop TMP_105 TMP_106 c e)))) in (let
+H20 \def (eq_ind K k0 TMP_107 H17 k H14) in (let TMP_111 \def (\lambda (k1:
+K).(let TMP_108 \def (r k h) in (let TMP_109 \def (S d) in (let TMP_110 \def
+(CHead e k1 u0) in (drop TMP_108 TMP_109 c TMP_110))))) in (let TMP_114 \def
+(\lambda (t: T).((eq nat (S h) (S h)) \to ((eq nat (r k d) O) \to ((eq C c
+(CHead c k t)) \to (let TMP_112 \def (r k h) in (let TMP_113 \def (r k d) in
+(drop TMP_112 TMP_113 c e))))))) in (let TMP_115 \def (S h) in (let TMP_116
+\def (r k d) in (let TMP_117 \def (lift TMP_115 TMP_116 u0) in (let H21 \def
+(eq_ind_r T u TMP_114 H19 TMP_117 H18) in (let TMP_118 \def (S d) in (let
+TMP_119 \def (\lambda (ee: nat).(match ee with [O \Rightarrow False | (S _)
+\Rightarrow True])) in (let H22 \def (eq_ind nat TMP_118 TMP_119 I O H6) in
+(let TMP_120 \def (r k h) in (let TMP_121 \def (S d) in (let TMP_122 \def
+(CHead e k u0) in (let TMP_123 \def (drop TMP_120 TMP_121 c TMP_122) in (let
+TMP_124 \def (False_ind TMP_123 H22) in (eq_ind_r K k TMP_111 TMP_124 k0
+H14))))))))))))))))))))))))))) in (let TMP_126 \def (TMP_125 H12) in (TMP_126
+H11)))))))))))))))))))))))))))))))))))))))))))) in (drop_ind TMP_15 TMP_25
+TMP_52 TMP_127 y1 y0 y x H2))))))) in (insert_eq nat TMP_10 TMP_11 TMP_13
+TMP_128 H1))))))) in (insert_eq nat O TMP_7 TMP_9 TMP_129 H0)))))) in
+(insert_eq C TMP_1 TMP_3 TMP_5 TMP_130 H)))))))))).
theorem drop_gen_skip_r:
\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: nat).(\forall
d) e c)))))))))
\def
\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h: nat).(\lambda
-(d: nat).(\lambda (k: K).(\lambda (H: (drop h (S d) x (CHead c k
-u))).(insert_eq C (CHead c k u) (\lambda (c0: C).(drop h (S d) x c0))
-(\lambda (_: C).(ex2 C (\lambda (e: C).(eq C x (CHead e k (lift h (r k d)
-u)))) (\lambda (e: C).(drop h (r k d) e c)))) (\lambda (y: C).(\lambda (H0:
-(drop h (S d) x y)).(insert_eq nat (S d) (\lambda (n: nat).(drop h n x y))
-(\lambda (_: nat).((eq C y (CHead c k u)) \to (ex2 C (\lambda (e: C).(eq C x
-(CHead e k (lift h (r k d) u)))) (\lambda (e: C).(drop h (r k d) e c)))))
-(\lambda (y0: nat).(\lambda (H1: (drop h y0 x y)).(drop_ind (\lambda (n:
-nat).(\lambda (n0: nat).(\lambda (c0: C).(\lambda (c1: C).((eq nat n0 (S d))
-\to ((eq C c1 (CHead c k u)) \to (ex2 C (\lambda (e: C).(eq C c0 (CHead e k
-(lift n (r k d) u)))) (\lambda (e: C).(drop n (r k d) e c))))))))) (\lambda
-(c0: C).(\lambda (H2: (eq nat O (S d))).(\lambda (H3: (eq C c0 (CHead c k
-u))).(eq_ind_r C (CHead c k u) (\lambda (c1: C).(ex2 C (\lambda (e: C).(eq C
-c1 (CHead e k (lift O (r k d) u)))) (\lambda (e: C).(drop O (r k d) e c))))
-(let H4 \def (eq_ind nat O (\lambda (ee: nat).(match ee in nat return
-(\lambda (_: nat).Prop) with [O \Rightarrow True | (S _) \Rightarrow False]))
-I (S d) H2) in (False_ind (ex2 C (\lambda (e: C).(eq C (CHead c k u) (CHead e
-k (lift O (r k d) u)))) (\lambda (e: C).(drop O (r k d) e c))) H4)) c0 H3))))
-(\lambda (k0: K).(\lambda (h0: nat).(\lambda (c0: C).(\lambda (e: C).(\lambda
-(H2: (drop (r k0 h0) O c0 e)).(\lambda (H3: (((eq nat O (S d)) \to ((eq C e
-(CHead c k u)) \to (ex2 C (\lambda (e0: C).(eq C c0 (CHead e0 k (lift (r k0
-h0) (r k d) u)))) (\lambda (e0: C).(drop (r k0 h0) (r k d) e0
-c))))))).(\lambda (u0: T).(\lambda (H4: (eq nat O (S d))).(\lambda (H5: (eq C
-e (CHead c k u))).(let H6 \def (eq_ind C e (\lambda (c1: C).((eq nat O (S d))
-\to ((eq C c1 (CHead c k u)) \to (ex2 C (\lambda (e0: C).(eq C c0 (CHead e0 k
-(lift (r k0 h0) (r k d) u)))) (\lambda (e0: C).(drop (r k0 h0) (r k d) e0
-c)))))) H3 (CHead c k u) H5) in (let H7 \def (eq_ind C e (\lambda (c1:
-C).(drop (r k0 h0) O c0 c1)) H2 (CHead c k u) H5) in (let H8 \def (eq_ind nat
-O (\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow True | (S _) \Rightarrow False])) I (S d) H4) in (False_ind (ex2
-C (\lambda (e0: C).(eq C (CHead c0 k0 u0) (CHead e0 k (lift (S h0) (r k d)
-u)))) (\lambda (e0: C).(drop (S h0) (r k d) e0 c))) H8))))))))))))) (\lambda
-(k0: K).(\lambda (h0: nat).(\lambda (d0: nat).(\lambda (c0: C).(\lambda (e:
-C).(\lambda (H2: (drop h0 (r k0 d0) c0 e)).(\lambda (H3: (((eq nat (r k0 d0)
-(S d)) \to ((eq C e (CHead c k u)) \to (ex2 C (\lambda (e0: C).(eq C c0
-(CHead e0 k (lift h0 (r k d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0
-c))))))).(\lambda (u0: T).(\lambda (H4: (eq nat (S d0) (S d))).(\lambda (H5:
-(eq C (CHead e k0 u0) (CHead c k u))).(let H6 \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 k0 u0) (CHead c k u) H5) in ((let
-H7 \def (f_equal C K (\lambda (e0: C).(match e0 in C return (\lambda (_:
-C).K) with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1]))
-(CHead e k0 u0) (CHead c k u) H5) in ((let H8 \def (f_equal C T (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 |
-(CHead _ _ t) \Rightarrow t])) (CHead e k0 u0) (CHead c k u) H5) in (\lambda
-(H9: (eq K k0 k)).(\lambda (H10: (eq C e c)).(eq_ind_r T u (\lambda (t:
-T).(ex2 C (\lambda (e0: C).(eq C (CHead c0 k0 (lift h0 (r k0 d0) t)) (CHead
-e0 k (lift h0 (r k d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0 c)))) (let
-H11 \def (eq_ind C e (\lambda (c1: C).((eq nat (r k0 d0) (S d)) \to ((eq C c1
+(d: nat).(\lambda (k: K).(\lambda (H: (drop h (S d) x (CHead c k u))).(let
+TMP_1 \def (CHead c k u) in (let TMP_3 \def (\lambda (c0: C).(let TMP_2 \def
+(S d) in (drop h TMP_2 x c0))) in (let TMP_10 \def (\lambda (_: C).(let TMP_7
+\def (\lambda (e: C).(let TMP_4 \def (r k d) in (let TMP_5 \def (lift h TMP_4
+u) in (let TMP_6 \def (CHead e k TMP_5) in (eq C x TMP_6))))) in (let TMP_9
+\def (\lambda (e: C).(let TMP_8 \def (r k d) in (drop h TMP_8 e c))) in (ex2
+C TMP_7 TMP_9)))) in (let TMP_162 \def (\lambda (y: C).(\lambda (H0: (drop h
