X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2Fcsubc%2Fdrop.ma;h=eb4169f05f84d5f45460dfbc01786bba97b6db68;hb=57e01777627e779555dc091a58ec2f4f860ee51f;hp=195d3649147f132fc0ce3bff467b48fb8e4d1365;hpb=049d55c73d1746e15a40e89b17fd88b62f002d93;p=helm.git diff --git a/matita/matita/contribs/lambdadelta/basic_1/csubc/drop.ma b/matita/matita/contribs/lambdadelta/basic_1/csubc/drop.ma index 195d36491..eb4169f05 100644 --- a/matita/matita/contribs/lambdadelta/basic_1/csubc/drop.ma +++ b/matita/matita/contribs/lambdadelta/basic_1/csubc/drop.ma @@ -14,462 +14,806 @@ (* This file was automatically generated: do not edit *********************) -include "Basic-1/csubc/fwd.ma". +include "basic_1/csubc/fwd.ma". -include "Basic-1/sc3/props.ma". +include "basic_1/sc3/props.ma". theorem csubc_drop_conf_O: \forall (g: G).(\forall (c1: C).(\forall (e1: C).(\forall (h: nat).((drop h O c1 e1) \to (\forall (c2: C).((csubc g c1 c2) \to (ex2 C (\lambda (e2: C).(drop h O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))))))))) \def - \lambda (g: G).(\lambda (c1: C).(C_ind (\lambda (c: C).(\forall (e1: -C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2: C).((csubc g c c2) -\to (ex2 C (\lambda (e2: C).(drop h O c2 e2)) (\lambda (e2: C).(csubc g e1 -e2))))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (h: nat).(\lambda (H: + \lambda (g: G).(\lambda (c1: C).(let TMP_3 \def (\lambda (c: C).(\forall +(e1: C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2: C).((csubc g c +c2) \to (let TMP_1 \def (\lambda (e2: C).(drop h O c2 e2)) in (let TMP_2 \def +(\lambda (e2: C).(csubc g e1 e2)) in (ex2 C TMP_1 TMP_2))))))))) in (let +TMP_26 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (h: nat).(\lambda (H: (drop h O (CSort n) e1)).(\lambda (c2: C).(\lambda (H0: (csubc g (CSort n) -c2)).(and3_ind (eq C e1 (CSort n)) (eq nat h O) (eq nat O O) (ex2 C (\lambda -(e2: C).(drop h O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (H1: -(eq C e1 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (_: (eq nat O -O)).(eq_ind_r nat O (\lambda (n0: nat).(ex2 C (\lambda (e2: C).(drop n0 O c2 -e2)) (\lambda (e2: C).(csubc g e1 e2)))) (eq_ind_r C (CSort n) (\lambda (c: -C).(ex2 C (\lambda (e2: C).(drop O O c2 e2)) (\lambda (e2: C).(csubc g c -e2)))) (ex_intro2 C (\lambda (e2: C).(drop O O c2 e2)) (\lambda (e2: -C).(csubc g (CSort n) e2)) c2 (drop_refl c2) H0) e1 H1) h H2)))) -(drop_gen_sort n h O e1 H)))))))) (\lambda (c: C).(\lambda (H: ((\forall (e1: -C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2: C).((csubc g c c2) -\to (ex2 C (\lambda (e2: C).(drop h O c2 e2)) (\lambda (e2: C).(csubc g e1 -e2)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e1: C).(\lambda (h: -nat).(nat_ind (\lambda (n: nat).((drop n O (CHead c k t) e1) \to (\forall -(c2: C).((csubc g (CHead c k t) c2) \to (ex2 C (\lambda (e2: C).(drop n O c2 -e2)) (\lambda (e2: C).(csubc g e1 e2))))))) (\lambda (H0: (drop O O (CHead c -k t) e1)).(\lambda (c2: C).(\lambda (H1: (csubc g (CHead c k t) c2)).(eq_ind -C (CHead c k t) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(drop O O c2 e2)) -(\lambda (e2: C).(csubc g c0 e2)))) (ex_intro2 C (\lambda (e2: C).(drop O O -c2 e2)) (\lambda (e2: C).(csubc g (CHead c k t) e2)) c2 (drop_refl c2) H1) e1 -(drop_gen_refl (CHead c k t) e1 H0))))) (\lambda (n: nat).(\lambda (H0: -(((drop n O (CHead c k t) e1) \to (\forall (c2: C).((csubc g (CHead c k t) -c2) \to (ex2 C (\lambda (e2: C).(drop n O c2 e2)) (\lambda (e2: C).(csubc g -e1 e2)))))))).(\lambda (H1: (drop (S n) O (CHead c k t) e1)).(\lambda (c2: +c2)).(let TMP_4 \def (CSort n) in (let TMP_5 \def (eq C e1 TMP_4) in (let +TMP_6 \def (eq nat h O) in (let TMP_7 \def (eq nat O O) in (let TMP_8 \def +(\lambda (e2: C).(drop h O c2 e2)) in (let TMP_9 \def (\lambda (e2: C).(csubc +g e1 e2)) in (let TMP_10 \def (ex2 C TMP_8 TMP_9) in (let TMP_24 \def +(\lambda (H1: (eq C e1 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (_: +(eq nat O O)).(let TMP_13 \def (\lambda (n0: nat).(let TMP_11 \def (\lambda +(e2: C).(drop n0 O c2 e2)) in (let TMP_12 \def (\lambda (e2: C).(csubc g e1 +e2)) in (ex2 C TMP_11 TMP_12)))) in (let TMP_14 \def (CSort n) in (let TMP_17 +\def (\lambda (c: C).(let TMP_15 \def (\lambda (e2: C).(drop O O c2 e2)) in +(let TMP_16 \def (\lambda (e2: C).(csubc g c e2)) in (ex2 C TMP_15 TMP_16)))) +in (let TMP_18 \def (\lambda (e2: C).(drop O O c2 e2)) in (let TMP_20 \def +(\lambda (e2: C).(let TMP_19 \def (CSort n) in (csubc g TMP_19 e2))) in (let +TMP_21 \def (drop_refl c2) in (let TMP_22 \def (ex_intro2 C TMP_18 TMP_20 c2 +TMP_21 H0) in (let TMP_23 \def (eq_ind_r C TMP_14 TMP_17 TMP_22 e1 H1) in +(eq_ind_r nat O TMP_13 TMP_23 h H2)))))))))))) in (let TMP_25 \def +(drop_gen_sort n h O e1 H) in (and3_ind TMP_5 TMP_6 TMP_7 TMP_10 TMP_24 +TMP_25)))))))))))))))) in (let TMP_196 \def (\lambda (c: C).(\lambda (H: +((\forall (e1: C).(\forall (h: nat).((drop h O c e1) \to (\forall (c2: +C).((csubc g c c2) \to (ex2 C (\lambda (e2: C).(drop h O c2 e2)) (\lambda +(e2: C).(csubc g e1 e2)))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda +(e1: C).(\lambda (h: nat).(let TMP_29 \def (\lambda (n: nat).((drop n O +(CHead c k t) e1) \to (\forall (c2: C).((csubc g (CHead c k t) c2) \to (let +TMP_27 \def (\lambda (e2: C).(drop n O c2 e2)) in (let TMP_28 \def (\lambda +(e2: C).(csubc g e1 e2)) in (ex2 C TMP_27 TMP_28))))))) in (let TMP_41 \def +(\lambda (H0: (drop O O (CHead c k t) e1)).(\lambda (c2: C).(\lambda (H1: +(csubc g (CHead c k t) c2)).(let TMP_30 \def (CHead c k t) in (let TMP_33 +\def (\lambda (c0: C).(let TMP_31 \def (\lambda (e2: C).(drop O O c2 e2)) in +(let TMP_32 \def (\lambda (e2: C).(csubc g c0 e2)) in (ex2 C TMP_31 +TMP_32)))) in (let TMP_34 \def (\lambda (e2: C).(drop O O c2 e2)) in (let +TMP_36 \def (\lambda (e2: C).(let TMP_35 \def (CHead c k t) in (csubc g +TMP_35 e2))) in (let TMP_37 \def (drop_refl c2) in (let TMP_38 \def +(ex_intro2 C TMP_34 TMP_36 c2 TMP_37 H1) in (let TMP_39 \def (CHead c k t) in +(let TMP_40 \def (drop_gen_refl TMP_39 e1 H0) in (eq_ind C TMP_30 TMP_33 +TMP_38 e1 TMP_40)))))))))))) in (let TMP_195 \def (\lambda (n: nat).(\lambda +(H0: (((drop n O (CHead c k t) e1) \to (\forall (c2: C).((csubc g (CHead c k +t) c2) \to (ex2 C (\lambda (e2: C).(drop n O c2 e2)) (\lambda (e2: C).(csubc +g e1 e2)))))))).(\lambda (H1: (drop (S n) O (CHead c k t) e1)).(\lambda (c2: C).(\lambda (H2: (csubc g (CHead c k t) c2)).(let H_x \def (csubc_gen_head_l -g c c2 t k H2) in (let H3 \def H_x in (or3_ind (ex2 C (\lambda (c3: C).(eq C -c2 (CHead c3 k t))) (\lambda (c3: C).(csubc g c c3))) (ex5_3 C T A (\lambda -(_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3: -C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) -(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) (\lambda -(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c t)))) (\lambda -(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w))))) (ex4_3 B C T -(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) -v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind -Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b -Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c c3))))) -(ex2 C (\lambda (e2: C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 -e2))) (\lambda (H4: (ex2 C (\lambda (c3: C).(eq C c2 (CHead c3 k t))) -(\lambda (c3: C).(csubc g c c3)))).(ex2_ind C (\lambda (c3: C).(eq C c2 -(CHead c3 k t))) (\lambda (c3: C).(csubc g c c3)) (ex2 C (\lambda (e2: -C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x: -C).(\lambda (H5: (eq C c2 (CHead x k t))).(\lambda (H6: (csubc g c -x)).(eq_ind_r C (CHead x k t) (\lambda (c0: C).(ex2 C (\lambda (e2: C).(drop -(S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2)))) (let H_x0 \def (H e1 (r k -n) (drop_gen_drop k c e1 t n H1) x H6) in (let H7 \def H_x0 in (ex2_ind C -(\lambda (e2: C).(drop (r k n) O x e2)) (\lambda (e2: C).(csubc g e1 e2)) -(ex2 C (\lambda (e2: C).(drop (S n) O (CHead x k t) e2)) (\lambda (e2: -C).(csubc g e1 e2))) (\lambda (x0: C).(\lambda (H8: (drop (r k n) O x -x0)).(\lambda (H9: (csubc g e1 x0)).(ex_intro2 C (\lambda (e2: C).(drop (S n) -O (CHead x k t) e2)) (\lambda (e2: C).(csubc g e1 e2)) x0 (drop_drop k n x x0 -H8 t) H9)))) H7))) c2 H5)))) H4)) (\lambda (H4: (ex5_3 C T A (\lambda (_: -C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3: -C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind Abbr) w))))) -(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) (\lambda -(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c t)))) (\lambda -(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A -(\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) -(\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C c2 (CHead c3 (Bind -Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c -c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) c -t)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) (ex2 -C (\lambda (e2: C).(drop (S n) O c2 e2)) (\lambda (e2: C).(csubc g e1 e2))) -(\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: A).(\lambda (H5: (eq K k -(Bind Abst))).(\lambda (H6: (eq C c2 (CHead x0 (Bind Abbr) x1))).(\lambda -(H7: (csubc g c x0)).(\lambda (_: (sc3 g (asucc g x2) c t)).(\lambda (_: (sc3 -g x2 x0 x1)).(eq_ind_r C (CHead x0 (Bind Abbr) x1) (\lambda (c0: C).(ex2 C -(\lambda (e2: C).(drop (S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2)))) -(let H10 \def (eq_ind K k (\lambda (k0: K).(drop (r k0 n) O c e1)) -(drop_gen_drop k c e1 t n H1) (Bind Abst) H5) in (let H11 \def (eq_ind K k -(\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3: C).((csubc g -(CHead c k0 t) c3) \to (ex2 C (\lambda (e2: C).(drop n O c3 e2)) (\lambda -(e2: C).(csubc g e1 e2))))))) H0 (Bind Abst) H5) in (let H_x0 \def (H e1 (r -(Bind Abst) n) H10 x0 H7) in (let H12 \def H_x0 in (ex2_ind C (\lambda (e2: -C).(drop n O x0 e2)) (\lambda (e2: C).(csubc g e1 e2)) (ex2 C (\lambda (e2: -C).(drop (S n) O (CHead x0 (Bind Abbr) x1) e2)) (\lambda (e2: C).(csubc g e1 -e2))) (\lambda (x: C).(\lambda (H13: (drop n O x0 x)).(\lambda (H14: (csubc g -e1 x)).(ex_intro2 C (\lambda (e2: C).(drop (S n) O (CHead x0 (Bind Abbr) x1) -e2)) (\lambda (e2: C).(csubc g e1 e2)) x (drop_drop (Bind Abbr) n x0 x H13 -x1) H14)))) H12))))) c2 H6))))))))) H4)) (\lambda (H4: (ex4_3 B C T (\lambda -(b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) -(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) -(\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) -(\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c -c3)))))).(ex4_3_ind B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: -T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: -C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_: -C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: -C).(\lambda (_: T).(csubc g c c3)))) (ex2 C (\lambda (e2: C).(drop (S n) O c2 -e2)) (\lambda (e2: C).(csubc g e1 e2))) (\lambda (x0: B).(\lambda (x1: -C).(\lambda (x2: T).(\lambda (H5: (eq C c2 (CHead x1 (Bind x0) x2))).(\lambda -(H6: (eq K k (Bind Void))).(\lambda (_: (not (eq B x0 Void))).(\lambda (H8: -(csubc g c x1)).(eq_ind_r C (CHead x1 (Bind x0) x2) (\lambda (c0: C).(ex2 C -(\lambda (e2: C).(drop (S n) O c0 e2)) (\lambda (e2: C).(csubc g e1 e2)))) -(let H9 \def (eq_ind K k (\lambda (k0: K).(drop (r k0 n) O c e1)) -(drop_gen_drop k c e1 t n H1) (Bind Void) H6) in (let H10 \def (eq_ind K k -(\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3: C).((csubc g -(CHead c k0 t) c3) \to (ex2 C (\lambda (e2: C).(drop n O c3 e2)) (\lambda -(e2: C).(csubc g e1 e2))))))) H0 (Bind Void) H6) in (let H_x0 \def (H e1 (r -(Bind Void) n) H9 x1 H8) in (let H11 \def H_x0 in (ex2_ind C (\lambda (e2: -C).(drop n O x1 e2)) (\lambda (e2: C).(csubc g e1 e2)) (ex2 C (\lambda (e2: -C).(drop (S n) O (CHead x1 (Bind x0) x2) e2)) (\lambda (e2: C).(csubc g e1 -e2))) (\lambda (x: C).(\lambda (H12: (drop n O x1 x)).(\lambda (H13: (csubc g -e1 x)).(ex_intro2 C (\lambda (e2: C).(drop (S n) O (CHead x1 (Bind x0) x2) -e2)) (\lambda (e2: C).(csubc g e1 e2)) x (drop_drop (Bind x0) n x1 x H12 x2) -H13)))) H11))))) c2 H5)))))))) H4)) H3)))))))) h))))))) c1)). -(* COMMENTS -Initial nodes: 2389 -END *) +g c c2 t k H2) in (let H3 \def H_x in (let TMP_43 \def (\lambda (c3: C).(let +TMP_42 \def (CHead c3 k t) in (eq C c2 TMP_42))) in (let TMP_44 \def (\lambda +(c3: C).(csubc g c c3)) in (let TMP_45 \def (ex2 C TMP_43 TMP_44) in (let +TMP_47 \def (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(let TMP_46 \def +(Bind Abst) in (eq K k TMP_46))))) in (let TMP_50 \def (\lambda (c3: +C).(\lambda (w: T).(\lambda (_: A).(let TMP_48 \def (Bind Abbr) in (let +TMP_49 \def (CHead c3 TMP_48 w) in (eq C c2 TMP_49)))))) in (let TMP_51 \def +(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g c c3)))) in (let +TMP_53 \def (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(let TMP_52 \def +(asucc g a) in (sc3 g TMP_52 c t))))) in (let TMP_54 \def (\lambda (c3: +C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_55 \def +(ex5_3 C T A TMP_47 TMP_50 TMP_51 TMP_53 TMP_54) in (let TMP_58 \def (\lambda +(b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_56 \def (Bind b) in (let +TMP_57 \def (CHead c3 TMP_56 v2) in (eq C c2 TMP_57)))))) in (let TMP_60 \def +(\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_59 \def (Bind Void) +in (eq K k TMP_59))))) in (let TMP_62 \def (\lambda (b: B).(\lambda (_: +C).(\lambda (_: T).(let TMP_61 \def (eq B b Void) in (not TMP_61))))) in (let +TMP_63 \def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc g c +c3)))) in (let TMP_64 \def (ex4_3 B C T TMP_58 TMP_60 TMP_62 TMP_63) in (let +TMP_66 \def (\lambda (e2: C).(let TMP_65 \def (S n) in (drop TMP_65 O c2 +e2))) in (let TMP_67 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_68 +\def (ex2 C TMP_66 TMP_67) in (let TMP_99 \def (\lambda (H4: (ex2 C (\lambda +(c3: C).(eq C c2 (CHead c3 k t))) (\lambda (c3: C).(csubc g c c3)))).(let +TMP_70 \def (\lambda (c3: C).(let TMP_69 \def (CHead c3 k t) in (eq C c2 +TMP_69))) in (let TMP_71 \def (\lambda (c3: C).(csubc g c c3)) in (let TMP_73 +\def (\lambda (e2: C).(let TMP_72 \def (S n) in (drop TMP_72 O c2 e2))) in +(let TMP_74 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_75 \def (ex2 C +TMP_73 TMP_74) in (let TMP_98 \def (\lambda (x: C).(\lambda (H5: (eq C c2 +(CHead x k t))).(\lambda (H6: (csubc g c x)).(let TMP_76 \def (CHead x k t) +in (let TMP_80 \def (\lambda (c0: C).(let TMP_78 \def (\lambda (e2: C).(let +TMP_77 \def (S n) in (drop TMP_77 O c0 e2))) in (let TMP_79 \def (\lambda +(e2: C).(csubc g e1 e2)) in (ex2 C TMP_78 TMP_79)))) in (let TMP_81 \def (r k +n) in (let TMP_82 \def (drop_gen_drop k c e1 t n H1) in (let H_x0 \def (H e1 +TMP_81 TMP_82 x H6) in (let H7 \def H_x0 in (let TMP_84 \def (\lambda (e2: +C).(let TMP_83 \def (r k n) in (drop TMP_83 O x e2))) in (let TMP_85 \def +(\lambda (e2: C).(csubc g e1 e2)) in (let TMP_88 \def (\lambda (e2: C).(let +TMP_86 \def (S n) in (let TMP_87 \def (CHead x k t) in (drop TMP_86 O TMP_87 +e2)))) in (let TMP_89 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_90 +\def (ex2 C TMP_88 TMP_89) in (let TMP_96 \def (\lambda (x0: C).(\lambda (H8: +(drop (r k n) O x x0)).(\lambda (H9: (csubc g e1 x0)).(let TMP_93 \def +(\lambda (e2: C).(let TMP_91 \def (S n) in (let TMP_92 \def (CHead x k t) in +(drop TMP_91 O TMP_92 e2)))) in (let TMP_94 \def (\lambda (e2: C).(csubc g e1 +e2)) in (let TMP_95 \def (drop_drop k n x x0 H8 t) in (ex_intro2 C TMP_93 +TMP_94 x0 TMP_95 H9))))))) in (let TMP_97 \def (ex2_ind C TMP_84 TMP_85 +TMP_90 TMP_96 H7) in (eq_ind_r C TMP_76 TMP_80 TMP_97 c2 H5))))))))))))))))) +in (ex2_ind C TMP_70 TMP_71 TMP_75 TMP_98 H4)))))))) in (let TMP_147 \def +(\lambda (H4: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: +A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: +A).(eq C c2 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: +T).(\lambda (_: A).(csubc g c c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda +(a: A).(sc3 g (asucc g a) c t)))) (\lambda (c3: C).(\lambda (w: T).(\lambda +(a: A).(sc3 g a c3 w)))))).(let TMP_101 \def (\lambda (_: C).(\lambda (_: +T).(\lambda (_: A).(let TMP_100 \def (Bind Abst) in (eq K k TMP_100))))) in +(let TMP_104 \def (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(let +TMP_102 \def (Bind Abbr) in (let TMP_103 \def (CHead c3 TMP_102 w) in (eq C +c2 TMP_103)))))) in (let TMP_105 \def (\lambda (c3: C).(\lambda (_: +T).(\lambda (_: A).(csubc g c c3)))) in (let TMP_107 \def (\lambda (_: +C).(\lambda (_: T).(\lambda (a: A).(let TMP_106 \def (asucc g a) in (sc3 g +TMP_106 c t))))) in (let TMP_108 \def (\lambda (c3: C).(\lambda (w: +T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_110 \def (\lambda (e2: +C).(let TMP_109 \def (S n) in (drop TMP_109 O c2 e2))) in (let TMP_111 \def +(\lambda (e2: C).(csubc g e1 e2)) in (let TMP_112 \def (ex2 C TMP_110 +TMP_111) in (let TMP_146 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: +A).(\lambda (H5: (eq K k (Bind Abst))).(\lambda (H6: (eq C c2 (CHead x0 (Bind +Abbr) x1))).(\lambda (H7: (csubc g c x0)).(\lambda (_: (sc3 g (asucc g x2) c +t)).(\lambda (_: (sc3 g x2 x0 x1)).(let TMP_113 \def (Bind Abbr) in (let +TMP_114 \def (CHead x0 TMP_113 x1) in (let TMP_118 \def (\lambda (c0: C).(let +TMP_116 \def (\lambda (e2: C).(let TMP_115 \def (S n) in (drop TMP_115 O c0 +e2))) in (let TMP_117 \def (\lambda (e2: C).(csubc g e1 e2)) in (ex2 C +TMP_116 TMP_117)))) in (let TMP_120 \def (\lambda (k0: K).(let TMP_119 \def +(r k0 n) in (drop TMP_119 O c e1))) in (let TMP_121 \def (drop_gen_drop k c +e1 t n H1) in (let TMP_122 \def (Bind Abst) in (let H10 \def (eq_ind K k +TMP_120 TMP_121 TMP_122 H5) in (let TMP_125 \def (\lambda (k0: K).((drop n O +(CHead c k0 t) e1) \to (\forall (c3: C).((csubc g (CHead c k0 t) c3) \to (let +TMP_123 \def (\lambda (e2: C).(drop n O c3 e2)) in (let TMP_124 \def (\lambda +(e2: C).(csubc g e1 e2)) in (ex2 C TMP_123 TMP_124))))))) in (let TMP_126 +\def (Bind Abst) in (let H11 \def (eq_ind K k TMP_125 H0 TMP_126 H5) in (let +TMP_127 \def (Bind Abst) in (let TMP_128 \def (r TMP_127 n) in (let H_x0 \def +(H e1 TMP_128 H10 x0 H7) in (let H12 \def H_x0 in (let TMP_129 \def (\lambda +(e2: C).(drop n O x0 e2)) in (let TMP_130 \def (\lambda (e2: C).(csubc g e1 +e2)) in (let TMP_134 \def (\lambda (e2: C).(let TMP_131 \def (S n) in (let +TMP_132 \def (Bind Abbr) in (let TMP_133 \def (CHead x0 TMP_132 x1) in (drop +TMP_131 O TMP_133 e2))))) in (let TMP_135 \def (\lambda (e2: C).(csubc g e1 +e2)) in (let TMP_136 \def (ex2 C TMP_134 TMP_135) in (let TMP_144 \def +(\lambda (x: C).(\lambda (H13: (drop n O x0 x)).(\lambda (H14: (csubc g e1 +x)).(let TMP_140 \def (\lambda (e2: C).(let TMP_137 \def (S n) in (let +TMP_138 \def (Bind Abbr) in (let TMP_139 \def (CHead x0 TMP_138 x1) in (drop +TMP_137 O TMP_139 e2))))) in (let TMP_141 \def (\lambda (e2: C).(csubc g e1 +e2)) in (let TMP_142 \def (Bind Abbr) in (let TMP_143 \def (drop_drop TMP_142 +n x0 x H13 x1) in (ex_intro2 C TMP_140 TMP_141 x TMP_143 H14)))))))) in (let +TMP_145 \def (ex2_ind C TMP_129 TMP_130 TMP_136 TMP_144 H12) in (eq_ind_r C +TMP_114 TMP_118 TMP_145 c2 H6)))))))))))))))))))))))))))))) in (ex5_3_ind C T +A TMP_101 TMP_104 TMP_105 TMP_107 TMP_108 TMP_112 TMP_146 H4))))))))))) in +(let TMP_194 \def (\lambda (H4: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: +C).(\lambda (v2: T).(eq C c2 (CHead c3 (Bind b) v2))))) (\lambda (_: +B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: +B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: +B).(\lambda (c3: C).(\lambda (_: T).(csubc g c c3)))))).(let TMP_150 \def +(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_148 \def (Bind b) +in (let TMP_149 \def (CHead c3 TMP_148 v2) in (eq C c2 TMP_149)))))) in (let +TMP_152 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_151 +\def (Bind Void) in (eq K k TMP_151))))) in (let TMP_154 \def (\lambda (b: +B).(\lambda (_: C).(\lambda (_: T).(let TMP_153 \def (eq B b Void) in (not +TMP_153))))) in (let TMP_155 \def (\lambda (_: B).(\lambda (c3: C).