+(S d) x y)).(let TMP_11 \def (S d) in (let TMP_12 \def (\lambda (n:
+nat).(drop h n x y)) in (let TMP_19 \def (\lambda (_: nat).((eq C y (CHead c
+k u)) \to (let TMP_16 \def (\lambda (e: C).(let TMP_13 \def (r k d) in (let
+TMP_14 \def (lift h TMP_13 u) in (let TMP_15 \def (CHead e k TMP_14) in (eq C
+x TMP_15))))) in (let TMP_18 \def (\lambda (e: C).(let TMP_17 \def (r k d) in
+(drop h TMP_17 e c))) in (ex2 C TMP_16 TMP_18))))) in (let TMP_161 \def
+(\lambda (y0: nat).(\lambda (H1: (drop h y0 x y)).(let TMP_26 \def (\lambda
+(n: nat).(\lambda (n0: nat).(\lambda (c0: C).(\lambda (c1: C).((eq nat n0 (S
+d)) \to ((eq C c1 (CHead c k u)) \to (let TMP_23 \def (\lambda (e: C).(let
+TMP_20 \def (r k d) in (let TMP_21 \def (lift n TMP_20 u) in (let TMP_22 \def
+(CHead e k TMP_21) in (eq C c0 TMP_22))))) in (let TMP_25 \def (\lambda (e:
+C).(let TMP_24 \def (r k d) in (drop n TMP_24 e c))) in (ex2 C TMP_23
+TMP_25))))))))) in (let TMP_46 \def (\lambda (c0: C).(\lambda (H2: (eq nat O
+(S d))).(\lambda (H3: (eq C c0 (CHead c k u))).(let TMP_27 \def (CHead c k u)
+in (let TMP_34 \def (\lambda (c1: C).(let TMP_31 \def (\lambda (e: C).(let
+TMP_28 \def (r k d) in (let TMP_29 \def (lift O TMP_28 u) in (let TMP_30 \def
+(CHead e k TMP_29) in (eq C c1 TMP_30))))) in (let TMP_33 \def (\lambda (e:
+C).(let TMP_32 \def (r k d) in (drop O TMP_32 e c))) in (ex2 C TMP_31
+TMP_33)))) in (let TMP_35 \def (\lambda (ee: nat).(match ee with [O
+\Rightarrow True | (S _) \Rightarrow False])) in (let TMP_36 \def (S d) in
+(let H4 \def (eq_ind nat O TMP_35 I TMP_36 H2) in (let TMP_41 \def (\lambda
+(e: C).(let TMP_37 \def (CHead c k u) in (let TMP_38 \def (r k d) in (let
+TMP_39 \def (lift O TMP_38 u) in (let TMP_40 \def (CHead e k TMP_39) in (eq C
+TMP_37 TMP_40)))))) in (let TMP_43 \def (\lambda (e: C).(let TMP_42 \def (r k
+d) in (drop O TMP_42 e c))) in (let TMP_44 \def (ex2 C TMP_41 TMP_43) in (let
+TMP_45 \def (False_ind TMP_44 H4) in (eq_ind_r C TMP_27 TMP_34 TMP_45 c0
+H3))))))))))))) in (let TMP_72 \def (\lambda (k0: K).(\lambda (h0:
+nat).(\lambda (c0: C).(\lambda (e: C).(\lambda (H2: (drop (r k0 h0) O c0
+e)).(\lambda (H3: (((eq nat O (S d)) \to ((eq C e (CHead c k u)) \to (ex2 C
+(\lambda (e0: C).(eq C c0 (CHead e0 k (lift (r k0 h0) (r k d) u)))) (\lambda
+(e0: C).(drop (r k0 h0) (r k d) e0 c))))))).(\lambda (u0: T).(\lambda (H4:
+(eq nat O (S d))).(\lambda (H5: (eq C e (CHead c k u))).(let TMP_55 \def
+(\lambda (c1: C).((eq nat O (S d)) \to ((eq C c1 (CHead c k u)) \to (let
+TMP_51 \def (\lambda (e0: C).(let TMP_47 \def (r k0 h0) in (let TMP_48 \def
+(r k d) in (let TMP_49 \def (lift TMP_47 TMP_48 u) in (let TMP_50 \def (CHead
+e0 k TMP_49) in (eq C c0 TMP_50)))))) in (let TMP_54 \def (\lambda (e0:
+C).(let TMP_52 \def (r k0 h0) in (let TMP_53 \def (r k d) in (drop TMP_52
+TMP_53 e0 c)))) in (ex2 C TMP_51 TMP_54)))))) in (let TMP_56 \def (CHead c k
+u) in (let H6 \def (eq_ind C e TMP_55 H3 TMP_56 H5) in (let TMP_58 \def
+(\lambda (c1: C).(let TMP_57 \def (r k0 h0) in (drop TMP_57 O c0 c1))) in
+(let TMP_59 \def (CHead c k u) in (let H7 \def (eq_ind C e TMP_58 H2 TMP_59
+H5) in (let TMP_60 \def (\lambda (ee: nat).(match ee with [O \Rightarrow True
+| (S _) \Rightarrow False])) in (let TMP_61 \def (S d) in (let H8 \def
+(eq_ind nat O TMP_60 I TMP_61 H4) in (let TMP_67 \def (\lambda (e0: C).(let
+TMP_62 \def (CHead c0 k0 u0) in (let TMP_63 \def (S h0) in (let TMP_64 \def
+(r k d) in (let TMP_65 \def (lift TMP_63 TMP_64 u) in (let TMP_66 \def (CHead
+e0 k TMP_65) in (eq C TMP_62 TMP_66))))))) in (let TMP_70 \def (\lambda (e0:
+C).(let TMP_68 \def (S h0) in (let TMP_69 \def (r k d) in (drop TMP_68 TMP_69
+e0 c)))) in (let TMP_71 \def (ex2 C TMP_67 TMP_70) in (False_ind TMP_71
+H8)))))))))))))))))))))) in (let TMP_160 \def (\lambda (k0: K).(\lambda (h0:
+nat).(\lambda (d0: nat).(\lambda (c0: C).(\lambda (e: C).(\lambda (H2: (drop
+h0 (r k0 d0) c0 e)).(\lambda (H3: (((eq nat (r k0 d0) (S d)) \to ((eq C e
(CHead c k u)) \to (ex2 C (\lambda (e0: C).(eq C c0 (CHead e0 k (lift h0 (r k
-d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0 c)))))) H3 c H10) in (let H12
-\def (eq_ind C e (\lambda (c1: C).(drop h0 (r k0 d0) c0 c1)) H2 c H10) in
-(let H13 \def (eq_ind K k0 (\lambda (k1: K).((eq nat (r k1 d0) (S d)) \to
-((eq C c (CHead c k u)) \to (ex2 C (\lambda (e0: C).(eq C c0 (CHead e0 k
-(lift h0 (r k d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0 c)))))) H11 k H9)
-in (let H14 \def (eq_ind K k0 (\lambda (k1: K).(drop h0 (r k1 d0) c0 c)) H12
-k H9) in (eq_ind_r K k (\lambda (k1: K).(ex2 C (\lambda (e0: C).(eq C (CHead
-c0 k1 (lift h0 (r k1 d0) u)) (CHead e0 k (lift h0 (r k d) u)))) (\lambda (e0:
-C).(drop h0 (r k d) e0 c)))) (let H15 \def (f_equal nat nat (\lambda (e0:
-nat).(match e0 in nat return (\lambda (_: nat).nat) with [O \Rightarrow d0 |
-(S n) \Rightarrow n])) (S d0) (S d) H4) in (let H16 \def (eq_ind nat d0
-(\lambda (n: nat).((eq nat (r k n) (S d)) \to ((eq C c (CHead c k u)) \to
-(ex2 C (\lambda (e0: C).(eq C c0 (CHead e0 k (lift h0 (r k d) u)))) (\lambda
-(e0: C).(drop h0 (r k d) e0 c)))))) H13 d H15) in (let H17 \def (eq_ind nat
-d0 (\lambda (n: nat).(drop h0 (r k n) c0 c)) H14 d H15) in (eq_ind_r nat d
-(\lambda (n: nat).(ex2 C (\lambda (e0: C).(eq C (CHead c0 k (lift h0 (r k n)
-u)) (CHead e0 k (lift h0 (r k d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0
-c)))) (ex_intro2 C (\lambda (e0: C).(eq C (CHead c0 k (lift h0 (r k d) u))
-(CHead e0 k (lift h0 (r k d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0 c))
-c0 (refl_equal C (CHead c0 k (lift h0 (r k d) u))) H17) d0 H15)))) k0 H9)))))
-u0 H8)))) H7)) H6)))))))))))) h y0 x y H1))) H0))) H))))))).