(\lambda +(_: T).(csubc g c c3)))) in (let TMP_157 \def (\lambda (e2: C).(let TMP_156 +\def (S n) in (drop TMP_156 O c2 e2))) in (let TMP_158 \def (\lambda (e2: +C).(csubc g e1 e2)) in (let TMP_159 \def (ex2 C TMP_157 TMP_158) in (let +TMP_193 \def (\lambda (x0: B).(\lambda (x1: C).(\lambda (x2: T).(\lambda (H5: +(eq C c2 (CHead x1 (Bind x0) x2))).(\lambda (H6: (eq K k (Bind +Void))).(\lambda (_: (not (eq B x0 Void))).(\lambda (H8: (csubc g c x1)).(let +TMP_160 \def (Bind x0) in (let TMP_161 \def (CHead x1 TMP_160 x2) in (let +TMP_165 \def (\lambda (c0: C).(let TMP_163 \def (\lambda (e2: C).(let TMP_162 +\def (S n) in (drop TMP_162 O c0 e2))) in (let TMP_164 \def (\lambda (e2: +C).(csubc g e1 e2)) in (ex2 C TMP_163 TMP_164)))) in (let TMP_167 \def +(\lambda (k0: K).(let TMP_166 \def (r k0 n) in (drop TMP_166 O c e1))) in +(let TMP_168 \def (drop_gen_drop k c e1 t n H1) in (let TMP_169 \def (Bind +Void) in (let H9 \def (eq_ind K k TMP_167 TMP_168 TMP_169 H6) in (let TMP_172 +\def (\lambda (k0: K).((drop n O (CHead c k0 t) e1) \to (\forall (c3: +C).((csubc g (CHead c k0 t) c3) \to (let TMP_170 \def (\lambda (e2: C).(drop +n O c3 e2)) in (let TMP_171 \def (\lambda (e2: C).(csubc g e1 e2)) in (ex2 C +TMP_170 TMP_171))))))) in (let TMP_173 \def (Bind Void) in (let H10 \def +(eq_ind K k TMP_172 H0 TMP_173 H6) in (let TMP_174 \def (Bind Void) in (let +TMP_175 \def (r TMP_174 n) in (let H_x0 \def (H e1 TMP_175 H9 x1 H8) in (let +H11 \def H_x0 in (let TMP_176 \def (\lambda (e2: C).(drop n O x1 e2)) in (let +TMP_177 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_181 \def (\lambda +(e2: C).(let TMP_178 \def (S n) in (let TMP_179 \def (Bind x0) in (let +TMP_180 \def (CHead x1 TMP_179 x2) in (drop TMP_178 O TMP_180 e2))))) in (let +TMP_182 \def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_183 \def (ex2 C +TMP_181 TMP_182) in (let TMP_191 \def (\lambda (x: C).(\lambda (H12: (drop n +O x1 x)).(\lambda (H13: (csubc g e1 x)).(let TMP_187 \def (\lambda (e2: +C).(let TMP_184 \def (S n) in (let TMP_185 \def (Bind x0) in (let TMP_186 +\def (CHead x1 TMP_185 x2) in (drop TMP_184 O TMP_186 e2))))) in (let TMP_188 +\def (\lambda (e2: C).(csubc g e1 e2)) in (let TMP_189 \def (Bind x0) in (let +TMP_190 \def (drop_drop TMP_189 n x1 x H12 x2) in (ex_intro2 C TMP_187 +TMP_188 x TMP_190 H13)))))))) in (let TMP_192 \def (ex2_ind C TMP_176 TMP_177 +TMP_183 TMP_191 H11) in (eq_ind_r C TMP_161 TMP_165 TMP_192 c2 +H5))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_150 TMP_152 TMP_154 +TMP_155 TMP_159 TMP_193 H4)))))))))) in (or3_ind TMP_45 TMP_55 TMP_64 TMP_68 +TMP_99 TMP_147 TMP_194 H3)))))))))))))))))))))))))))) in (nat_ind TMP_29 +TMP_41 TMP_195 h)))))))))) in (C_ind TMP_3 TMP_26 TMP_196 c1))))). theorem drop_csubc_trans: \forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))) \def - \lambda (g: G).(\lambda (c2: C).(C_ind (\lambda (c: C).(\forall (e2: -C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall (e1: -C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda -(c1: C).(csubc g c c1)))))))))) (\lambda (n: nat).(\lambda (e2: C).(\lambda -(d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n) e2)).(\lambda -(e1: C).(\lambda (H0: (csubc g e2 e1)).(and3_ind (eq C e2 (CSort n)) (eq nat -h O) (eq nat d O) (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: -C).(csubc g (CSort n) c1))) (\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: -(eq nat h O)).(\lambda (H3: (eq nat d O)).(eq_ind_r nat O (\lambda (n0: -nat).(ex2 C (\lambda (c1: C).(drop n0 d c1 e1)) (\lambda (c1: C).(csubc g -(CSort n) c1)))) (eq_ind_r nat O (\lambda (n0: nat).(ex2 C (\lambda (c1: -C).(drop O n0 c1 e1)) (\lambda (c1: C).(csubc g (CSort n) c1)))) (let H4 \def -(eq_ind C e2 (\lambda (c: C).(csubc g c e1)) H0 (CSort n) H1) in (ex_intro2 C -(\lambda (c1: C).(drop O O c1 e1)) (\lambda (c1: C).(csubc g (CSort n) c1)) -e1 (drop_refl e1) H4)) d H3) h H2)))) (drop_gen_sort n h d e2 H))))))))) -(\lambda (c: C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: -nat).((drop h d c e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C -(\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c -c1))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: -nat).(nat_ind (\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) -e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: C).(drop h -n c1 e1)) (\lambda (c1: C).(csubc g (CHead c k t) c1)))))))) (\lambda (h: -nat).(nat_ind (\lambda (n: nat).((drop n O (CHead c k t) e2) \to (\forall -(e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) -(\lambda (c1: C).(csubc g (CHead c k t) c1))))))) (\lambda (H0: (drop O O -(CHead c k t) e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e2 e1)).(let H2 -\def (eq_ind_r C e2 (\lambda (c0: C).(csubc g c0 e1)) H1 (CHead c k t) -(drop_gen_refl (CHead c k t) e2 H0)) in (ex_intro2 C (\lambda (c1: C).(drop O -O c1 e1)) (\lambda (c1: C).(csubc g (CHead c k t) c1)) e1 (drop_refl e1) -H2))))) (\lambda (n: nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to -(\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: C).(drop n O c1 -e1)) (\lambda (c1: C).(csubc g (CHead c k t) c1)))))))).(\lambda (H1: (drop -(S n) O (CHead c k t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 -e1)).(let H_x \def (H e2 O (r k n) (drop_gen_drop k c e2 t n H1) e1 H2) in -(let H3 \def H_x in (ex2_ind C (\lambda (c1: C).(drop (r k n) O c1 e1)) -(\lambda (c1: C).(csubc g c c1)) (ex2 C (\lambda (c1: C).(drop (S n) O c1 -e1)) (\lambda (c1: C).(csubc g (CHead c k t) c1))) (\lambda (x: C).(\lambda -(H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g c x)).(ex_intro2 C -(\lambda (c1: C).(drop (S n) O c1 e1)) (\lambda (c1: C).(csubc g (CHead c k -t) c1)) (CHead x k t) (drop_drop k n x e1 H4 t) (csubc_head g c x H5 k t))))) -H3)))))))) h)) (\lambda (n: nat).(\lambda (H0: ((\forall (h: nat).((drop h n -(CHead c k t) e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda -(c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g (CHead c k t) -c1))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t) -e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 e1)).(ex3_2_ind C T (\lambda -(e: C).(\lambda (v: T).(eq C e2 (CHead e k v)))) (\lambda (_: C).(\lambda (v: -T).(eq T t (lift h (r k n) v)))) (\lambda (e: C).(\lambda (_: T).(drop h (r k -n) c e))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1: -C).(csubc g (CHead c k t) c1))) (\lambda (x0: C).(\lambda (x1: T).(\lambda -(H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r k n) -x1))).(\lambda (H5: (drop h (r k n) c x0)).(let H6 \def (eq_ind C e2 (\lambda -(c0: C).(csubc g c0 e1)) H2 (CHead x0 k x1) H3) in (let H7 \def (eq_ind C e2 -(\lambda (c0: C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to -(\forall (e3: C).((csubc g c0 e3) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 -e3)) (\lambda (c1: C).(csubc g (CHead c k t) c1)))))))) H0 (CHead x0 k x1) -H3) in (let H8 \def (eq_ind T t (\lambda (t0: T).(\forall (h0: nat).((drop h0 -n (CHead c k t0) (CHead x0 k x1)) \to (\forall (e3: C).((csubc g (CHead x0 k -x1) e3) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 e3)) (\lambda (c1: -C).(csubc g (CHead c k t0) c1)))))))) H7 (lift h (r k n) x1) H4) in (eq_ind_r -T (lift h (r k n) x1) (\lambda (t0: T).(ex2 C (\lambda (c1: C).(drop h (S n) -c1 e1)) (\lambda (c1: C).(csubc g (CHead c k t0) c1)))) (let H_x \def -(csubc_gen_head_l g x0 e1 x1 k H6) in (let H9 \def H_x in (or3_ind (ex2 C -(\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda (c3: C).(csubc g x0 -c3))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k -(Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C e1 -(CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: -A).(csubc g x0 c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g -(asucc g a) x0 x1)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g -a c3 w))))) (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: -T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: -C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_: -C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: -C).(\lambda (_: T).(csubc g x0 c3))))) (ex2 C (\lambda (c1: C).(drop h (S n) -c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) -(\lambda (H10: (ex2 C (\lambda (c3: C).(eq C e1 (CHead c3 k x1))) (\lambda -(c3: C).(csubc g x0 c3)))).(ex2_ind C (\lambda (c3: C).(eq C e1 (CHead c3 k -x1))) (\lambda (c3: C).(csubc g x0 c3)) (ex2 C (\lambda (c1: C).(drop h (S n) -c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) -(\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12: -(csubc g x0 x)).(eq_ind_r C (CHead x k x1) (\lambda (c0: C).(ex2 C (\lambda -(c1: C).(drop h (S n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r -k n) x1)) c1)))) (let H_x0 \def (H x0 (r k n) h H5 x H12) in (let H13 \def -H_x0 in (ex2_ind C (\lambda (c1: C).(drop h (r k n) c1 x)) (\lambda (c1: -C).(csubc g c c1)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) -(\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1))) (\lambda (x2: -C).(\lambda (H14: (drop h (r k n) x2 x)).(\lambda (H15: (csubc g c -x2)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) (\lambda -(c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1)) (CHead x2 k (lift h (r -k n) x1)) (drop_skip k h n x2 x H14 x1) (csubc_head g c x2 H15 k (lift h (r k -n) x1)))))) H13))) e1 H11)))) H10)) (\lambda (H10: (ex5_3 C T A (\lambda (_: -C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) (\lambda (c3: -C).(\lambda (w: T).(\lambda (_: A).(eq C e1 (CHead c3 (Bind Abbr) w))))) -(\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x0 c3)))) (\lambda -(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) x0 x1)))) (\lambda -(c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))))).(ex5_3_ind C T A -(\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abst))))) -(\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(eq C e1 (CHead c3 (Bind -Abbr) w))))) (\lambda (c3: C).(\lambda (_: T).(\lambda (_: A).(csubc g x0 -c3)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g (asucc g a) x0 -x1)))) (\lambda (c3: C).(\lambda (w: T).(\lambda (a: A).(sc3 g a c3 w)))) -(ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1: C).(csubc g -(CHead c k (lift h (r k n) x1)) c1))) (\lambda (x2: C).(\lambda (x3: -T).(\lambda (x4: A).(\lambda (H11: (eq K k (Bind Abst))).(\lambda (H12: (eq C -e1 (CHead x2 (Bind Abbr) x3))).(\lambda (H13: (csubc g x0 x2)).(\lambda (H14: -(sc3 g (asucc g x4) x0 x1)).(\lambda (H15: (sc3 g x4 x2 x3)).(eq_ind_r C -(CHead x2 (Bind Abbr) x3) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(drop h (S -n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) x1)) c1)))) -(let H16 \def (eq_ind K k (\lambda (k0: K).(\forall (h0: nat).((drop h0 n -(CHead c k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3: -C).((csubc g (CHead x0 k0 x1) e3) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 -e3)) (\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n) x1)) c1)))))))) -H8 (Bind Abst) H11) in (let H17 \def (eq_ind K k (\lambda (k0: K).(drop h (r -k0 n) c x0)) H5 (Bind Abst) H11) in (eq_ind_r K (Bind Abst) (\lambda (k0: -K).(ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x2 (Bind Abbr) x3))) -(\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n) x1)) c1)))) (let H_x0 -\def (H x0 (r (Bind Abst) n) h H17 x2 H13) in (let H18 \def H_x0 in (ex2_ind -C (\lambda (c1: C).(drop h n c1 x2)) (\lambda (c1: C).(csubc g c c1)) (ex2 C -(\lambda (c1: C).(drop h (S n) c1 (CHead x2 (Bind Abbr) x3))) (\lambda (c1: -C).(csubc g (CHead c (Bind Abst) (lift h (r (Bind Abst) n) x1)) c1))) + \lambda (g: G).(\lambda (c2: C).(let TMP_3 \def (\lambda (c: C).(\forall +(e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall +(e1: C).((csubc g e2 e1) \to (let TMP_1 \def (\lambda (c1: C).(drop h d c1 +e1)) in (let TMP_2 \def (\lambda (c1: C).(csubc g c c1)) in (ex2 C TMP_1 +TMP_2)))))))))) in (let TMP_30 \def (\lambda (n: nat).(\lambda (e2: +C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n) +e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let TMP_4 \def (CSort +n) in (let TMP_5 \def (eq C e2 TMP_4) in (let TMP_6 \def (eq nat h O) in (let +TMP_7 \def (eq nat d O) in (let TMP_8 \def (\lambda (c1: C).(drop h d c1 e1)) +in (let TMP_10 \def (\lambda (c1: C).(let TMP_9 \def (CSort n) in (csubc g +TMP_9 c1))) in (let TMP_11 \def (ex2 C TMP_8 TMP_10) in (let TMP_28 \def +(\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (H3: +(eq nat d O)).(let TMP_15 \def (\lambda (n0: nat).(let TMP_12 \def (\lambda +(c1: C).(drop n0 d c1 e1)) in (let TMP_14 \def (\lambda (c1: C).(let TMP_13 +\def (CSort n) in (csubc g TMP_13 c1))) in (ex2 C TMP_12 TMP_14)))) in (let +TMP_19 \def (\lambda (n0: nat).(let TMP_16 \def (\lambda (c1: C).(drop O n0 +c1 e1)) in (let TMP_18 \def (\lambda (c1: C).(let TMP_17 \def (CSort n) in +(csubc g TMP_17 c1))) in (ex2 C TMP_16 TMP_18)))) in (let TMP_20 \def +(\lambda (c: C).(csubc g c e1)) in (let TMP_21 \def (CSort n) in (let H4 \def +(eq_ind C e2 TMP_20 H0 TMP_21 H1) in (let TMP_22 \def (\lambda (c1: C).(drop +O O c1 e1)) in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (CSort n) +in (csubc g TMP_23 c1))) in (let TMP_25 \def (drop_refl e1) in (let TMP_26 +\def (ex_intro2 C TMP_22 TMP_24 e1 TMP_25 H4) in (let TMP_27 \def (eq_ind_r +nat O TMP_19 TMP_26 d H3) in (eq_ind_r nat O TMP_15 TMP_27 h H2)))))))))))))) +in (let TMP_29 \def (drop_gen_sort n h d e2 H) in (and3_ind TMP_5 TMP_6 TMP_7 +TMP_11 TMP_28 TMP_29))))))))))))))))) in (let TMP_354 \def (\lambda (c: +C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop +h d c e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda (c1: +C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c c1))))))))))).(\lambda (k: +K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: nat).(let TMP_34 \def +(\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) e2) \to (\forall +(e1: C).((csubc g e2 e1) \to (let TMP_31 \def (\lambda (c1: C).(drop h n c1 +e1)) in (let TMP_33 \def (\lambda (c1: C).(let TMP_32 \def (CHead c k t) in +(csubc g TMP_32 c1))) in (ex2 C TMP_31 TMP_33)))))))) in (let TMP_67 \def +(\lambda (h: nat).(let TMP_38 \def (\lambda (n: nat).((drop n O (CHead c k t) +e2) \to (\forall (e1: C).((csubc g e2 e1) \to (let TMP_35 \def (\lambda (c1: +C).(drop n O c1 e1)) in (let TMP_37 \def (\lambda (c1: C).(let TMP_36 \def +(CHead c k t) in (csubc g TMP_36 c1))) in (ex2 C TMP_35 TMP_37))))))) in (let +TMP_47 \def (\lambda (H0: (drop O O (CHead c k t) e2)).(\lambda (e1: +C).(\lambda (H1: (csubc g e2 e1)).(let TMP_39 \def (\lambda (c0: C).(csubc g +c0 e1)) in (let TMP_40 \def (CHead c k t) in (let TMP_41 \def (CHead c k t) +in (let TMP_42 \def (drop_gen_refl TMP_41 e2 H0) in (let H2 \def (eq_ind_r C +e2 TMP_39 H1 TMP_40 TMP_42) in (let TMP_43 \def (\lambda (c1: C).(drop O O c1 +e1)) in (let TMP_45 \def (\lambda (c1: C).(let TMP_44 \def (CHead c k t) in +(csubc g TMP_44 c1))) in (let TMP_46 \def (drop_refl e1) in (ex_intro2 C +TMP_43 TMP_45 e1 TMP_46 H2)))))))))))) in (let TMP_66 \def (\lambda (n: +nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to (\forall (e1: C).((csubc +g e2 e1) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) (\lambda (c1: +C).(csubc g (CHead c k t) c1)))))))).(\lambda (H1: (drop (S n) O (CHead c k +t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 e1)).(let TMP_48 \def (r k +n) in (let TMP_49 \def (drop_gen_drop k c e2 t n H1) in (let H_x \def (H e2 O +TMP_48 TMP_49 e1 H2) in (let H3 \def H_x in (let TMP_51 \def (\lambda (c1: +C).(let TMP_50 \def (r k n) in (drop TMP_50 O c1 e1))) in (let TMP_52 \def +(\lambda (c1: C).(csubc g c c1)) in (let TMP_54 \def (\lambda (c1: C).(let +TMP_53 \def (S n) in (drop TMP_53 O c1 e1))) in (let TMP_56 \def (\lambda +(c1: C).(let TMP_55 \def (CHead c k t) in (csubc g TMP_55 c1))) in (let +TMP_57 \def (ex2 C TMP_54 TMP_56) in (let TMP_65 \def (\lambda (x: +C).(\lambda (H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g c x)).(let +TMP_59 \def (\lambda (c1: C).(let TMP_58 \def (S n) in (drop TMP_58 O c1 +e1))) in (let TMP_61 \def (\lambda (c1: C).(let TMP_60 \def (CHead c k t) in +(csubc g TMP_60 c1))) in (let TMP_62 \def (CHead x k t) in (let TMP_63 \def +(drop_drop k n x e1 H4 t) in (let TMP_64 \def (csubc_head g c x H5 k t) in +(ex_intro2 C TMP_59 TMP_61 TMP_62 TMP_63 TMP_64))))))))) in (ex2_ind C TMP_51 +TMP_52 TMP_57 TMP_65 H3)))))))))))))))) in (nat_ind TMP_38 TMP_47 TMP_66 +h))))) in (let TMP_353 \def (\lambda (n: nat).(\lambda (H0: ((\forall (h: +nat).((drop h n (CHead c k t) e2) \to (\forall (e1: C).((csubc g e2 e1) \to +(ex2 C (\lambda (c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g (CHead c +k t) c1))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t) +e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e2 e1)).(let TMP_69 \def +(\lambda (e: C).(\lambda (v: T).(let TMP_68 \def (CHead e k v) in (eq C e2 +TMP_68)))) in (let TMP_72 \def (\lambda (_: C).(\lambda (v: T).(let TMP_70 +\def (r k n) in (let TMP_71 \def (lift h TMP_70 v) in (eq T t TMP_71))))) in +(let TMP_74 \def (\lambda (e: C).(\lambda (_: T).(let TMP_73 \def (r k n) in +(drop h TMP_73 c e)))) in (let TMP_76 \def (\lambda (c1: C).(let TMP_75 \def +(S n) in (drop h TMP_75 c1 e1))) in (let TMP_78 \def (\lambda (c1: C).(let +TMP_77 \def (CHead c k t) in (csubc g TMP_77 c1))) in (let TMP_79 \def (ex2 C +TMP_76 TMP_78) in (let TMP_351 \def (\lambda (x0: C).(\lambda (x1: +T).(\lambda (H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r +k n) x1))).(\lambda (H5: (drop h (r k n) c x0)).(let TMP_80 \def (\lambda +(c0: C).(csubc g c0 e1)) in (let TMP_81 \def (CHead x0 k x1) in (let H6 \def +(eq_ind C e2 TMP_80 H2 TMP_81 H3) in (let TMP_85 \def (\lambda (c0: +C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to (\forall (e3: +C).((csubc g c0 e3) \to (let TMP_82 \def (\lambda (c1: C).(drop h0 n c1 e3)) +in (let TMP_84 \def (\lambda (c1: C).(let TMP_83 \def (CHead c k t) in (csubc +g TMP_83 c1))) in (ex2 C TMP_82 TMP_84)))))))) in (let TMP_86 \def (CHead x0 +k x1) in (let H7 \def (eq_ind C e2 TMP_85 H0 TMP_86 H3) in (let TMP_90 \def +(\lambda (t0: T).(\forall (h0: nat).((drop h0 n (CHead c k t0) (CHead x0 k +x1)) \to (\forall (e3: C).((csubc g (CHead x0 k x1) e3) \to (let TMP_87 \def +(\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_89 \def (\lambda (c1: C).(let +TMP_88 \def (CHead c k t0) in (csubc g TMP_88 c1))) in (ex2 C TMP_87 +TMP_89)))))))) in (let TMP_91 \def (r k n) in (let TMP_92 \def (lift h TMP_91 +x1) in (let H8 \def (eq_ind T t TMP_90 H7 TMP_92 H4) in (let TMP_93 \def (r k +n) in (let TMP_94 \def (lift h TMP_93 x1) in (let TMP_99 \def (\lambda (t0: +T).(let TMP_96 \def (\lambda (c1: C).(let TMP_95 \def (S n) in (drop h TMP_95 +c1 e1))) in (let TMP_98 \def (\lambda (c1: C).(let TMP_97 \def (CHead c k t0) +in (csubc g TMP_97 c1))) in (ex2 C TMP_96 TMP_98)))) in (let H_x \def +(csubc_gen_head_l g x0 e1 x1 k H6) in (let H9 \def H_x in (let TMP_101 \def +(\lambda (c3: C).(let TMP_100 \def (CHead c3 k x1) in (eq C e1 TMP_100))) in +(let TMP_102 \def (\lambda (c3: C).(csubc g x0 c3)) in (let TMP_103 \def (ex2 +C TMP_101 TMP_102) in (let TMP_105 \def (\lambda (_: C).(\lambda (_: +T).(\lambda (_: A).(let TMP_104 \def (Bind Abst) in (eq K k TMP_104))))) in +(let TMP_108 \def (\lambda (c3: C).(\lambda (w: T).(\lambda (_: A).(let +TMP_106 \def (Bind Abbr) in (let TMP_107 \def (CHead c3 TMP_106 w) in (eq C +e1 TMP_107)))))) in (let TMP_109 \def (\lambda (c3: C).(\lambda (_: +T).(\lambda (_: A).(csubc g x0 c3)))) in (let TMP_111 \def (\lambda (_: +C).(\lambda (_: T).(\lambda (a: A).(let TMP_110 \def (asucc g a) in (sc3 g +TMP_110 x0 x1))))) in (let TMP_112 \def (\lambda (c3: C).(\lambda (w: +T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_113 \def (ex5_3 C T A +TMP_105 TMP_108 TMP_109 TMP_111 TMP_112) in (let TMP_116 \def (\lambda (b: +B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_114 \def (Bind b) in (let +TMP_115 \def (CHead c3 TMP_114 v2) in (eq C e1 TMP_115)))))) in (let TMP_118 +\def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_117 \def (Bind +Void) in (eq K k TMP_117))))) in (let TMP_120 \def (\lambda (b: B).