-(* COMMENTS
-Initial nodes: 1758
-END *)
+d) u)))) (\lambda (e0: C).(drop h0 (r k d) e0 c))))))).(\lambda (u0:
+T).(\lambda (H4: (eq nat (S d0) (S d))).(\lambda (H5: (eq C (CHead e k0 u0)
+(CHead c k u))).(let TMP_73 \def (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow e | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_74 \def (CHead e
+k0 u0) in (let TMP_75 \def (CHead c k u) in (let H6 \def (f_equal C C TMP_73
+TMP_74 TMP_75 H5) in (let TMP_76 \def (\lambda (e0: C).(match e0 with [(CSort
+_) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) in (let TMP_77 \def
+(CHead e k0 u0) in (let TMP_78 \def (CHead c k u) in (let H7 \def (f_equal C
+K TMP_76 TMP_77 TMP_78 H5) in (let TMP_79 \def (\lambda (e0: C).(match e0
+with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) in (let
+TMP_80 \def (CHead e k0 u0) in (let TMP_81 \def (CHead c k u) in (let H8 \def
+(f_equal C T TMP_79 TMP_80 TMP_81 H5) in (let TMP_158 \def (\lambda (H9: (eq
+K k0 k)).(\lambda (H10: (eq C e c)).(let TMP_91 \def (\lambda (t: T).(let
+TMP_88 \def (\lambda (e0: C).(let TMP_82 \def (r k0 d0) in (let TMP_83 \def
+(lift h0 TMP_82 t) in (let TMP_84 \def (CHead c0 k0 TMP_83) in (let TMP_85
+\def (r k d) in (let TMP_86 \def (lift h0 TMP_85 u) in (let TMP_87 \def
+(CHead e0 k TMP_86) in (eq C TMP_84 TMP_87)))))))) in (let TMP_90 \def
+(\lambda (e0: C).(let TMP_89 \def (r k d) in (drop h0 TMP_89 e0 c))) in (ex2
+C TMP_88 TMP_90)))) in (let TMP_98 \def (\lambda (c1: C).((eq nat (r k0 d0)
+(S d)) \to ((eq C c1 (CHead c k u)) \to (let TMP_95 \def (\lambda (e0:
+C).(let TMP_92 \def (r k d) in (let TMP_93 \def (lift h0 TMP_92 u) in (let
+TMP_94 \def (CHead e0 k TMP_93) in (eq C c0 TMP_94))))) in (let TMP_97 \def
+(\lambda (e0: C).(let TMP_96 \def (r k d) in (drop h0 TMP_96 e0 c))) in (ex2
+C TMP_95 TMP_97)))))) in (let H11 \def (eq_ind C e TMP_98 H3 c H10) in (let
+TMP_100 \def (\lambda (c1: C).(let TMP_99 \def (r k0 d0) in (drop h0 TMP_99
+c0 c1))) in (let H12 \def (eq_ind C e TMP_100 H2 c H10) in (let TMP_107 \def
+(\lambda (k1: K).((eq nat (r k1 d0) (S d)) \to ((eq C c (CHead c k u)) \to
+(let TMP_104 \def (\lambda (e0: C).(let TMP_101 \def (r k d) in (let TMP_102
+\def (lift h0 TMP_101 u) in (let TMP_103 \def (CHead e0 k TMP_102) in (eq C
+c0 TMP_103))))) in (let TMP_106 \def (\lambda (e0: C).(let TMP_105 \def (r k
+d) in (drop h0 TMP_105 e0 c))) in (ex2 C TMP_104 TMP_106)))))) in (let H13
+\def (eq_ind K k0 TMP_107 H11 k H9) in (let TMP_109 \def (\lambda (k1:
+K).(let TMP_108 \def (r k1 d0) in (drop h0 TMP_108 c0 c))) in (let H14 \def
+(eq_ind K k0 TMP_109 H12 k H9) in (let TMP_119 \def (\lambda (k1: K).(let
+TMP_116 \def (\lambda (e0: C).(let TMP_110 \def (r k1 d0) in (let TMP_111
+\def (lift h0 TMP_110 u) in (let TMP_112 \def (CHead c0 k1 TMP_111) in (let
+TMP_113 \def (r k d) in (let TMP_114 \def (lift h0 TMP_113 u) in (let TMP_115
+\def (CHead e0 k TMP_114) in (eq C TMP_112 TMP_115)))))))) in (let TMP_118
+\def (\lambda (e0: C).(let TMP_117 \def (r k d) in (drop h0 TMP_117 e0 c)))
+in (ex2 C TMP_116 TMP_118)))) in (let TMP_120 \def (\lambda (e0: nat).(match
+e0 with [O \Rightarrow d0 | (S n) \Rightarrow n])) in (let TMP_121 \def (S
+d0) in (let TMP_122 \def (S d) in (let H15 \def (f_equal nat nat TMP_120
+TMP_121 TMP_122 H4) in (let TMP_129 \def (\lambda (n: nat).((eq nat (r k n)
+(S d)) \to ((eq C c (CHead c k u)) \to (let TMP_126 \def (\lambda (e0:
+C).(let TMP_123 \def (r k d) in (let TMP_124 \def (lift h0 TMP_123 u) in (let
+TMP_125 \def (CHead e0 k TMP_124) in (eq C c0 TMP_125))))) in (let TMP_128
+\def (\lambda (e0: C).(let TMP_127 \def (r k d) in (drop h0 TMP_127 e0 c)))
+in (ex2 C TMP_126 TMP_128)))))) in (let H16 \def (eq_ind nat d0 TMP_129 H13 d
+H15) in (let TMP_131 \def (\lambda (n: nat).(let TMP_130 \def (r k n) in
+(drop h0 TMP_130 c0 c))) in (let H17 \def (eq_ind nat d0 TMP_131 H14 d H15)
+in (let TMP_141 \def (\lambda (n: nat).(let TMP_138 \def (\lambda (e0:
+C).(let TMP_132 \def (r k n) in (let TMP_133 \def (lift h0 TMP_132 u) in (let
+TMP_134 \def (CHead c0 k TMP_133) in (let TMP_135 \def (r k d) in (let
+TMP_136 \def (lift h0 TMP_135 u) in (let TMP_137 \def (CHead e0 k TMP_136) in
+(eq C TMP_134 TMP_137)))))))) in (let TMP_140 \def (\lambda (e0: C).(let
+TMP_139 \def (r k d) in (drop h0 TMP_139 e0 c))) in (ex2 C TMP_138
+TMP_140)))) in (let TMP_148 \def (\lambda (e0: C).(let TMP_142 \def (r k d)
+in (let TMP_143 \def (lift h0 TMP_142 u) in (let TMP_144 \def (CHead c0 k
+TMP_143) in (let TMP_145 \def (r k d) in (let TMP_146 \def (lift h0 TMP_145
+u) in (let TMP_147 \def (CHead e0 k TMP_146) in (eq C TMP_144 TMP_147))))))))
+in (let TMP_150 \def (\lambda (e0: C).(let TMP_149 \def (r k d) in (drop h0
+TMP_149 e0 c))) in (let TMP_151 \def (r k d) in (let TMP_152 \def (lift h0
+TMP_151 u) in (let TMP_153 \def (CHead c0 k TMP_152) in (let TMP_154 \def
+(refl_equal C TMP_153) in (let TMP_155 \def (ex_intro2 C TMP_148 TMP_150 c0
+TMP_154 H17) in (let TMP_156 \def (eq_ind_r nat d TMP_141 TMP_155 d0 H15) in
+(let TMP_157 \def (eq_ind_r K k TMP_119 TMP_156 k0 H9) in (eq_ind_r T u
+TMP_91 TMP_157 u0 H8))))))))))))))))))))))))))))))) in (let TMP_159 \def
+(TMP_158 H7) in (TMP_159 H6))))))))))))))))))))))))) in (drop_ind TMP_26
+TMP_46 TMP_72 TMP_160 h y0 x y H1))))))) in (insert_eq nat TMP_11 TMP_12
+TMP_19 TMP_161 H0))))))) in (insert_eq C TMP_1 TMP_3 TMP_10 TMP_162
+H))))))))))).
theorem drop_gen_skip_l:
\forall (c: C).(\forall (x: C).(\forall (u: T).(\forall (h: nat).(\forall
T).(drop h (r k d) c e))))))))))
\def
\lambda (c: C).(\lambda (x: C).(\lambda (u: T).(\lambda (h: nat).(\lambda
-(d: nat).(\lambda (k: K).(\lambda (H: (drop h (S d) (CHead c k u)
-x)).(insert_eq C (CHead c k u) (\lambda (c0: C).(drop h (S d) c0 x)) (\lambda
-(_: C).(ex3_2 C T (\lambda (e: C).(\lambda (v: T).(eq C x (CHead e k v))))
-(\lambda (_: C).(\lambda (v: T).(eq T u (lift h (r k d) v)))) (\lambda (e:
-C).(\lambda (_: T).(drop h (r k d) c e))))) (\lambda (y: C).(\lambda (H0:
-(drop h (S d) y x)).(insert_eq nat (S d) (\lambda (n: nat).(drop h n y x))
-(\lambda (_: nat).((eq C y (CHead c k u)) \to (ex3_2 C T (\lambda (e:
-C).(\lambda (v: T).(eq C x (CHead e k v)))) (\lambda (_: C).(\lambda (v:
-T).(eq T u (lift h (r k d) v)))) (\lambda (e: C).(\lambda (_: T).(drop h (r k
-d) c e)))))) (\lambda (y0: nat).(\lambda (H1: (drop h y0 y x)).(drop_ind
-(\lambda (n: nat).(\lambda (n0: nat).(\lambda (c0: C).(\lambda (c1: C).((eq
-nat n0 (S d)) \to ((eq C c0 (CHead c k u)) \to (ex3_2 C T (\lambda (e:
-C).(\lambda (v: T).(eq C c1 (CHead e k v)))) (\lambda (_: C).(\lambda (v:
-T).(eq T u (lift n (r k d) v)))) (\lambda (e: C).(\lambda (_: T).(drop n (r k
-d) c e)))))))))) (\lambda (c0: C).(\lambda (H2: (eq nat O (S d))).(\lambda
-(H3: (eq C c0 (CHead c k u))).(eq_ind_r C (CHead c k u) (\lambda (c1:
-C).(ex3_2 C T (\lambda (e: C).(\lambda (v: T).(eq C c1 (CHead e k v))))
-(\lambda (_: C).(\lambda (v: T).(eq T u (lift O (r k d) v)))) (\lambda (e:
-C).(\lambda (_: T).(drop O (r k d) c e))))) (let H4 \def (eq_ind nat O
-(\lambda (ee: nat).(match ee in nat return (\lambda (_: nat).Prop) with [O