(\lambda +(_: C).(\lambda (_: T).(let TMP_119 \def (eq B b Void) in (not TMP_119))))) +in (let TMP_121 \def (\lambda (_: B).(\lambda (c3: C).(\lambda (_: T).(csubc +g x0 c3)))) in (let TMP_122 \def (ex4_3 B C T TMP_116 TMP_118 TMP_120 +TMP_121) in (let TMP_124 \def (\lambda (c1: C).(let TMP_123 \def (S n) in +(drop h TMP_123 c1 e1))) in (let TMP_128 \def (\lambda (c1: C).(let TMP_125 +\def (r k n) in (let TMP_126 \def (lift h TMP_125 x1) in (let TMP_127 \def +(CHead c k TMP_126) in (csubc g TMP_127 c1))))) in (let TMP_129 \def (ex2 C +TMP_124 TMP_128) in (let TMP_177 \def (\lambda (H10: (ex2 C (\lambda (c3: +C).(eq C e1 (CHead c3 k x1))) (\lambda (c3: C).(csubc g x0 c3)))).(let +TMP_131 \def (\lambda (c3: C).(let TMP_130 \def (CHead c3 k x1) in (eq C e1 +TMP_130))) in (let TMP_132 \def (\lambda (c3: C).(csubc g x0 c3)) in (let +TMP_134 \def (\lambda (c1: C).(let TMP_133 \def (S n) in (drop h TMP_133 c1 +e1))) in (let TMP_138 \def (\lambda (c1: C).(let TMP_135 \def (r k n) in (let +TMP_136 \def (lift h TMP_135 x1) in (let TMP_137 \def (CHead c k TMP_136) in +(csubc g TMP_137 c1))))) in (let TMP_139 \def (ex2 C TMP_134 TMP_138) in (let +TMP_176 \def (\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k +x1))).(\lambda (H12: (csubc g x0 x)).(let TMP_140 \def (CHead x k x1) in (let +TMP_147 \def (\lambda (c0: C).(let TMP_142 \def (\lambda (c1: C).(let TMP_141 +\def (S n) in (drop h TMP_141 c1 c0))) in (let TMP_146 \def (\lambda (c1: +C).(let TMP_143 \def (r k n) in (let TMP_144 \def (lift h TMP_143 x1) in (let +TMP_145 \def (CHead c k TMP_144) in (csubc g TMP_145 c1))))) in (ex2 C +TMP_142 TMP_146)))) in (let TMP_148 \def (r k n) in (let H_x0 \def (H x0 +TMP_148 h H5 x H12) in (let H13 \def H_x0 in (let TMP_150 \def (\lambda (c1: +C).(let TMP_149 \def (r k n) in (drop h TMP_149 c1 x))) in (let TMP_151 \def +(\lambda (c1: C).(csubc g c c1)) in (let TMP_154 \def (\lambda (c1: C).(let +TMP_152 \def (S n) in (let TMP_153 \def (CHead x k x1) in (drop h TMP_152 c1 +TMP_153)))) in (let TMP_158 \def (\lambda (c1: C).(let TMP_155 \def (r k n) +in (let TMP_156 \def (lift h TMP_155 x1) in (let TMP_157 \def (CHead c k +TMP_156) in (csubc g TMP_157 c1))))) in (let TMP_159 \def (ex2 C TMP_154 +TMP_158) in (let TMP_174 \def (\lambda (x2: C).(\lambda (H14: (drop h (r k n) +x2 x)).(\lambda (H15: (csubc g c x2)).(let TMP_162 \def (\lambda (c1: C).(let +TMP_160 \def (S n) in (let TMP_161 \def (CHead x k x1) in (drop h TMP_160 c1 +TMP_161)))) in (let TMP_166 \def (\lambda (c1: C).(let TMP_163 \def (r k n) +in (let TMP_164 \def (lift h TMP_163 x1) in (let TMP_165 \def (CHead c k +TMP_164) in (csubc g TMP_165 c1))))) in (let TMP_167 \def (r k n) in (let +TMP_168 \def (lift h TMP_167 x1) in (let TMP_169 \def (CHead x2 k TMP_168) in +(let TMP_170 \def (drop_skip k h n x2 x H14 x1) in (let TMP_171 \def (r k n) +in (let TMP_172 \def (lift h TMP_171 x1) in (let TMP_173 \def (csubc_head g c +x2 H15 k TMP_172) in (ex_intro2 C TMP_162 TMP_166 TMP_169 TMP_170 +TMP_173))))))))))))) in (let TMP_175 \def (ex2_ind C TMP_150 TMP_151 TMP_159 +TMP_174 H13) in (eq_ind_r C TMP_140 TMP_147 TMP_175 e1 H11)))))))))))))))) in +(ex2_ind C TMP_131 TMP_132 TMP_139 TMP_176 H10)))))))) in (let TMP_266 \def +(\lambda (H10: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: +A).(eq K k (Bind Abst))))) (\lambda (c3: C).(\lambda (w: T).(\lambda (_: +A).(eq C e1 (CHead c3 (Bind Abbr) w))))) (\lambda (c3: C).(\lambda (_: +T).(\lambda (_: A).(csubc g x0 c3)))) (\lambda (_: C).(\lambda (_: +T).(\lambda (a: A).(sc3 g (asucc g a) x0 x1)))) (\lambda (c3: C).(\lambda (w: +T).(\lambda (a: A).(sc3 g a c3 w)))))).(let TMP_179 \def (\lambda (_: +C).(\lambda (_: T).(\lambda (_: A).(let TMP_178 \def (Bind Abst) in (eq K k +TMP_178))))) in (let TMP_182 \def (\lambda (c3: C).(\lambda (w: T).(\lambda +(_: A).(let TMP_180 \def (Bind Abbr) in (let TMP_181 \def (CHead c3 TMP_180 +w) in (eq C e1 TMP_181)))))) in (let TMP_183 \def (\lambda (c3: C).(\lambda +(_: T).(\lambda (_: A).(csubc g x0 c3)))) in (let TMP_185 \def (\lambda (_: +C).(\lambda (_: T).(\lambda (a: A).(let TMP_184 \def (asucc g a) in (sc3 g +TMP_184 x0 x1))))) in (let TMP_186 \def (\lambda (c3: C).(\lambda (w: +T).(\lambda (a: A).(sc3 g a c3 w)))) in (let TMP_188 \def (\lambda (c1: +C).(let TMP_187 \def (S n) in (drop h TMP_187 c1 e1))) in (let TMP_192 \def +(\lambda (c1: C).(let TMP_189 \def (r k n) in (let TMP_190 \def (lift h +TMP_189 x1) in (let TMP_191 \def (CHead c k TMP_190) in (csubc g TMP_191 +c1))))) in (let TMP_193 \def (ex2 C TMP_188 TMP_192) in (let TMP_265 \def +(\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H11: (eq K k +(Bind Abst))).(\lambda (H12: (eq C e1 (CHead x2 (Bind Abbr) x3))).(\lambda +(H13: (csubc g x0 x2)).(\lambda (H14: (sc3 g (asucc g x4) x0 x1)).(\lambda +(H15: (sc3 g x4 x2 x3)).(let TMP_194 \def (Bind Abbr) in (let TMP_195 \def +(CHead x2 TMP_194 x3) in (let TMP_202 \def (\lambda (c0: C).(let TMP_197 \def +(\lambda (c1: C).(let TMP_196 \def (S n) in (drop h TMP_196 c1 c0))) in (let +TMP_201 \def (\lambda (c1: C).(let TMP_198 \def (r k n) in (let TMP_199 \def +(lift h TMP_198 x1) in (let TMP_200 \def (CHead c k TMP_199) in (csubc g +TMP_200 c1))))) in (ex2 C TMP_197 TMP_201)))) in (let TMP_208 \def (\lambda +(k0: K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1)) +(CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g (CHead x0 k0 x1) e3) \to +(let TMP_203 \def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_207 \def +(\lambda (c1: C).(let TMP_204 \def (r k0 n) in (let TMP_205 \def (lift h +TMP_204 x1) in (let TMP_206 \def (CHead c k0 TMP_205) in (csubc g TMP_206 +c1))))) in (ex2 C TMP_203 TMP_207)))))))) in (let TMP_209 \def (Bind Abst) in +(let H16 \def (eq_ind K k TMP_208 H8 TMP_209 H11) in (let TMP_211 \def +(\lambda (k0: K).(let TMP_210 \def (r k0 n) in (drop h TMP_210 c x0))) in +(let TMP_212 \def (Bind Abst) in (let H17 \def (eq_ind K k TMP_211 H5 TMP_212 +H11) in (let TMP_213 \def (Bind Abst) in (let TMP_222 \def (\lambda (k0: +K).(let TMP_217 \def (\lambda (c1: C).(let TMP_214 \def (S n) in (let TMP_215 +\def (Bind Abbr) in (let TMP_216 \def (CHead x2 TMP_215 x3) in (drop h +TMP_214 c1 TMP_216))))) in (let TMP_221 \def (\lambda (c1: C).(let TMP_218 +\def (r k0 n) in (let TMP_219 \def (lift h TMP_218 x1) in (let TMP_220 \def +(CHead c k0 TMP_219) in (csubc g TMP_220 c1))))) in (ex2 C TMP_217 +TMP_221)))) in (let TMP_223 \def (Bind Abst) in (let TMP_224 \def (r TMP_223 +n) in (let H_x0 \def (H x0 TMP_224 h H17 x2 H13) in (let H18 \def H_x0 in +(let TMP_225 \def (\lambda (c1: C).(drop h n c1 x2)) in (let TMP_226 \def +(\lambda (c1: C).(csubc g c c1)) in (let TMP_230 \def (\lambda (c1: C).(let +TMP_227 \def (S n) in (let TMP_228 \def (Bind Abbr) in (let TMP_229 \def +(CHead x2 TMP_228 x3) in (drop h TMP_227 c1 TMP_229))))) in (let TMP_236 \def +(\lambda (c1: C).(let TMP_231 \def (Bind Abst) in (let TMP_232 \def (Bind +Abst) in (let TMP_233 \def (r TMP_232 n) in (let TMP_234 \def (lift h TMP_233 +x1) in (let TMP_235 \def (CHead c TMP_231 TMP_234) in (csubc g TMP_235 +c1))))))) in (let TMP_237 \def (ex2 C TMP_230 TMP_236) in (let TMP_262 \def (\lambda (x: C).(\lambda (H19: (drop h n x x2)).(\lambda (H20: (csubc g c -x)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x2 (Bind Abbr) -x3))) (\lambda (c1: C).(csubc g (CHead c (Bind Abst) (lift h (r (Bind Abst) -n) x1)) c1)) (CHead x (Bind Abbr) (lift h n x3)) (drop_skip_bind h n x x2 H19 -Abbr x3) (csubc_abst g c x H20 (lift h (r (Bind Abst) n) x1) x4 (sc3_lift g -(asucc g x4) x0 x1 H14 c h (r (Bind Abst) n) H17) (lift h n x3) (sc3_lift g -x4 x2 x3 H15 x h n H19)))))) H18))) k H11))) e1 H12))))))))) H10)) (\lambda -(H10: (ex4_3 B C T (\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(eq C e1 -(CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: -T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: -T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c3: C).(\lambda (_: -T).(csubc g x0 c3)))))).(ex4_3_ind B C T (\lambda (b: B).(\lambda (c3: -C).(\lambda (v2: T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_: +x)).(let TMP_241 \def (\lambda (c1: C).(let TMP_238 \def (S n) in (let +TMP_239 \def (Bind Abbr) in (let TMP_240 \def (CHead x2 TMP_239 x3) in (drop +h TMP_238 c1 TMP_240))))) in (let TMP_247 \def (\lambda (c1: C).(let TMP_242 +\def (Bind Abst) in (let TMP_243 \def (Bind Abst) in (let TMP_244 \def (r +TMP_243 n) in (let TMP_245 \def (lift h TMP_244 x1) in (let TMP_246 \def +(CHead c TMP_242 TMP_245) in (csubc g TMP_246 c1))))))) in (let TMP_248 \def +(Bind Abbr) in (let TMP_249 \def (lift h n x3) in (let TMP_250 \def (CHead x +TMP_248 TMP_249) in (let TMP_251 \def (drop_skip_bind h n x x2 H19 Abbr x3) +in (let TMP_252 \def (Bind Abst) in (let TMP_253 \def (r TMP_252 n) in (let +TMP_254 \def (lift h TMP_253 x1) in (let TMP_255 \def (asucc g x4) in (let +TMP_256 \def (Bind Abst) in (let TMP_257 \def (r TMP_256 n) in (let TMP_258 +\def (sc3_lift g TMP_255 x0 x1 H14 c h TMP_257 H17) in (let TMP_259 \def +(lift h n x3) in (let TMP_260 \def (sc3_lift g x4 x2 x3 H15 x h n H19) in +(let TMP_261 \def (csubc_abst g c x H20 TMP_254 x4 TMP_258 TMP_259 TMP_260) +in (ex_intro2 C TMP_241 TMP_247 TMP_250 TMP_251 TMP_261)))))))))))))))))))) +in (let TMP_263 \def (ex2_ind C TMP_225 TMP_226 TMP_237 TMP_262 H18) in (let +TMP_264 \def (eq_ind_r K TMP_213 TMP_222 TMP_263 k H11) in (eq_ind_r C +TMP_195 TMP_202 TMP_264 e1 H12)))))))))))))))))))))))))))))))) in (ex5_3_ind +C T A TMP_179 TMP_182 TMP_183 TMP_185 TMP_186 TMP_193 TMP_265 H10))))))))))) +in (let TMP_349 \def (\lambda (H10: (ex4_3 B C T (\lambda (b: B).(\lambda +(c3: C).(\lambda (v2: T).(eq C e1 (CHead c3 (Bind b) v2))))) (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind Void))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: -B).(\lambda (c3: C).(\lambda (_: T).(csubc g x0 c3)))) (ex2 C (\lambda (c1: -C).