-\Rightarrow True | (S _) \Rightarrow False])) I (S d) H2) in (False_ind
-(ex3_2 C T (\lambda (e: C).(\lambda (v: T).(eq C (CHead c k u) (CHead e k
-v)))) (\lambda (_: C).(\lambda (v: T).(eq T u (lift O (r k d) v)))) (\lambda
-(e: C).(\lambda (_: T).(drop O (r k d) c e)))) H4)) c0 H3)))) (\lambda (k0:
-K).(\lambda (h0: nat).(\lambda (c0: C).(\lambda (e: C).(\lambda (H2: (drop (r
-k0 h0) O c0 e)).(\lambda (H3: (((eq nat O (S d)) \to ((eq C c0 (CHead c k u))
-\to (ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C e (CHead e0 k v))))
-(\lambda (_: C).(\lambda (v: T).(eq T u (lift (r k0 h0) (r k d) v))))
-(\lambda (e0: C).(\lambda (_: T).(drop (r k0 h0) (r k d) c
+(d: nat).(\lambda (k: K).(\lambda (H: (drop h (S d) (CHead c k u) x)).(let
+TMP_1 \def (CHead c k u) in (let TMP_3 \def (\lambda (c0: C).(let TMP_2 \def
+(S d) in (drop h TMP_2 c0 x))) in (let TMP_11 \def (\lambda (_: C).(let TMP_5
+\def (\lambda (e: C).(\lambda (v: T).(let TMP_4 \def (CHead e k v) in (eq C x
+TMP_4)))) in (let TMP_8 \def (\lambda (_: C).(\lambda (v: T).(let TMP_6 \def
+(r k d) in (let TMP_7 \def (lift h TMP_6 v) in (eq T u TMP_7))))) in (let
+TMP_10 \def (\lambda (e: C).(\lambda (_: T).(let TMP_9 \def (r k d) in (drop
+h TMP_9 c e)))) in (ex3_2 C T TMP_5 TMP_8 TMP_10))))) in (let TMP_223 \def
+(\lambda (y: C).(\lambda (H0: (drop h (S d) y x)).(let TMP_12 \def (S d) in
+(let TMP_13 \def (\lambda (n: nat).(drop h n y x)) in (let TMP_21 \def
+(\lambda (_: nat).((eq C y (CHead c k u)) \to (let TMP_15 \def (\lambda (e:
+C).(\lambda (v: T).(let TMP_14 \def (CHead e k v) in (eq C x TMP_14)))) in
+(let TMP_18 \def (\lambda (_: C).(\lambda (v: T).(let TMP_16 \def (r k d) in
+(let TMP_17 \def (lift h TMP_16 v) in (eq T u TMP_17))))) in (let TMP_20 \def
+(\lambda (e: C).(\lambda (_: T).(let TMP_19 \def (r k d) in (drop h TMP_19 c
+e)))) in (ex3_2 C T TMP_15 TMP_18 TMP_20)))))) in (let TMP_222 \def (\lambda
+(y0: nat).(\lambda (H1: (drop h y0 y x)).(let TMP_29 \def (\lambda (n:
+nat).(\lambda (n0: nat).(\lambda (c0: C).(\lambda (c1: C).((eq nat n0 (S d))
+\to ((eq C c0 (CHead c k u)) \to (let TMP_23 \def (\lambda (e: C).(\lambda
+(v: T).(let TMP_22 \def (CHead e k v) in (eq C c1 TMP_22)))) in (let TMP_26
+\def (\lambda (_: C).(\lambda (v: T).(let TMP_24 \def (r k d) in (let TMP_25
+\def (lift n TMP_24 v) in (eq T u TMP_25))))) in (let TMP_28 \def (\lambda
+(e: C).(\lambda (_: T).(let TMP_27 \def (r k d) in (drop n TMP_27 c e)))) in
+(ex3_2 C T TMP_23 TMP_26 TMP_28)))))))))) in (let TMP_51 \def (\lambda (c0:
+C).(\lambda (H2: (eq nat O (S d))).(\lambda (H3: (eq C c0 (CHead c k
+u))).(let TMP_30 \def (CHead c k u) in (let TMP_38 \def (\lambda (c1: C).(let
+TMP_32 \def (\lambda (e: C).(\lambda (v: T).(let TMP_31 \def (CHead e k v) in
+(eq C c1 TMP_31)))) in (let TMP_35 \def (\lambda (_: C).(\lambda (v: T).(let
+TMP_33 \def (r k d) in (let TMP_34 \def (lift O TMP_33 v) in (eq T u
+TMP_34))))) in (let TMP_37 \def (\lambda (e: C).(\lambda (_: T).(let TMP_36
+\def (r k d) in (drop O TMP_36 c e)))) in (ex3_2 C T TMP_32 TMP_35
+TMP_37))))) in (let TMP_39 \def (\lambda (ee: nat).(match ee with [O
+\Rightarrow True | (S _) \Rightarrow False])) in (let TMP_40 \def (S d) in
+(let H4 \def (eq_ind nat O TMP_39 I TMP_40 H2) in (let TMP_43 \def (\lambda
+(e: C).(\lambda (v: T).(let TMP_41 \def (CHead c k u) in (let TMP_42 \def
+(CHead e k v) in (eq C TMP_41 TMP_42))))) in (let TMP_46 \def (\lambda (_:
+C).(\lambda (v: T).(let TMP_44 \def (r k d) in (let TMP_45 \def (lift O
+TMP_44 v) in (eq T u TMP_45))))) in (let TMP_48 \def (\lambda (e: C).(\lambda
+(_: T).(let TMP_47 \def (r k d) in (drop O TMP_47 c e)))) in (let TMP_49 \def
+(ex3_2 C T TMP_43 TMP_46 TMP_48) in (let TMP_50 \def (False_ind TMP_49 H4) in
+(eq_ind_r C TMP_30 TMP_38 TMP_50 c0 H3)))))))))))))) in (let TMP_99 \def
+(\lambda (k0: K).(\lambda (h0: nat).(\lambda (c0: C).(\lambda (e: C).(\lambda
+(H2: (drop (r k0 h0) O c0 e)).(\lambda (H3: (((eq nat O (S d)) \to ((eq C c0
+(CHead c k u)) \to (ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C e (CHead
+e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq T u (lift (r k0 h0) (r k d)
+v)))) (\lambda (e0: C).(\lambda (_: T).(drop (r k0 h0) (r k d) c
e0)))))))).(\lambda (u0: T).(\lambda (H4: (eq nat O (S d))).(\lambda (H5: (eq
-C (CHead c0 k0 u0) (CHead c k u))).(let H6 \def (f_equal C C (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow c0 |
-(CHead c1 _ _) \Rightarrow c1])) (CHead c0 k0 u0) (CHead c k u) H5) in ((let
-H7 \def (f_equal C K (\lambda (e0: C).(match e0 in C return (\lambda (_:
-C).K) with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1]))
-(CHead c0 k0 u0) (CHead c k u) H5) in ((let H8 \def (f_equal C T (\lambda
-(e0: C).(match e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow
-u0 | (CHead _ _ t) \Rightarrow t])) (CHead c0 k0 u0) (CHead c k u) H5) in
-(\lambda (H9: (eq K k0 k)).(\lambda (H10: (eq C c0 c)).(let H11 \def (eq_ind
-C c0 (\lambda (c1: C).((eq nat O (S d)) \to ((eq C c1 (CHead c k u)) \to
-(ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C e (CHead e0 k v))))
-(\lambda (_: C).(\lambda (v: T).(eq T u (lift (r k0 h0) (r k d) v))))
-(\lambda (e0: C).(\lambda (_: T).(drop (r k0 h0) (r k d) c e0))))))) H3 c
-H10) in (let H12 \def (eq_ind C c0 (\lambda (c1: C).(drop (r k0 h0) O c1 e))
-H2 c H10) in (let H13 \def (eq_ind K k0 (\lambda (k1: K).((eq nat O (S d))
-\to ((eq C c (CHead c k u)) \to (ex3_2 C T (\lambda (e0: C).(\lambda (v:
-T).(eq C e (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq T u (lift (r
-k1 h0) (r k d) v)))) (\lambda (e0: C).(\lambda (_: T).(drop (r k1 h0) (r k d)
-c e0))))))) H11 k H9) in (let H14 \def (eq_ind K k0 (\lambda (k1: K).(drop (r
-k1 h0) O c e)) H12 k H9) in (let H15 \def (eq_ind nat O (\lambda (ee:
-nat).(match ee in nat return (\lambda (_: nat).Prop) with [O \Rightarrow True
-| (S _) \Rightarrow False])) I (S d) H4) in (False_ind (ex3_2 C T (\lambda
-(e0: C).(\lambda (v: T).(eq C e (CHead e0 k v)))) (\lambda (_: C).(\lambda
-(v: T).(eq T u (lift (S h0) (r k d) v)))) (\lambda (e0: C).(\lambda (_:
-T).(drop (S h0) (r k d) c e0)))) H15))))))))) H7)) H6))))))))))) (\lambda
-(k0: K).(\lambda (h0: nat).(\lambda (d0: nat).(\lambda (c0: C).(\lambda (e:
-C).(\lambda (H2: (drop h0 (r k0 d0) c0 e)).(\lambda (H3: (((eq nat (r k0 d0)
-(S d)) \to ((eq C c0 (CHead c k u)) \to (ex3_2 C T (\lambda (e0: C).(\lambda
-(v: T).(eq C e (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq T u
-(lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_: T).(drop h0 (r k d) c
-e0)))))))).(\lambda (u0: T).(\lambda (H4: (eq nat (S d0) (S d))).(\lambda
-(H5: (eq C (CHead c0 k0 (lift h0 (r k0 d0) u0)) (CHead c k u))).(let H6 \def
-(f_equal C C (\lambda (e0: C).(match e0 in C return (\lambda (_: C).C) with
-[(CSort _) \Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) (CHead c0 k0
-(lift h0 (r k0 d0) u0)) (CHead c k u) H5) in ((let H7 \def (f_equal C K
-(\lambda (e0: C).(match e0 in C return (\lambda (_: C).K) with [(CSort _)
-\Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) (CHead c0 k0 (lift h0 (r k0
-d0) u0)) (CHead c k u) H5) in ((let H8 \def (f_equal C T (\lambda (e0:
-C).(match e0 in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow ((let
-rec lref_map (f: ((nat \to nat))) (d1: nat) (t: T) on t: T \def (match t with
-[(TSort n) \Rightarrow (TSort n) | (TLRef i) \Rightarrow (TLRef (match (blt i
-d1) with [true \Rightarrow i | false \Rightarrow (f i)])) | (THead k1 u1 t0)
-\Rightarrow (THead k1 (lref_map f d1 u1) (lref_map f (s k1 d1) t0))]) in
-lref_map) (\lambda (x0: nat).(plus x0 h0)) (r k0 d0) u0) | (CHead _ _ t)
-\Rightarrow t])) (CHead c0 k0 (lift h0 (r k0 d0) u0)) (CHead c k u) H5) in
-(\lambda (H9: (eq K k0 k)).(\lambda (H10: (eq C c0 c)).(let H11 \def (eq_ind
-C c0 (\lambda (c1: C).((eq nat (r k0 d0) (S d)) \to ((eq C c1 (CHead c k u))
-\to (ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C e (CHead e0 k v))))
-(\lambda (_: C).(\lambda (v: T).(eq T u (lift h0 (r k d) v)))) (\lambda (e0:
-C).(\lambda (_: T).(drop h0 (r k d) c e0))))))) H3 c H10) in (let H12 \def
-(eq_ind C c0 (\lambda (c1: C).(drop h0 (r k0 d0) c1 e)) H2 c H10) in (let H13
-\def (eq_ind K k0 (\lambda (k1: K).(eq T (lift h0 (r k1 d0) u0) u)) H8 k H9)
-in (let H14 \def (eq_ind K k0 (\lambda (k1: K).((eq nat (r k1 d0) (S d)) \to
-((eq C c (CHead c k u)) \to (ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C
-e (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq T u (lift h0 (r k d)
-v)))) (\lambda (e0: C).(\lambda (_: T).(drop h0 (r k d) c e0))))))) H11 k H9)
-in (let H15 \def (eq_ind K k0 (\lambda (k1: K).(drop h0 (r k1 d0) c e)) H12 k
-H9) in (eq_ind_r K k (\lambda (k1: K).(ex3_2 C T (\lambda (e0: C).(\lambda
-(v: T).(eq C (CHead e k1 u0) (CHead e0 k v)))) (\lambda (_: C).(\lambda (v:
-T).(eq T u (lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_: T).(drop h0
-(r k d) c e0))))) (let H16 \def (eq_ind_r T u (\lambda (t: T).((eq nat (r k
-d0) (S d)) \to ((eq C c (CHead c k t)) \to (ex3_2 C T (\lambda (e0:
-C).(\lambda (v: T).(eq C e (CHead e0 k v)))) (\lambda (_: C).(\lambda (v:
-T).(eq T t (lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_: T).(drop h0
-(r k d) c e0))))))) H14 (lift h0 (r k d0) u0) H13) in (eq_ind T (lift h0 (r k
-d0) u0) (\lambda (t: T).(ex3_2 C T (\lambda (e0: C).(\lambda (v: T).(eq C
-(CHead e k u0) (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq T t
-(lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_: T).(drop h0 (r k d) c
-e0))))) (let H17 \def (f_equal nat nat (\lambda (e0: nat).(match e0 in nat
-return (\lambda (_: nat).nat) with [O \Rightarrow d0 | (S n) \Rightarrow n]))
-(S d0) (S d) H4) in (let H18 \def (eq_ind nat d0 (\lambda (n: nat).((eq nat
-(r k n) (S d)) \to ((eq C c (CHead c k (lift h0 (r k n) u0))) \to (ex3_2 C T
+C (CHead c0 k0 u0) (CHead c k u))).(let TMP_52 \def (\lambda (e0: C).(match
+e0 with [(CSort _) \Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) in (let
+TMP_53 \def (CHead c0 k0 u0) in (let TMP_54 \def (CHead c k u) in (let H6
+\def (f_equal C C TMP_52 TMP_53 TMP_54 H5) in (let TMP_55 \def (\lambda (e0:
+C).(match e0 with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow
+k1])) in (let TMP_56 \def (CHead c0 k0 u0) in (let TMP_57 \def (CHead c k u)
+in (let H7 \def (f_equal C K TMP_55 TMP_56 TMP_57 H5) in (let TMP_58 \def
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow u0 | (CHead _ _ t)
+\Rightarrow t])) in (let TMP_59 \def (CHead c0 k0 u0) in (let TMP_60 \def
+(CHead c k u) in (let H8 \def (f_equal C T TMP_58 TMP_59 TMP_60 H5) in (let
+TMP_97 \def (\lambda (H9: (eq K k0 k)).(\lambda (H10: (eq C c0 c)).(let
+TMP_70 \def (\lambda (c1: C).((eq nat O (S d)) \to ((eq C c1 (CHead c k u))
+\to (let TMP_62 \def (\lambda (e0: C).(\lambda (v: T).(let TMP_61 \def (CHead
+e0 k v) in (eq C e TMP_61)))) in (let TMP_66 \def (\lambda (_: C).(\lambda
+(v: T).(let TMP_63 \def (r k0 h0) in (let TMP_64 \def (r k d) in (let TMP_65
+\def (lift TMP_63 TMP_64 v) in (eq T u TMP_65)))))) in (let TMP_69 \def
+(\lambda (e0: C).(\lambda (_: T).(let TMP_67 \def (r k0 h0) in (let TMP_68
+\def (r k d) in (drop TMP_67 TMP_68 c e0))))) in (ex3_2 C T TMP_62 TMP_66
+TMP_69))))))) in (let H11 \def (eq_ind C c0 TMP_70 H3 c H10) in (let TMP_72
+\def (\lambda (c1: C).(let TMP_71 \def (r k0 h0) in (drop TMP_71 O c1 e))) in
+(let H12 \def (eq_ind C c0 TMP_72 H2 c H10) in (let TMP_82 \def (\lambda (k1:
+K).((eq nat O (S d)) \to ((eq C c (CHead c k u)) \to (let TMP_74 \def
+(\lambda (e0: C).(\lambda (v: T).(let TMP_73 \def (CHead e0 k v) in (eq C e
+TMP_73)))) in (let TMP_78 \def (\lambda (_: C).(\lambda (v: T).(let TMP_75
+\def (r k1 h0) in (let TMP_76 \def (r k d) in (let TMP_77 \def (lift TMP_75
+TMP_76 v) in (eq T u TMP_77)))))) in (let TMP_81 \def (\lambda (e0:
+C).(\lambda (_: T).(let TMP_79 \def (r k1 h0) in (let TMP_80 \def (r k d) in
+(drop TMP_79 TMP_80 c e0))))) in (ex3_2 C T TMP_74 TMP_78 TMP_81))))))) in
+(let H13 \def (eq_ind K k0 TMP_82 H11 k H9) in (let TMP_84 \def (\lambda (k1:
+K).(let TMP_83 \def (r k1 h0) in (drop TMP_83 O c e))) in (let H14 \def
+(eq_ind K k0 TMP_84 H12 k H9) in (let TMP_85 \def (\lambda (ee: nat).(match
+ee with [O \Rightarrow True | (S _) \Rightarrow False])) in (let TMP_86 \def
+(S d) in (let H15 \def (eq_ind nat O TMP_85 I TMP_86 H4) in (let TMP_88 \def
+(\lambda (e0: C).(\lambda (v: T).(let TMP_87 \def (CHead e0 k v) in (eq C e
+TMP_87)))) in (let TMP_92 \def (\lambda (_: C).(\lambda (v: T).(let TMP_89
+\def (S h0) in (let TMP_90 \def (r k d) in (let TMP_91 \def (lift TMP_89
+TMP_90 v) in (eq T u TMP_91)))))) in (let TMP_95 \def (\lambda (e0:
+C).(\lambda (_: T).(let TMP_93 \def (S h0) in (let TMP_94 \def (r k d) in
+(drop TMP_93 TMP_94 c e0))))) in (let TMP_96 \def (ex3_2 C T TMP_88 TMP_92
+TMP_95) in (False_ind TMP_96 H15)))))))))))))))))) in (let TMP_98 \def
+(TMP_97 H7) in (TMP_98 H6)))))))))))))))))))))))) in (let TMP_221 \def
+(\lambda (k0: K).(\lambda (h0: nat).(\lambda (d0: nat).(\lambda (c0:
+C).(\lambda (e: C).(\lambda (H2: (drop h0 (r k0 d0) c0 e)).(\lambda (H3:
+(((eq nat (r k0 d0) (S d)) \to ((eq C c0 (CHead c k u)) \to (ex3_2 C T
(\lambda (e0: C).(\lambda (v: T).(eq C e (CHead e0 k v)))) (\lambda (_:
-C).(\lambda (v: T).(eq T (lift h0 (r k n) u0) (lift h0 (r k d) v)))) (\lambda
-(e0: C).(\lambda (_: T).(drop h0 (r k d) c e0))))))) H16 d H17) in (let H19
-\def (eq_ind nat d0 (\lambda (n: nat).(drop h0 (r k n) c e)) H15 d H17) in
-(eq_ind_r nat d (\lambda (n: nat).(ex3_2 C T (\lambda (e0: C).(\lambda (v:
-T).(eq C (CHead e k u0) (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq
-T (lift h0 (r k n) u0) (lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_:
-T).(drop h0 (r k d) c e0))))) (ex3_2_intro C T (\lambda (e0: C).(\lambda (v:
-T).(eq C (CHead e k u0) (CHead e0 k v)))) (\lambda (_: C).(\lambda (v: T).(eq
-T (lift h0 (r k d) u0) (lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda (_:
-T).(drop h0 (r k d) c e0))) e u0 (refl_equal C (CHead e k u0)) (refl_equal T
-(lift h0 (r k d) u0)) H19) d0 H17)))) u H13)) k0 H9))))))))) H7))
-H6)))))))))))) h y0 y x H1))) H0))) H))))))).