(drop h (S n) c1 e1)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r k n) -x1)) c1))) (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11: -(eq C e1 (CHead x3 (Bind x2) x4))).(\lambda (H12: (eq K k (Bind -Void))).(\lambda (H13: (not (eq B x2 Void))).(\lambda (H14: (csubc g x0 -x3)).(eq_ind_r C (CHead x3 (Bind x2) x4) (\lambda (c0: C).(ex2 C (\lambda -(c1: C).(drop h (S n) c1 c0)) (\lambda (c1: C).(csubc g (CHead c k (lift h (r -k n) x1)) c1)))) (let H15 \def (eq_ind K k (\lambda (k0: K).(\forall (h0: -nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to -(\forall (e3: C).((csubc g (CHead x0 k0 x1) e3) \to (ex2 C (\lambda (c1: -C).(drop h0 n c1 e3)) (\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n) -x1)) c1)))))))) H8 (Bind Void) H12) in (let H16 \def (eq_ind K k (\lambda -(k0: K).(drop h (r k0 n) c x0)) H5 (Bind Void) H12) in (eq_ind_r K (Bind -Void) (\lambda (k0: K).(ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3 -(Bind x2) x4))) (\lambda (c1: C).(csubc g (CHead c k0 (lift h (r k0 n) x1)) -c1)))) (let H_x0 \def (H x0 (r (Bind Void) n) h H16 x3 H14) in (let H17 \def -H_x0 in (ex2_ind C (\lambda (c1: C).(drop h n c1 x3)) (\lambda (c1: C).(csubc -g c c1)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3 (Bind x2) x4))) -(\lambda (c1: C).(csubc g (CHead c (Bind Void) (lift h (r (Bind Void) n) x1)) -c1))) (\lambda (x: C).(\lambda (H18: (drop h n x x3)).(\lambda (H19: (csubc g -c x)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x3 (Bind x2) -x4))) (\lambda (c1: C).(csubc g (CHead c (Bind Void) (lift h (r (Bind Void) -n) x1)) c1)) (CHead x (Bind x2) (lift h n x4)) (drop_skip_bind h n x x3 H18 -x2 x4) (csubc_void g c x H19 x2 H13 (lift h (r (Bind Void) n) x1) (lift h n -x4)))))) H17))) k H12))) e1 H11)))))))) H10)) H9))) t H4))))))))) -(drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)). -(* COMMENTS -Initial nodes: 3747 -END *) +B).(\lambda (c3: C).(\lambda (_: T).(csubc g x0 c3)))))).(let TMP_269 \def +(\lambda (b: B).(\lambda (c3: C).(\lambda (v2: T).(let TMP_267 \def (Bind b) +in (let TMP_268 \def (CHead c3 TMP_267 v2) in (eq C e1 TMP_268)))))) in (let +TMP_271 \def (\lambda (_: B).(\lambda (_: C).(\lambda (_: T).(let TMP_270 +\def (Bind Void) in (eq K k TMP_270))))) in (let TMP_273 \def (\lambda (b: +B).(\lambda (_: C).(\lambda (_: T).(let TMP_272 \def (eq B b Void) in (not +TMP_272))))) in (let TMP_274 \def (\lambda (_: B).(\lambda (c3: C).(\lambda +(_: T).(csubc g x0 c3)))) in (let TMP_276 \def (\lambda (c1: C).(let TMP_275 +\def (S n) in (drop h TMP_275 c1 e1))) in (let TMP_280 \def (\lambda (c1: +C).(let TMP_277 \def (r k n) in (let TMP_278 \def (lift h TMP_277 x1) in (let +TMP_279 \def (CHead c k TMP_278) in (csubc g TMP_279 c1))))) in (let TMP_281 +\def (ex2 C TMP_276 TMP_280) in (let TMP_348 \def (\lambda (x2: B).(\lambda +(x3: C).(\lambda (x4: T).(\lambda (H11: (eq C e1 (CHead x3 (Bind x2) +x4))).(\lambda (H12: (eq K k (Bind Void))).(\lambda (H13: (not (eq B x2 +Void))).(\lambda (H14: (csubc g x0 x3)).(let TMP_282 \def (Bind x2) in (let +TMP_283 \def (CHead x3 TMP_282 x4) in (let TMP_290 \def (\lambda (c0: C).(let +TMP_285 \def (\lambda (c1: C).(let TMP_284 \def (S n) in (drop h TMP_284 c1 +c0))) in (let TMP_289 \def (\lambda (c1: C).(let TMP_286 \def (r k n) in (let +TMP_287 \def (lift h TMP_286 x1) in (let TMP_288 \def (CHead c k TMP_287) in +(csubc g TMP_288 c1))))) in (ex2 C TMP_285 TMP_289)))) in (let TMP_296 \def +(\lambda (k0: K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n) +x1)) (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g (CHead x0 k0 x1) e3) +\to (let TMP_291 \def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_295 +\def (\lambda (c1: C).(let TMP_292 \def (r k0 n) in (let TMP_293 \def (lift h +TMP_292 x1) in (let TMP_294 \def (CHead c k0 TMP_293) in (csubc g TMP_294 +c1))))) in (ex2 C TMP_291 TMP_295)))))))) in (let TMP_297 \def (Bind Void) in +(let H15 \def (eq_ind K k TMP_296 H8 TMP_297 H12) in (let TMP_299 \def +(\lambda (k0: K).(let TMP_298 \def (r k0 n) in (drop h TMP_298 c x0))) in +(let TMP_300 \def (Bind Void) in (let H16 \def (eq_ind K k TMP_299 H5 TMP_300 +H12) in (let TMP_301 \def (Bind Void) in (let TMP_310 \def (\lambda (k0: +K).(let TMP_305 \def (\lambda (c1: C).(let TMP_302 \def (S n) in (let TMP_303 +\def (Bind x2) in (let TMP_304 \def (CHead x3 TMP_303 x4) in (drop h TMP_302 +c1 TMP_304))))) in (let TMP_309 \def (\lambda (c1: C).(let TMP_306 \def (r k0 +n) in (let TMP_307 \def (lift h TMP_306 x1) in (let TMP_308 \def (CHead c k0 +TMP_307) in (csubc g TMP_308 c1))))) in (ex2 C TMP_305 TMP_309)))) in (let +TMP_311 \def (Bind Void) in (let TMP_312 \def (r TMP_311 n) in (let H_x0 \def +(H x0 TMP_312 h H16 x3 H14) in (let H17 \def H_x0 in (let TMP_313 \def +(\lambda (c1: C).(drop h n c1 x3)) in (let TMP_314 \def (\lambda (c1: +C).(csubc g c c1)) in (let TMP_318 \def (\lambda (c1: C).(let TMP_315 \def (S +n) in (let TMP_316 \def (Bind x2) in (let TMP_317 \def (CHead x3 TMP_316 x4) +in (drop h TMP_315 c1 TMP_317))))) in (let TMP_324 \def (\lambda (c1: C).(let +TMP_319 \def (Bind Void) in (let TMP_320 \def (Bind Void) in (let TMP_321 +\def (r TMP_320 n) in (let TMP_322 \def (lift h TMP_321 x1) in (let TMP_323 +\def (CHead c TMP_319 TMP_322) in (csubc g TMP_323 c1))))))) in (let TMP_325 +\def (ex2 C TMP_318 TMP_324) in (let TMP_345 \def (\lambda (x: C).(\lambda +(H18: (drop h n x x3)).(\lambda (H19: (csubc g c x)).(let TMP_329 \def +(\lambda (c1: C).(let TMP_326 \def (S n) in (let TMP_327 \def (Bind x2) in +(let TMP_328 \def (CHead x3 TMP_327 x4) in (drop h TMP_326 c1 TMP_328))))) in +(let TMP_335 \def (\lambda (c1: C).(let TMP_330 \def (Bind Void) in (let +TMP_331 \def (Bind Void) in (let TMP_332 \def (r TMP_331 n) in (let TMP_333 +\def (lift h TMP_332 x1) in (let TMP_334 \def (CHead c TMP_330 TMP_333) in +(csubc g TMP_334 c1))))))) in (let TMP_336 \def (Bind x2) in (let TMP_337 +\def (lift h n x4) in (let TMP_338 \def (CHead x TMP_336 TMP_337) in (let +TMP_339 \def (drop_skip_bind h n x x3 H18 x2 x4) in (let TMP_340 \def (Bind +Void) in (let TMP_341 \def (r TMP_340 n) in (let TMP_342 \def (lift h TMP_341 +x1) in (let TMP_343 \def (lift h n x4) in (let TMP_344 \def (csubc_void g c x +H19 x2 H13 TMP_342 TMP_343) in (ex_intro2 C TMP_329 TMP_335 TMP_338 TMP_339 +TMP_344))))))))))))))) in (let TMP_346 \def (ex2_ind C TMP_313 TMP_314 +TMP_325 TMP_345 H17) in (let TMP_347 \def (eq_ind_r K TMP_301 TMP_310 TMP_346 +k H12) in (eq_ind_r C TMP_283 TMP_290 TMP_347 e1 +H11))))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_269 TMP_271 +TMP_273 TMP_274 TMP_281 TMP_348 H10)))))))))) in (let TMP_350 \def (or3_ind +TMP_103 TMP_113 TMP_122 TMP_129 TMP_177 TMP_266 TMP_349 H9) in (eq_ind_r T +TMP_94 TMP_99 TMP_350 t H4)))))))))))))))))))))))))))))))))))))))))) in (let +TMP_352 \def (drop_gen_skip_l c e2 t h n k H1) in (ex3_2_ind C T TMP_69 +TMP_72 TMP_74 TMP_79 TMP_351 TMP_352))))))))))))))) in (nat_ind TMP_34 TMP_67 +TMP_353 d)))))))))) in (C_ind TMP_3 TMP_30 TMP_354 c2))))). theorem csubc_drop_conf_rev: \forall (g: G).(\forall (c2: C).(\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))) \def - \lambda (g: G).(\lambda (c2: C).(C_ind (\lambda (c: C).(\forall (e2: -C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall (e1: -C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda -(c1: C).(csubc g c1 c)))))))))) (\lambda (n: nat).(\lambda (e2: C).(\lambda -(d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n) e2)).(\lambda -(e1: C).(\lambda (H0: (csubc g e1 e2)).(and3_ind (eq C e2 (CSort n)) (eq nat -h O) (eq nat d O) (ex2 C (\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: -C).(csubc g c1 (CSort n)))) (\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: -(eq nat h O)).(\lambda (H3: (eq nat d O)).(eq_ind_r nat O (\lambda (n0: -nat).(ex2 C (\lambda (c1: C).(drop n0 d c1 e1)) (\lambda (c1: C).(csubc g c1 -(CSort n))))) (eq_ind_r nat O (\lambda (n0: nat).(ex2 C (\lambda (c1: -C).(drop O n0 c1 e1)) (\lambda (c1: C).(csubc g c1 (CSort n))))) (let H4 \def -(eq_ind C e2 (\lambda (c: C).(csubc g e1 c)) H0 (CSort n) H1) in (ex_intro2 C -(\lambda (c1: C).(drop O O c1 e1)) (\lambda (c1: C).(csubc g c1 (CSort n))) -e1 (drop_refl e1) H4)) d H3) h H2)))) (drop_gen_sort n h d e2 H))))))))) -(\lambda (c: C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: -nat).((drop h d c e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C -(\lambda (c1: C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c1 -c))))))))))).(\lambda (k: K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: -nat).(nat_ind (\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) -e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: C).(drop h -n c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c k t))))))))) (\lambda (h: -nat).(nat_ind (\lambda (n: nat).((drop n O (CHead c k t) e2) \to (\forall -(e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) -(\lambda (c1: C).(csubc g c1 (CHead c k t)))))))) (\lambda (H0: (drop O O -(CHead c k t) e2)).(\lambda (e1: C).(\lambda (H1: (csubc g e1 e2)).(let H2 -\def (eq_ind_r C e2 (\lambda (c0: C).(csubc g e1 c0)) H1 (CHead c k t) -(drop_gen_refl (CHead c k t) e2 H0)) in (ex_intro2 C (\lambda (c1: C).(drop O -O c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c k t))) e1 (drop_refl e1) -H2))))) (\lambda (n: nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to -(\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: C).(drop n O c1 -e1)) (\lambda (c1: C).(csubc g c1 (CHead c k t))))))))).(\lambda (H1: (drop -(S n) O (CHead c k t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 -e2)).(let H_x \def (H e2 O (r k n) (drop_gen_drop k c e2 t n H1) e1 H2) in -(let H3 \def H_x in (ex2_ind C (\lambda (c1: C).(drop (r k n) O c1 e1)) -(\lambda (c1: C).(csubc g c1 c)) (ex2 C (\lambda (c1: C).(drop (S n) O c1 -e1)) (\lambda (c1: C).(csubc g c1 (CHead c k t)))) (\lambda (x: C).(\lambda -(H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g x c)).(ex_intro2 C -(\lambda (c1: C).(drop (S n) O c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c -k t))) (CHead x k t) (drop_drop k n x e1 H4 t) (csubc_head g x c H5 k t))))) -H3)))))))) h)) (\lambda (n: nat).