-(* COMMENTS
-Initial nodes: 2574
-END *)
+C).(\lambda (v: T).(eq T u (lift h0 (r k d) v)))) (\lambda (e0: C).(\lambda
+(_: T).(drop h0 (r k d) c e0)))))))).(\lambda (u0: T).(\lambda (H4: (eq nat
+(S d0) (S d))).(\lambda (H5: (eq C (CHead c0 k0 (lift h0 (r k0 d0) u0))
+(CHead c k u))).(let TMP_100 \def (\lambda (e0: C).(match e0 with [(CSort _)
+\Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_101 \def (r k0
+d0) in (let TMP_102 \def (lift h0 TMP_101 u0) in (let TMP_103 \def (CHead c0
+k0 TMP_102) in (let TMP_104 \def (CHead c k u) in (let H6 \def (f_equal C C
+TMP_100 TMP_103 TMP_104 H5) in (let TMP_105 \def (\lambda (e0: C).(match e0
+with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) in (let
+TMP_106 \def (r k0 d0) in (let TMP_107 \def (lift h0 TMP_106 u0) in (let
+TMP_108 \def (CHead c0 k0 TMP_107) in (let TMP_109 \def (CHead c k u) in (let
+H7 \def (f_equal C K TMP_105 TMP_108 TMP_109 H5) in (let TMP_117 \def
+(\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow (let TMP_115 \def
+(\lambda (x0: nat).(plus x0 h0)) in (let TMP_116 \def (r k0 d0) in (lref_map
+TMP_115 TMP_116 u0))) | (CHead _ _ t) \Rightarrow t])) in (let TMP_118 \def
+(r k0 d0) in (let TMP_119 \def (lift h0 TMP_118 u0) in (let TMP_120 \def
+(CHead c0 k0 TMP_119) in (let TMP_121 \def (CHead c k u) in (let H8 \def
+(f_equal C T TMP_117 TMP_120 TMP_121 H5) in (let TMP_219 \def (\lambda (H9:
+(eq K k0 k)).(\lambda (H10: (eq C c0 c)).(let TMP_129 \def (\lambda (c1:
+C).((eq nat (r k0 d0) (S d)) \to ((eq C c1 (CHead c k u)) \to (let TMP_123
+\def (\lambda (e0: C).(\lambda (v: T).(let TMP_122 \def (CHead e0 k v) in (eq
+C e TMP_122)))) in (let TMP_126 \def (\lambda (_: C).(\lambda (v: T).(let
+TMP_124 \def (r k d) in (let TMP_125 \def (lift h0 TMP_124 v) in (eq T u
+TMP_125))))) in (let TMP_128 \def (\lambda (e0: C).(\lambda (_: T).(let
+TMP_127 \def (r k d) in (drop h0 TMP_127 c e0)))) in (ex3_2 C T TMP_123
+TMP_126 TMP_128))))))) in (let H11 \def (eq_ind C c0 TMP_129 H3 c H10) in
+(let TMP_131 \def (\lambda (c1: C).(let TMP_130 \def (r k0 d0) in (drop h0
+TMP_130 c1 e))) in (let H12 \def (eq_ind C c0 TMP_131 H2 c H10) in (let
+TMP_134 \def (\lambda (k1: K).(let TMP_132 \def (r k1 d0) in (let TMP_133
+\def (lift h0 TMP_132 u0) in (eq T TMP_133 u)))) in (let H13 \def (eq_ind K
+k0 TMP_134 H8 k H9) in (let TMP_142 \def (\lambda (k1: K).((eq nat (r k1 d0)
+(S d)) \to ((eq C c (CHead c k u)) \to (let TMP_136 \def (\lambda (e0:
+C).(\lambda (v: T).(let TMP_135 \def (CHead e0 k v) in (eq C e TMP_135)))) in
+(let TMP_139 \def (\lambda (_: C).(\lambda (v: T).(let TMP_137 \def (r k d)
+in (let TMP_138 \def (lift h0 TMP_137 v) in (eq T u TMP_138))))) in (let
+TMP_141 \def (\lambda (e0: C).(\lambda (_: T).(let TMP_140 \def (r k d) in
+(drop h0 TMP_140 c e0)))) in (ex3_2 C T TMP_136 TMP_139 TMP_141))))))) in
+(let H14 \def (eq_ind K k0 TMP_142 H11 k H9) in (let TMP_144 \def (\lambda
+(k1: K).(let TMP_143 \def (r k1 d0) in (drop h0 TMP_143 c e))) in (let H15
+\def (eq_ind K k0 TMP_144 H12 k H9) in (let TMP_153 \def (\lambda (k1:
+K).(let TMP_147 \def (\lambda (e0: C).(\lambda (v: T).(let TMP_145 \def
+(CHead e k1 u0) in (let TMP_146 \def (CHead e0 k v) in (eq C TMP_145
+TMP_146))))) in (let TMP_150 \def (\lambda (_: C).(\lambda (v: T).(let
+TMP_148 \def (r k d) in (let TMP_149 \def (lift h0 TMP_148 v) in (eq T u
+TMP_149))))) in (let TMP_152 \def (\lambda (e0: C).(\lambda (_: T).(let
+TMP_151 \def (r k d) in (drop h0 TMP_151 c e0)))) in (ex3_2 C T TMP_147
+TMP_150 TMP_152))))) in (let TMP_161 \def (\lambda (t: T).((eq nat (r k d0)
+(S d)) \to ((eq C c (CHead c k t)) \to (let TMP_155 \def (\lambda (e0:
+C).(\lambda (v: T).(let TMP_154 \def (CHead e0 k v) in (eq C e TMP_154)))) in
+(let TMP_158 \def (\lambda (_: C).(\lambda (v: T).(let TMP_156 \def (r k d)
+in (let TMP_157 \def (lift h0 TMP_156 v) in (eq T t TMP_157))))) in (let
+TMP_160 \def (\lambda (e0: C).(\lambda (_: T).(let TMP_159 \def (r k d) in
+(drop h0 TMP_159 c e0)))) in (ex3_2 C T TMP_155 TMP_158 TMP_160))))))) in
+(let TMP_162 \def (r k d0) in (let TMP_163 \def (lift h0 TMP_162 u0) in (let
+H16 \def (eq_ind_r T u TMP_161 H14 TMP_163 H13) in (let TMP_164 \def (r k d0)
+in (let TMP_165 \def (lift h0 TMP_164 u0) in (let TMP_174 \def (\lambda (t:
+T).(let TMP_168 \def (\lambda (e0: C).(\lambda (v: T).(let TMP_166 \def
+(CHead e k u0) in (let TMP_167 \def (CHead e0 k v) in (eq C TMP_166
+TMP_167))))) in (let TMP_171 \def (\lambda (_: C).(\lambda (v: T).(let
+TMP_169 \def (r k d) in (let TMP_170 \def (lift h0 TMP_169 v) in (eq T t
+TMP_170))))) in (let TMP_173 \def (\lambda (e0: C).(\lambda (_: T).(let
+TMP_172 \def (r k d) in (drop h0 TMP_172 c e0)))) in (ex3_2 C T TMP_168
+TMP_171 TMP_173))))) in (let TMP_175 \def (\lambda (e0: nat).(match e0 with
+[O \Rightarrow d0 | (S n) \Rightarrow n])) in (let TMP_176 \def (S d0) in
+(let TMP_177 \def (S d) in (let H17 \def (f_equal nat nat TMP_175 TMP_176
+TMP_177 H4) in (let TMP_187 \def (\lambda (n: nat).((eq nat (r k n) (S d))
+\to ((eq C c (CHead c k (lift h0 (r k n) u0))) \to (let TMP_179 \def (\lambda
+(e0: C).(\lambda (v: T).(let TMP_178 \def (CHead e0 k v) in (eq C e
+TMP_178)))) in (let TMP_184 \def (\lambda (_: C).(\lambda (v: T).(let TMP_180
+\def (r k n) in (let TMP_181 \def (lift h0 TMP_180 u0) in (let TMP_182 \def
+(r k d) in (let TMP_183 \def (lift h0 TMP_182 v) in (eq T TMP_181
+TMP_183))))))) in (let TMP_186 \def (\lambda (e0: C).(\lambda (_: T).(let
+TMP_185 \def (r k d) in (drop h0 TMP_185 c e0)))) in (ex3_2 C T TMP_179
+TMP_184 TMP_186))))))) in (let H18 \def (eq_ind nat d0 TMP_187 H16 d H17) in
+(let TMP_189 \def (\lambda (n: nat).(let TMP_188 \def (r k n) in (drop h0
+TMP_188 c e))) in (let H19 \def (eq_ind nat d0 TMP_189 H15 d H17) in (let
+TMP_200 \def (\lambda (n: nat).(let TMP_192 \def (\lambda (e0: C).(\lambda
+(v: T).(let TMP_190 \def (CHead e k u0) in (let TMP_191 \def (CHead e0 k v)
+in (eq C TMP_190 TMP_191))))) in (let TMP_197 \def (\lambda (_: C).(\lambda
+(v: T).(let TMP_193 \def (r k n) in (let TMP_194 \def (lift h0 TMP_193 u0) in
+(let TMP_195 \def (r k d) in (let TMP_196 \def (lift h0 TMP_195 v) in (eq T
+TMP_194 TMP_196))))))) in (let TMP_199 \def (\lambda (e0: C).(\lambda (_:
+T).(let TMP_198 \def (r k d) in (drop h0 TMP_198 c e0)))) in (ex3_2 C T
+TMP_192 TMP_197 TMP_199))))) in (let TMP_203 \def (\lambda (e0: C).(\lambda
+(v: T).(let TMP_201 \def (CHead e k u0) in (let TMP_202 \def (CHead e0 k v)
+in (eq C TMP_201 TMP_202))))) in (let TMP_208 \def (\lambda (_: C).(\lambda
+(v: T).(let TMP_204 \def (r k d) in (let TMP_205 \def (lift h0 TMP_204 u0) in
+(let TMP_206 \def (r k d) in (let TMP_207 \def (lift h0 TMP_206 v) in (eq T
+TMP_205 TMP_207))))))) in (let TMP_210 \def (\lambda (e0: C).(\lambda (_:
+T).(let TMP_209 \def (r k d) in (drop h0 TMP_209 c e0)))) in (let TMP_211
+\def (CHead e k u0) in (let TMP_212 \def (refl_equal C TMP_211) in (let
+TMP_213 \def (r k d) in (let TMP_214 \def (lift h0 TMP_213 u0) in (let
+TMP_215 \def (refl_equal T TMP_214) in (let TMP_216 \def (ex3_2_intro C T
+TMP_203 TMP_208 TMP_210 e u0 TMP_212 TMP_215 H19) in (let TMP_217 \def
+(eq_ind_r nat d TMP_200 TMP_216 d0 H17) in (let TMP_218 \def (eq_ind T
+TMP_165 TMP_174 TMP_217 u H13) in (eq_ind_r K k TMP_153 TMP_218 k0
+H9))))))))))))))))))))))))))))))))))))))))) in (let TMP_220 \def (TMP_219 H7)
+in (TMP_220 H6))))))))))))))))))))))))))))))) in (drop_ind TMP_29 TMP_51
+TMP_99 TMP_221 h y0 y x H1))))))) in (insert_eq nat TMP_12 TMP_13 TMP_21
+TMP_222 H0))))))) in (insert_eq C TMP_1 TMP_3 TMP_11 TMP_223 H))))))))))).