(\lambda (H0: ((\forall (h: nat).((drop h n -(CHead c k t) e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda -(c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c k -t)))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t) -e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 e2)).(ex3_2_ind C T (\lambda -(e: C).(\lambda (v: T).(eq C e2 (CHead e k v)))) (\lambda (_: C).(\lambda (v: -T).(eq T t (lift h (r k n) v)))) (\lambda (e: C).(\lambda (_: T).(drop h (r k -n) c e))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1: -C).(csubc g c1 (CHead c k t)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda -(H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r k n) -x1))).(\lambda (H5: (drop h (r k n) c x0)).(let H6 \def (eq_ind C e2 (\lambda -(c0: C).(csubc g e1 c0)) H2 (CHead x0 k x1) H3) in (let H7 \def (eq_ind C e2 -(\lambda (c0: C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to -(\forall (e3: C).((csubc g e3 c0) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 -e3)) (\lambda (c1: C).(csubc g c1 (CHead c k t))))))))) H0 (CHead x0 k x1) -H3) in (let H8 \def (eq_ind T t (\lambda (t0: T).(\forall (h0: nat).((drop h0 -n (CHead c k t0) (CHead x0 k x1)) \to (\forall (e3: C).((csubc g e3 (CHead x0 -k x1)) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 e3)) (\lambda (c1: C).(csubc -g c1 (CHead c k t0))))))))) H7 (lift h (r k n) x1) H4) in (eq_ind_r T (lift h -(r k n) x1) (\lambda (t0: T).(ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) -(\lambda (c1: C).(csubc g c1 (CHead c k t0))))) (let H_x \def -(csubc_gen_head_r g x0 e1 x1 k H6) in (let H9 \def H_x in (or3_ind (ex2 C -(\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1: C).(csubc g c1 -x0))) (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k -(Bind Abbr))))) (\lambda (c1: C).(\lambda (v: T).(\lambda (_: A).(eq C e1 -(CHead c1 (Bind Abst) v))))) (\lambda (c1: C).(\lambda (_: T).(\lambda (_: -A).(csubc g c1 x0)))) (\lambda (c1: C).(\lambda (v: T).(\lambda (a: A).(sc3 g -(asucc g a) c1 v)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g a -x0 x1))))) (ex4_3 B C T (\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(eq -C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b: B).(\lambda (_: C).(\lambda -(_: T).(eq K k (Bind b))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: -T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c1: C).(\lambda (_: -T).(csubc g c1 x0))))) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda -(c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) (\lambda (H10: (ex2 C -(\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1: C).(csubc g c1 -x0)))).(ex2_ind C (\lambda (c1: C).(eq C e1 (CHead c1 k x1))) (\lambda (c1: -C).(csubc g c1 x0)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda -(c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) (\lambda (x: -C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12: (csubc g x -x0)).(eq_ind_r C (CHead x k x1) (\lambda (c0: C).(ex2 C (\lambda (c1: -C).(drop h (S n) c1 c0)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k -n) x1)))))) (let H_x0 \def (H x0 (r k n) h H5 x H12) in (let H13 \def H_x0 in -(ex2_ind C (\lambda (c1: C).(drop h (r k n) c1 x)) (\lambda (c1: C).(csubc g -c1 c)) (ex2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) (\lambda -(c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) (\lambda (x2: -C).(\lambda (H14: (drop h (r k n) x2 x)).(\lambda (H15: (csubc g x2 -c)).(ex_intro2 C (\lambda (c1: C).(drop h (S n) c1 (CHead x k x1))) (\lambda -(c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1)))) (CHead x2 k (lift h (r -k n) x1)) (drop_skip k h n x2 x H14 x1) (csubc_head g x2 c H15 k (lift h (r k -n) x1)))))) H13))) e1 H11)))) H10)) (\lambda (H10: (ex5_3 C T A (\lambda (_: -C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abbr))))) (\lambda (c1: -C).(\lambda (v: T).(\lambda (_: A).(eq C e1 (CHead c1 (Bind Abst) v))))) -(\lambda (c1: C).(\lambda (_: T).(\lambda (_: A).(csubc g c1 x0)))) (\lambda -(c1: C).(\lambda (v: T).(\lambda (a: A).(sc3 g (asucc g a) c1 v)))) (\lambda -(_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g a x0 x1)))))).(ex5_3_ind C T A -(\lambda (_: C).(\lambda (_: T).(\lambda (_: A).(eq K k (Bind Abbr))))) -(\lambda (c1: C).(\lambda (v: T).(\lambda (_: A).(eq C e1 (CHead c1 (Bind -Abst) v))))) (\lambda (c1: C).(\lambda (_: T).(\lambda (_: A).(csubc g c1 -x0)))) (\lambda (c1: C).(\lambda (v: T).(\lambda (a: A).(sc3 g (asucc g a) c1 -v)))) (\lambda (_: C).(\lambda (_: T).(\lambda (a: A).(sc3 g a x0 x1)))) (ex2 -C (\lambda (c1: C).(drop h (S n) c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead -c k (lift h (r k n) x1))))) (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: -A).(\lambda (H11: (eq K k (Bind Abbr))).(\lambda (H12: (eq C e1 (CHead x2 -(Bind Abst) x3))).(\lambda (H13: (csubc g x2 x0)).(\lambda (H14: (sc3 g -(asucc g x4) x2 x3)).(\lambda (H15: (sc3 g x4 x0 x1)).(eq_ind_r C (CHead x2 -(Bind Abst) x3) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(drop h (S n) c1 -c0)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1)))))) (let -H16 \def (eq_ind K k (\lambda (k0: K).(\forall (h0: nat).((drop h0 n (CHead c -k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g e3 -(CHead x0 k0 x1)) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 e3)) (\lambda -(c1: C).(csubc g c1 (CHead c k0 (lift h (r k0 n) x1)))))))))) H8 (Bind Abbr) -H11) in (let H17 \def (eq_ind K k (\lambda (k0: K).(drop h (r k0 n) c x0)) H5 -(Bind Abbr) H11) in (eq_ind_r K (Bind Abbr) (\lambda (k0: K).(ex2 C (\lambda -(c1: C).(drop h (S n) c1 (CHead x2 (Bind Abst) x3))) (\lambda (c1: C).(csubc -g c1 (CHead c k0 (lift h (r k0 n) x1)))))) (let H_x0 \def (H x0 (r (Bind -Abbr) n) h H17 x2 H13) in (let H18 \def H_x0 in (ex2_ind C (\lambda (c1: -C).(drop h n c1 x2)) (\lambda (c1: C).(csubc g c1 c)) (ex2 C (\lambda (c1: -C).(drop h (S n) c1 (CHead x2 (Bind Abst) x3))) (\lambda (c1: C).(csubc g c1 -(CHead c (Bind Abbr) (lift h (r (Bind Abbr) n) x1))))) (\lambda (x: -C).(\lambda (H19: (drop h n x x2)).(\lambda (H20: (csubc g x c)).(ex_intro2 C -(\lambda (c1: C).(drop h (S n) c1 (CHead x2 (Bind Abst) x3))) (\lambda (c1: -C).(csubc g c1 (CHead c (Bind Abbr) (lift h (r (Bind Abbr) n) x1)))) (CHead x -(Bind Abst) (lift h n x3)) (drop_skip_bind h n x x2 H19 Abst x3) (csubc_abst -g x c H20 (lift h n x3) x4 (sc3_lift g (asucc g x4) x2 x3 H14 x h n H19) -(lift h (r (Bind Abbr) n) x1) (sc3_lift g x4 x0 x1 H15 c h (r (Bind Abbr) n) -H17)))))) H18))) k H11))) e1 H12))))))))) H10)) (\lambda (H10: (ex4_3 B C T -(\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(eq C e1 (CHead c1 (Bind -Void) v1))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind -b))))) (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) -(\lambda (_: B).(\lambda (c1: C).(\lambda (_: T).(csubc g c1 -x0)))))).(ex4_3_ind B C T (\lambda (_: B).(\lambda (c1: C).(\lambda (v1: -T).(eq C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b: B).(\lambda (_: -C).(\lambda (_: T).(eq K k (Bind b))))) (\lambda (b: B).(\lambda (_: -C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: B).(\lambda (c1: -C).(\lambda (_: T).(csubc g c1 x0)))) (ex2 C (\lambda (c1: C).(drop h (S n) -c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1))))) -(\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11: (eq C e1 -(CHead x3 (Bind Void) x4))).(\lambda (H12: (eq K k (Bind x2))).(\lambda (H13: -(not (eq B x2 Void))).(\lambda (H14: (csubc g x3 x0)).(eq_ind_r C (CHead x3 -(Bind Void) x4) (\lambda (c0: C).(ex2 C (\lambda (c1: C).(drop h (S n) c1 -c0)) (\lambda (c1: C).(csubc g c1 (CHead c k (lift h (r k n) x1)))))) (let -H15 \def (eq_ind K k (\lambda (k0: K).(\forall (h0: nat).((drop h0 n (CHead c -k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3: C).((csubc g e3 -(CHead x0 k0 x1)) \to (ex2 C (\lambda (c1: C).(drop h0 n c1 e3)) (\lambda -(c1: C).(csubc g c1 (CHead c k0 (lift h (r k0 n) x1)))))))))) H8 (Bind x2) -H12) in (let H16 \def (eq_ind K k (\lambda (k0: K).(drop h (r k0 n) c x0)) H5 -(Bind x2) H12) in (eq_ind_r K (Bind x2) (\lambda (k0: K).(ex2 C (\lambda (c1: -C).(drop h (S n) c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1 -(CHead c k0 (lift h (r k0 n) x1)))))) (let H_x0 \def (H x0 (r (Bind x2) n) h -H16 x3 H14) in (let H17 \def H_x0 in (ex2_ind C (\lambda (c1: C).(drop h n c1 -x3)) (\lambda (c1: C).(csubc g c1 c)) (ex2 C (\lambda (c1: C).(drop h (S n) -c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1 (CHead c (Bind -x2) (lift h (r (Bind x2) n) x1))))) (\lambda (x: C).(\lambda (H18: (drop h n -x x3)).(\lambda (H19: (csubc g x c)).(ex_intro2 C (\lambda (c1: C).(drop h (S -n) c1 (CHead x3 (Bind Void) x4))) (\lambda (c1: C).(csubc g c1 (CHead c (Bind -x2) (lift h (r (Bind x2) n) x1)))) (CHead x (Bind Void) (lift h n x4)) -(drop_skip_bind h n x x3 H18 Void x4) (csubc_void g x c H19 x2 H13 (lift h n -x4) (lift h (r (Bind x2) n) x1)))))) H17))) k H12))) e1 H11)))))))) H10)) -H9))) t H4))))))))) (drop_gen_skip_l c e2 t h n k H1)))))))) d))))))) c2)). -(* COMMENTS -Initial nodes: 3747 -END *) + \lambda (g: G).(\lambda (c2: C).(let TMP_3 \def (\lambda (c: C).(\forall +(e2: C).(\forall (d: nat).(\forall (h: nat).((drop h d c e2) \to (\forall +(e1: C).((csubc g e1 e2) \to (let TMP_1 \def (\lambda (c1: C).(drop h d c1 +e1)) in (let TMP_2 \def (\lambda (c1: C).(csubc g c1 c)) in (ex2 C TMP_1 +TMP_2)))))))))) in (let TMP_30 \def (\lambda (n: nat).(\lambda (e2: +C).(\lambda (d: nat).(\lambda (h: nat).(\lambda (H: (drop h d (CSort n) +e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let TMP_4 \def (CSort +n) in (let TMP_5 \def (eq C e2 TMP_4) in (let TMP_6 \def (eq nat h O) in (let +TMP_7 \def (eq nat d O) in (let TMP_8 \def (\lambda (c1: C).(drop h d c1 e1)) +in (let TMP_10 \def (\lambda (c1: C).(let TMP_9 \def (CSort n) in (csubc g c1 +TMP_9))) in (let TMP_11 \def (ex2 C TMP_8 TMP_10) in (let TMP_28 \def +(\lambda (H1: (eq C e2 (CSort n))).(\lambda (H2: (eq nat h O)).