+
+theorem drop_S:
+ \forall (b: B).(\forall (c: C).(\forall (e: C).(\forall (u: T).(\forall (h:
+nat).((drop h O c (CHead e (Bind b) u)) \to (drop (S h) O c e))))))
+\def
+ \lambda (b: B).(\lambda (c: C).(let TMP_2 \def (\lambda (c0: C).(\forall (e:
+C).(\forall (u: T).(\forall (h: nat).((drop h O c0 (CHead e (Bind b) u)) \to
+(let TMP_1 \def (S h) in (drop TMP_1 O c0 e))))))) in (let TMP_27 \def
+(\lambda (n: nat).(\lambda (e: C).(\lambda (u: T).(\lambda (h: nat).(\lambda
+(H: (drop h O (CSort n) (CHead e (Bind b) u))).(let TMP_3 \def (Bind b) in
+(let TMP_4 \def (CHead e TMP_3 u) in (let TMP_5 \def (CSort n) in (let TMP_6
+\def (eq C TMP_4 TMP_5) in (let TMP_7 \def (eq nat h O) in (let TMP_8 \def
+(eq nat O O) in (let TMP_9 \def (S h) in (let TMP_10 \def (CSort n) in (let
+TMP_11 \def (drop TMP_9 O TMP_10 e) in (let TMP_23 \def (\lambda (H0: (eq C
+(CHead e (Bind b) u) (CSort n))).(\lambda (H1: (eq nat h O)).(\lambda (_: (eq
+nat O O)).(let TMP_14 \def (\lambda (n0: nat).(let TMP_12 \def (S n0) in (let
+TMP_13 \def (CSort n) in (drop TMP_12 O TMP_13 e)))) in (let TMP_15 \def
+(Bind b) in (let TMP_16 \def (CHead e TMP_15 u) in (let TMP_17 \def (\lambda
+(ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ _ _)
+\Rightarrow True])) in (let TMP_18 \def (CSort n) in (let H3 \def (eq_ind C
+TMP_16 TMP_17 I TMP_18 H0) in (let TMP_19 \def (S O) in (let TMP_20 \def
+(CSort n) in (let TMP_21 \def (drop TMP_19 O TMP_20 e) in (let TMP_22 \def
+(False_ind TMP_21 H3) in (eq_ind_r nat O TMP_14 TMP_22 h H1)))))))))))))) in
+(let TMP_24 \def (Bind b) in (let TMP_25 \def (CHead e TMP_24 u) in (let
+TMP_26 \def (drop_gen_sort n h O TMP_25 H) in (and3_ind TMP_6 TMP_7 TMP_8
+TMP_11 TMP_23 TMP_26))))))))))))))))))) in (let TMP_83 \def (\lambda (c0:
+C).(\lambda (H: ((\forall (e: C).(\forall (u: T).(\forall (h: nat).((drop h O
+c0 (CHead e (Bind b) u)) \to (drop (S h) O c0 e))))))).(\lambda (k:
+K).(\lambda (t: T).(\lambda (e: C).(\lambda (u: T).(\lambda (h: nat).(let
+TMP_30 \def (\lambda (n: nat).((drop n O (CHead c0 k t) (CHead e (Bind b) u))
+\to (let TMP_28 \def (S n) in (let TMP_29 \def (CHead c0 k t) in (drop TMP_28
+O TMP_29 e))))) in (let TMP_68 \def (\lambda (H0: (drop O O (CHead c0 k t)
+(CHead e (Bind b) u))).(let TMP_31 \def (\lambda (e0: C).(match e0 with
+[(CSort _) \Rightarrow c0 | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_32
+\def (CHead c0 k t) in (let TMP_33 \def (Bind b) in (let TMP_34 \def (CHead e
+TMP_33 u) in (let TMP_35 \def (CHead c0 k t) in (let TMP_36 \def (Bind b) in
+(let TMP_37 \def (CHead e TMP_36 u) in (let TMP_38 \def (drop_gen_refl TMP_35
+TMP_37 H0) in (let H1 \def (f_equal C C TMP_31 TMP_32 TMP_34 TMP_38) in (let
+TMP_39 \def (\lambda (e0: C).(match e0 with [(CSort _) \Rightarrow k | (CHead
+_ k0 _) \Rightarrow k0])) in (let TMP_40 \def (CHead c0 k t) in (let TMP_41
+\def (Bind b) in (let TMP_42 \def (CHead e TMP_41 u) in (let TMP_43 \def
+(CHead c0 k t) in (let TMP_44 \def (Bind b) in (let TMP_45 \def (CHead e
+TMP_44 u) in (let TMP_46 \def (drop_gen_refl TMP_43 TMP_45 H0) in (let H2
+\def (f_equal C K TMP_39 TMP_40 TMP_42 TMP_46) in (let TMP_47 \def (\lambda
+(e0: C).(match e0 with [(CSort _) \Rightarrow t | (CHead _ _ t0) \Rightarrow
+t0])) in (let TMP_48 \def (CHead c0 k t) in (let TMP_49 \def (Bind b) in (let
+TMP_50 \def (CHead e TMP_49 u) in (let TMP_51 \def (CHead c0 k t) in (let
+TMP_52 \def (Bind b) in (let TMP_53 \def (CHead e TMP_52 u) in (let TMP_54
+\def (drop_gen_refl TMP_51 TMP_53 H0) in (let H3 \def (f_equal C T TMP_47
+TMP_48 TMP_50 TMP_54) in (let TMP_66 \def (\lambda (H4: (eq K k (Bind
+b))).(\lambda (H5: (eq C c0 e)).(let TMP_57 \def (\lambda (c1: C).(let TMP_55
+\def (S O) in (let TMP_56 \def (CHead c0 k t) in (drop TMP_55 O TMP_56 c1))))
+in (let TMP_58 \def (Bind b) in (let TMP_61 \def (\lambda (k0: K).(let TMP_59
+\def (S O) in (let TMP_60 \def (CHead c0 k0 t) in (drop TMP_59 O TMP_60
+c0)))) in (let TMP_62 \def (Bind b) in (let TMP_63 \def (drop_refl c0) in
+(let TMP_64 \def (drop_drop TMP_62 O c0 c0 TMP_63 t) in (let TMP_65 \def
+(eq_ind_r K TMP_58 TMP_61 TMP_64 k H4) in (eq_ind C c0 TMP_57 TMP_65 e
+H5)))))))))) in (let TMP_67 \def (TMP_66 H2) in (TMP_67
+H1))))))))))))))))))))))))))))))) in (let TMP_82 \def (\lambda (n:
+nat).(\lambda (_: (((drop n O (CHead c0 k t) (CHead e (Bind b) u)) \to (drop
+(S n) O (CHead c0 k t) e)))).(\lambda (H1: (drop (S n) O (CHead c0 k t)
+(CHead e (Bind b) u))).(let TMP_69 \def (S n) in (let TMP_70 \def (r k n) in
+(let TMP_71 \def (S TMP_70) in (let TMP_72 \def (\lambda (n0: nat).(drop n0 O
+c0 e)) in (let TMP_73 \def (r k n) in (let TMP_74 \def (Bind b) in (let
+TMP_75 \def (CHead e TMP_74 u) in (let TMP_76 \def (drop_gen_drop k c0 TMP_75
+t n H1) in (let TMP_77 \def (H e u TMP_73 TMP_76) in (let TMP_78 \def (S n)
+in (let TMP_79 \def (r k TMP_78) in (let TMP_80 \def (r_S k n) in (let TMP_81
+\def (eq_ind_r nat TMP_71 TMP_72 TMP_77 TMP_79 TMP_80) in (drop_drop k TMP_69
+c0 e TMP_81 t))))))))))))))))) in (nat_ind TMP_30 TMP_68 TMP_82 h)))))))))))
+in (C_ind TMP_2 TMP_27 TMP_83 c))))).
+
+theorem drop_mono:
+ \forall (c: C).(\forall (x1: C).(\forall (d: nat).(\forall (h: nat).((drop h
+d c x1) \to (\forall (x2: C).((drop h d c x2) \to (eq C x1 x2)))))))
+\def
+ \lambda (c: C).(let TMP_1 \def (\lambda (c0: C).(\forall (x1: C).(\forall
+(d: nat).(\forall (h: nat).((drop h d c0 x1) \to (\forall (x2: C).((drop h d
+c0 x2) \to (eq C x1 x2)))))))) in (let TMP_26 \def (\lambda (n: nat).(\lambda
+(x1: C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n)
+x1)).(\lambda (x2: C).(\lambda (H0: (drop h d (CSort n) x2)).(let TMP_2 \def
+(CSort n) in (let TMP_3 \def (eq C x2 TMP_2) in (let TMP_4 \def (eq nat h O)
+in (let TMP_5 \def (eq nat d O) in (let TMP_6 \def (eq C x1 x2) in (let
+TMP_24 \def (\lambda (H1: (eq C x2 (CSort n))).(\lambda (H2: (eq nat h
+O)).(\lambda (H3: (eq nat d O)).(let TMP_7 \def (CSort n) in (let TMP_8 \def
+(eq C x1 TMP_7) in (let TMP_9 \def (eq nat h O) in (let TMP_10 \def (eq nat d
+O) in (let TMP_11 \def (eq C x1 x2) in (let TMP_22 \def (\lambda (H4: (eq C
+x1 (CSort n))).(\lambda (H5: (eq nat h O)).(\lambda (H6: (eq nat d O)).(let
+TMP_12 \def (CSort n) in (let TMP_13 \def (\lambda (c0: C).(eq C x1 c0)) in
+(let TMP_14 \def (\lambda (n0: nat).(eq nat n0 O)) in (let H7 \def (eq_ind
+nat h TMP_14 H2 O H5) in (let TMP_15 \def (\lambda (n0: nat).(eq nat n0 O))
+in (let H8 \def (eq_ind nat d TMP_15 H3 O H6) in (let TMP_16 \def (CSort n)
+in (let TMP_18 \def (\lambda (c0: C).(let TMP_17 \def (CSort n) in (eq C c0
+TMP_17))) in (let TMP_19 \def (CSort n) in (let TMP_20 \def (refl_equal C
+TMP_19) in (let TMP_21 \def (eq_ind_r C TMP_16 TMP_18 TMP_20 x1 H4) in
+(eq_ind_r C TMP_12 TMP_13 TMP_21 x2 H1))))))))))))))) in (let TMP_23 \def
+(drop_gen_sort n h d x1 H) in (and3_ind TMP_8 TMP_9 TMP_10 TMP_11 TMP_22
+TMP_23))))))))))) in (let TMP_25 \def (drop_gen_sort n h d x2 H0) in
+(and3_ind TMP_3 TMP_4 TMP_5 TMP_6 TMP_24 TMP_25))))))))))))))) in (let
+TMP_109 \def (\lambda (c0: C).(\lambda (H: ((\forall (x1: C).(\forall (d:
+nat).(\forall (h: nat).((drop h d c0 x1) \to (\forall (x2: C).((drop h d c0
+x2) \to (eq C x1 x2))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (x1:
+C).(\lambda (d: nat).(let TMP_27 \def (\lambda (n: nat).(\forall (h:
+nat).((drop h n (CHead c0 k t) x1) \to (\forall (x2: C).((drop h n (CHead c0
+k t) x2) \to (eq C x1 x2)))))) in (let TMP_46 \def (\lambda (h: nat).(let
+TMP_28 \def (\lambda (n: nat).((drop n O (CHead c0 k t) x1) \to (\forall (x2:
+C).((drop n O (CHead c0 k t) x2) \to (eq C x1 x2))))) in (let TMP_41 \def
+(\lambda (H0: (drop O O (CHead c0 k t) x1)).(\lambda (x2: C).(\lambda (H1:
+(drop O O (CHead c0 k t) x2)).(let TMP_29 \def (CHead c0 k t) in (let TMP_30
+\def (\lambda (c1: C).(eq C x1 c1)) in (let TMP_31 \def (CHead c0 k t) in
+(let TMP_33 \def (\lambda (c1: C).(let TMP_32 \def (CHead c0 k t) in (eq C c1
+TMP_32))) in (let TMP_34 \def (CHead c0 k t) in (let TMP_35 \def (refl_equal
+C TMP_34) in (let TMP_36 \def (CHead c0 k t) in (let TMP_37 \def
+(drop_gen_refl TMP_36 x1 H0) in (let TMP_38 \def (eq_ind C TMP_31 TMP_33
+TMP_35 x1 TMP_37) in (let TMP_39 \def (CHead c0 k t) in (let TMP_40 \def
+(drop_gen_refl TMP_39 x2 H1) in (eq_ind C TMP_29 TMP_30 TMP_38 x2
+TMP_40))))))))))))))) in (let TMP_45 \def (\lambda (n: nat).(\lambda (_:
+(((drop n O (CHead c0 k t) x1) \to (\forall (x2: C).((drop n O (CHead c0 k t)
+x2) \to (eq C x1 x2)))))).(\lambda (H1: (drop (S n) O (CHead c0 k t)
+x1)).(\lambda (x2: C).(\lambda (H2: (drop (S n) O (CHead c0 k t) x2)).(let
+TMP_42 \def (r k n) in (let TMP_43 \def (drop_gen_drop k c0 x1 t n H1) in
+(let TMP_44 \def (drop_gen_drop k c0 x2 t n H2) in (H x1 O TMP_42 TMP_43 x2
+TMP_44))))))))) in (nat_ind TMP_28 TMP_41 TMP_45 h))))) in (let TMP_108 \def
+(\lambda (n: nat).(\lambda (H0: ((\forall (h: nat).((drop h n (CHead c0 k t)
+x1) \to (\forall (x2: C).((drop h n (CHead c0 k t) x2) \to (eq C x1
+x2))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c0 k t)
+x1)).(\lambda (x2: C).(\lambda (H2: (drop h (S n) (CHead c0 k t) x2)).(let
+TMP_48 \def (\lambda (e: C).(\lambda (v: T).(let TMP_47 \def (CHead e k v) in
+(eq C x2 TMP_47)))) in (let TMP_51 \def (\lambda (_: C).(\lambda (v: T).(let
+TMP_49 \def (r k n) in (let TMP_50 \def (lift h TMP_49 v) in (eq T t
+TMP_50))))) in (let TMP_53 \def (\lambda (e: C).(\lambda (_: T).(let TMP_52
+\def (r k n) in (drop h TMP_52 c0 e)))) in (let TMP_54 \def (eq C x1 x2) in
+(let TMP_106 \def (\lambda (x0: C).(\lambda (x3: T).(\lambda (H3: (eq C x2
+(CHead x0 k x3))).(\lambda (H4: (eq T t (lift h (r k n) x3))).(\lambda (H5:
+(drop h (r k n) c0 x0)).(let TMP_56 \def (\lambda (e: C).(\lambda (v: T).(let
+TMP_55 \def (CHead e k v) in (eq C x1 TMP_55)))) in (let TMP_59 \def (\lambda
+(_: C).(\lambda (v: T).(let TMP_57 \def (r k n) in (let TMP_58 \def (lift h
+TMP_57 v) in (eq T t TMP_58))))) in (let TMP_61 \def (\lambda (e: C).(\lambda
+(_: T).(let TMP_60 \def (r k n) in (drop h TMP_60 c0 e)))) in (let TMP_62
+\def (eq C x1 x2) in (let TMP_104 \def (\lambda (x4: C).(\lambda (x5:
+T).(\lambda (H6: (eq C x1 (CHead x4 k x5))).(\lambda (H7: (eq T t (lift h (r
+k n) x5))).(\lambda (H8: (drop h (r k n) c0 x4)).(let TMP_63 \def (CHead x0 k
+x3) in (let TMP_64 \def (\lambda (c1: C).(eq C x1 c1)) in (let TMP_65 \def
+(\lambda (c1: C).(\forall (h0: nat).((drop h0 n (CHead c0 k t) c1) \to
+(\forall (x6: C).((drop h0 n (CHead c0 k t) x6) \to (eq C c1 x6)))))) in (let
+TMP_66 \def (CHead x4 k x5) in (let H9 \def (eq_ind C x1 TMP_65 H0 TMP_66 H6)
+in (let TMP_67 \def (CHead x4 k x5) in (let TMP_69 \def (\lambda (c1: C).(let
+TMP_68 \def (CHead x0 k x3) in (eq C c1 TMP_68))) in (let TMP_71 \def
+(\lambda (t0: T).(\forall (h0: nat).((drop h0 n (CHead c0 k t0) (CHead x4 k
+x5)) \to (\forall (x6: C).((drop h0 n (CHead c0 k t0) x6) \to (let TMP_70
+\def (CHead x4 k x5) in (eq C TMP_70 x6))))))) in (let TMP_72 \def (r k n) in
+(let TMP_73 \def (lift h TMP_72 x5) in (let H10 \def (eq_ind T t TMP_71 H9
+TMP_73 H7) in (let TMP_76 \def (\lambda (t0: T).(let TMP_74 \def (r k n) in
+(let TMP_75 \def (lift h TMP_74 x3) in (eq T t0 TMP_75)))) in (let TMP_77
+\def (r k n) in (let TMP_78 \def (lift h TMP_77 x5) in (let H11 \def (eq_ind
+T t TMP_76 H4 TMP_78 H7) in (let TMP_80 \def (\lambda (t0: T).(\forall (h0:
+nat).((drop h0 n (CHead c0 k (lift h (r k n) t0)) (CHead x4 k t0)) \to
+(\forall (x6: C).((drop h0 n (CHead c0 k (lift h (r k n) t0)) x6) \to (let
+TMP_79 \def (CHead x4 k t0) in (eq C TMP_79 x6))))))) in (let TMP_81 \def (r
+k n) in (let TMP_82 \def (lift_inj x5 x3 h TMP_81 H11) in (let H12 \def
+(eq_ind T x5 TMP_80 H10 x3 TMP_82) in (let TMP_85 \def (\lambda (t0: T).(let
+TMP_83 \def (CHead x4 k t0) in (let TMP_84 \def (CHead x0 k x3) in (eq C
+TMP_83 TMP_84)))) in (let TMP_86 \def (CHead x0 k x3) in (let TMP_87 \def
+(CHead x4 k x3) in (let TMP_88 \def (CHead x4 k x3) in (let TMP_89 \def
+(CHead x0 k x3) in (let TMP_90 \def (CHead x0 k x3) in (let TMP_91 \def
+(CHead x4 k x3) in (let TMP_92 \def (r k n) in (let TMP_93 \def (H x0 TMP_92
+h H5 x4 H8) in (let TMP_94 \def (refl_equal K k) in (let TMP_95 \def
+(refl_equal T x3) in (let TMP_96 \def (f_equal3 C K T C CHead x0 x4 k k x3 x3
+TMP_93 TMP_94 TMP_95) in (let TMP_97 \def (sym_eq C TMP_90 TMP_91 TMP_96) in
+(let TMP_98 \def (sym_eq C TMP_88 TMP_89 TMP_97) in (let TMP_99 \def (sym_eq
+C TMP_86 TMP_87 TMP_98) in (let TMP_100 \def (r k n) in (let TMP_101 \def
+(lift_inj x5 x3 h TMP_100 H11) in (let TMP_102 \def (eq_ind_r T x3 TMP_85
+TMP_99 x5 TMP_101) in (let TMP_103 \def (eq_ind_r C TMP_67 TMP_69 TMP_102 x1
+H6) in (eq_ind_r C TMP_63 TMP_64 TMP_103 x2
+H3)))))))))))))))))))))))))))))))))))))))))))) in (let TMP_105 \def
+(drop_gen_skip_l c0 x1 t h n k H1) in (ex3_2_ind C T TMP_56 TMP_59 TMP_61
+TMP_62 TMP_104 TMP_105)))))))))))) in (let TMP_107 \def (drop_gen_skip_l c0
+x2 t h n k H2) in (ex3_2_ind C T TMP_48 TMP_51 TMP_53 TMP_54 TMP_106
+TMP_107))))))))))))) in (nat_ind TMP_27 TMP_46 TMP_108 d)))))))))) in (C_ind
+TMP_1 TMP_26 TMP_109 c)))).
projects / helm.git / blobdiff