(\lambda (H3: +(eq nat d O)).(let TMP_15 \def (\lambda (n0: nat).(let TMP_12 \def (\lambda +(c1: C).(drop n0 d c1 e1)) in (let TMP_14 \def (\lambda (c1: C).(let TMP_13 +\def (CSort n) in (csubc g c1 TMP_13))) in (ex2 C TMP_12 TMP_14)))) in (let +TMP_19 \def (\lambda (n0: nat).(let TMP_16 \def (\lambda (c1: C).(drop O n0 +c1 e1)) in (let TMP_18 \def (\lambda (c1: C).(let TMP_17 \def (CSort n) in +(csubc g c1 TMP_17))) in (ex2 C TMP_16 TMP_18)))) in (let TMP_20 \def +(\lambda (c: C).(csubc g e1 c)) in (let TMP_21 \def (CSort n) in (let H4 \def +(eq_ind C e2 TMP_20 H0 TMP_21 H1) in (let TMP_22 \def (\lambda (c1: C).(drop +O O c1 e1)) in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (CSort n) +in (csubc g c1 TMP_23))) in (let TMP_25 \def (drop_refl e1) in (let TMP_26 +\def (ex_intro2 C TMP_22 TMP_24 e1 TMP_25 H4) in (let TMP_27 \def (eq_ind_r +nat O TMP_19 TMP_26 d H3) in (eq_ind_r nat O TMP_15 TMP_27 h H2)))))))))))))) +in (let TMP_29 \def (drop_gen_sort n h d e2 H) in (and3_ind TMP_5 TMP_6 TMP_7 +TMP_11 TMP_28 TMP_29))))))))))))))))) in (let TMP_354 \def (\lambda (c: +C).(\lambda (H: ((\forall (e2: C).(\forall (d: nat).(\forall (h: nat).((drop +h d c e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda (c1: +C).(drop h d c1 e1)) (\lambda (c1: C).(csubc g c1 c))))))))))).(\lambda (k: +K).(\lambda (t: T).(\lambda (e2: C).(\lambda (d: nat).(let TMP_34 \def +(\lambda (n: nat).(\forall (h: nat).((drop h n (CHead c k t) e2) \to (\forall +(e1: C).((csubc g e1 e2) \to (let TMP_31 \def (\lambda (c1: C).(drop h n c1 +e1)) in (let TMP_33 \def (\lambda (c1: C).(let TMP_32 \def (CHead c k t) in +(csubc g c1 TMP_32))) in (ex2 C TMP_31 TMP_33)))))))) in (let TMP_67 \def +(\lambda (h: nat).(let TMP_38 \def (\lambda (n: nat).((drop n O (CHead c k t) +e2) \to (\forall (e1: C).((csubc g e1 e2) \to (let TMP_35 \def (\lambda (c1: +C).(drop n O c1 e1)) in (let TMP_37 \def (\lambda (c1: C).(let TMP_36 \def +(CHead c k t) in (csubc g c1 TMP_36))) in (ex2 C TMP_35 TMP_37))))))) in (let +TMP_47 \def (\lambda (H0: (drop O O (CHead c k t) e2)).(\lambda (e1: +C).(\lambda (H1: (csubc g e1 e2)).(let TMP_39 \def (\lambda (c0: C).(csubc g +e1 c0)) in (let TMP_40 \def (CHead c k t) in (let TMP_41 \def (CHead c k t) +in (let TMP_42 \def (drop_gen_refl TMP_41 e2 H0) in (let H2 \def (eq_ind_r C +e2 TMP_39 H1 TMP_40 TMP_42) in (let TMP_43 \def (\lambda (c1: C).(drop O O c1 +e1)) in (let TMP_45 \def (\lambda (c1: C).(let TMP_44 \def (CHead c k t) in +(csubc g c1 TMP_44))) in (let TMP_46 \def (drop_refl e1) in (ex_intro2 C +TMP_43 TMP_45 e1 TMP_46 H2)))))))))))) in (let TMP_66 \def (\lambda (n: +nat).(\lambda (_: (((drop n O (CHead c k t) e2) \to (\forall (e1: C).((csubc +g e1 e2) \to (ex2 C (\lambda (c1: C).(drop n O c1 e1)) (\lambda (c1: +C).(csubc g c1 (CHead c k t))))))))).(\lambda (H1: (drop (S n) O (CHead c k +t) e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 e2)).(let TMP_48 \def (r k +n) in (let TMP_49 \def (drop_gen_drop k c e2 t n H1) in (let H_x \def (H e2 O +TMP_48 TMP_49 e1 H2) in (let H3 \def H_x in (let TMP_51 \def (\lambda (c1: +C).(let TMP_50 \def (r k n) in (drop TMP_50 O c1 e1))) in (let TMP_52 \def +(\lambda (c1: C).(csubc g c1 c)) in (let TMP_54 \def (\lambda (c1: C).(let +TMP_53 \def (S n) in (drop TMP_53 O c1 e1))) in (let TMP_56 \def (\lambda +(c1: C).(let TMP_55 \def (CHead c k t) in (csubc g c1 TMP_55))) in (let +TMP_57 \def (ex2 C TMP_54 TMP_56) in (let TMP_65 \def (\lambda (x: +C).(\lambda (H4: (drop (r k n) O x e1)).(\lambda (H5: (csubc g x c)).(let +TMP_59 \def (\lambda (c1: C).(let TMP_58 \def (S n) in (drop TMP_58 O c1 +e1))) in (let TMP_61 \def (\lambda (c1: C).(let TMP_60 \def (CHead c k t) in +(csubc g c1 TMP_60))) in (let TMP_62 \def (CHead x k t) in (let TMP_63 \def +(drop_drop k n x e1 H4 t) in (let TMP_64 \def (csubc_head g x c H5 k t) in +(ex_intro2 C TMP_59 TMP_61 TMP_62 TMP_63 TMP_64))))))))) in (ex2_ind C TMP_51 +TMP_52 TMP_57 TMP_65 H3)))))))))))))))) in (nat_ind TMP_38 TMP_47 TMP_66 +h))))) in (let TMP_353 \def (\lambda (n: nat).(\lambda (H0: ((\forall (h: +nat).((drop h n (CHead c k t) e2) \to (\forall (e1: C).((csubc g e1 e2) \to +(ex2 C (\lambda (c1: C).(drop h n c1 e1)) (\lambda (c1: C).(csubc g c1 (CHead +c k t)))))))))).(\lambda (h: nat).(\lambda (H1: (drop h (S n) (CHead c k t) +e2)).(\lambda (e1: C).(\lambda (H2: (csubc g e1 e2)).(let TMP_69 \def +(\lambda (e: C).(\lambda (v: T).(let TMP_68 \def (CHead e k v) in (eq C e2 +TMP_68)))) in (let TMP_72 \def (\lambda (_: C).(\lambda (v: T).(let TMP_70 +\def (r k n) in (let TMP_71 \def (lift h TMP_70 v) in (eq T t TMP_71))))) in +(let TMP_74 \def (\lambda (e: C).(\lambda (_: T).(let TMP_73 \def (r k n) in +(drop h TMP_73 c e)))) in (let TMP_76 \def (\lambda (c1: C).(let TMP_75 \def +(S n) in (drop h TMP_75 c1 e1))) in (let TMP_78 \def (\lambda (c1: C).(let +TMP_77 \def (CHead c k t) in (csubc g c1 TMP_77))) in (let TMP_79 \def (ex2 C +TMP_76 TMP_78) in (let TMP_351 \def (\lambda (x0: C).(\lambda (x1: +T).(\lambda (H3: (eq C e2 (CHead x0 k x1))).(\lambda (H4: (eq T t (lift h (r +k n) x1))).(\lambda (H5: (drop h (r k n) c x0)).(let TMP_80 \def (\lambda +(c0: C).(csubc g e1 c0)) in (let TMP_81 \def (CHead x0 k x1) in (let H6 \def +(eq_ind C e2 TMP_80 H2 TMP_81 H3) in (let TMP_85 \def (\lambda (c0: +C).(\forall (h0: nat).((drop h0 n (CHead c k t) c0) \to (\forall (e3: +C).((csubc g e3 c0) \to (let TMP_82 \def (\lambda (c1: C).(drop h0 n c1 e3)) +in (let TMP_84 \def (\lambda (c1: C).(let TMP_83 \def (CHead c k t) in (csubc +g c1 TMP_83))) in (ex2 C TMP_82 TMP_84)))))))) in (let TMP_86 \def (CHead x0 +k x1) in (let H7 \def (eq_ind C e2 TMP_85 H0 TMP_86 H3) in (let TMP_90 \def +(\lambda (t0: T).(\forall (h0: nat).((drop h0 n (CHead c k t0) (CHead x0 k +x1)) \to (\forall (e3: C).((csubc g e3 (CHead x0 k x1)) \to (let TMP_87 \def +(\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_89 \def (\lambda (c1: C).(let +TMP_88 \def (CHead c k t0) in (csubc g c1 TMP_88))) in (ex2 C TMP_87 +TMP_89)))))))) in (let TMP_91 \def (r k n) in (let TMP_92 \def (lift h TMP_91 +x1) in (let H8 \def (eq_ind T t TMP_90 H7 TMP_92 H4) in (let TMP_93 \def (r k +n) in (let TMP_94 \def (lift h TMP_93 x1) in (let TMP_99 \def (\lambda (t0: +T).(let TMP_96 \def (\lambda (c1: C).(let TMP_95 \def (S n) in (drop h TMP_95 +c1 e1))) in (let TMP_98 \def (\lambda (c1: C).(let TMP_97 \def (CHead c k t0) +in (csubc g c1 TMP_97))) in (ex2 C TMP_96 TMP_98)))) in (let H_x \def +(csubc_gen_head_r g x0 e1 x1 k H6) in (let H9 \def H_x in (let TMP_101 \def +(\lambda (c1: C).(let TMP_100 \def (CHead c1 k x1) in (eq C e1 TMP_100))) in +(let TMP_102 \def (\lambda (c1: C).(csubc g c1 x0)) in (let TMP_103 \def (ex2 +C TMP_101 TMP_102) in (let TMP_105 \def (\lambda (_: C).(\lambda (_: +T).(\lambda (_: A).(let TMP_104 \def (Bind Abbr) in (eq K k TMP_104))))) in +(let TMP_108 \def (\lambda (c1: C).(\lambda (v: T).(\lambda (_: A).(let +TMP_106 \def (Bind Abst) in (let TMP_107 \def (CHead c1 TMP_106 v) in (eq C +e1 TMP_107)))))) in (let TMP_109 \def (\lambda (c1: C).(\lambda (_: +T).(\lambda (_: A).(csubc g c1 x0)))) in (let TMP_111 \def (\lambda (c1: +C).(\lambda (v: T).(\lambda (a: A).(let TMP_110 \def (asucc g a) in (sc3 g +TMP_110 c1 v))))) in (let TMP_112 \def (\lambda (_: C).(\lambda (_: +T).(\lambda (a: A).(sc3 g a x0 x1)))) in (let TMP_113 \def (ex5_3 C T A +TMP_105 TMP_108 TMP_109 TMP_111 TMP_112) in (let TMP_116 \def (\lambda (_: +B).(\lambda (c1: C).(\lambda (v1: T).(let TMP_114 \def (Bind Void) in (let +TMP_115 \def (CHead c1 TMP_114 v1) in (eq C e1 TMP_115)))))) in (let TMP_118 +\def (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(let TMP_117 \def (Bind +b) in (eq K k TMP_117))))) in (let TMP_120 \def (\lambda (b: B).(\lambda (_: +C).(\lambda (_: T).(let TMP_119 \def (eq B b Void) in (not TMP_119))))) in +(let TMP_121 \def (\lambda (_: B).(\lambda (c1: C).(\lambda (_: T).(csubc g +c1 x0)))) in (let TMP_122 \def (ex4_3 B C T TMP_116 TMP_118 TMP_120 TMP_121) +in (let TMP_124 \def (\lambda (c1: C).(let TMP_123 \def (S n) in (drop h +TMP_123 c1 e1))) in (let TMP_128 \def (\lambda (c1: C).(let TMP_125 \def (r k +n) in (let TMP_126 \def (lift h TMP_125 x1) in (let TMP_127 \def (CHead c k +TMP_126) in (csubc g c1 TMP_127))))) in (let TMP_129 \def (ex2 C TMP_124 +TMP_128) in (let TMP_177 \def (\lambda (H10: (ex2 C (\lambda (c1: C).(eq C e1 +(CHead c1 k x1))) (\lambda (c1: C).(csubc g c1 x0)))).(let TMP_131 \def +(\lambda (c1: C).(let TMP_130 \def (CHead c1 k x1) in (eq C e1 TMP_130))) in +(let TMP_132 \def (\lambda (c1: C).(csubc g c1 x0)) in (let TMP_134 \def +(\lambda (c1: C).(let TMP_133 \def (S n) in (drop h TMP_133 c1 e1))) in (let +TMP_138 \def (\lambda (c1: C).(let TMP_135 \def (r k n) in (let TMP_136 \def +(lift h TMP_135 x1) in (let TMP_137 \def (CHead c k TMP_136) in (csubc g c1 +TMP_137))))) in (let TMP_139 \def (ex2 C TMP_134 TMP_138) in (let TMP_176 +\def (\lambda (x: C).(\lambda (H11: (eq C e1 (CHead x k x1))).(\lambda (H12: +(csubc g x x0)).(let TMP_140 \def (CHead x k x1) in (let TMP_147 \def +(\lambda (c0: C).(let TMP_142 \def (\lambda (c1: C).(let TMP_141 \def (S n) +in (drop h TMP_141 c1 c0))) in (let TMP_146 \def (\lambda (c1: C).(let +TMP_143 \def (r k n) in (let TMP_144 \def (lift h TMP_143 x1) in (let TMP_145 +\def (CHead c k TMP_144) in (csubc g c1 TMP_145))))) in (ex2 C TMP_142 +TMP_146)))) in (let TMP_148 \def (r k n) in (let H_x0 \def (H x0 TMP_148 h H5 +x H12) in (let H13 \def H_x0 in (let TMP_150 \def (\lambda (c1: C).(let +TMP_149 \def (r k n) in (drop h TMP_149 c1 x))) in (let TMP_151 \def (\lambda +(c1: C).(csubc g c1 c)) in (let TMP_154 \def (\lambda (c1: C).(let TMP_152 +\def (S n) in (let TMP_153 \def (CHead x k x1) in (drop h TMP_152 c1 +TMP_153)))) in (let TMP_158 \def (\lambda (c1: C).(let TMP_155 \def (r k n) +in (let TMP_156 \def (lift h TMP_155 x1) in (let TMP_157 \def (CHead c k +TMP_156) in (csubc g c1 TMP_157))))) in (let TMP_159 \def (ex2 C TMP_154 +TMP_158) in (let TMP_174 \def (\lambda (x2: C).(\lambda (H14: (drop h (r k n) +x2 x)).(\lambda (H15: (csubc g x2 c)).(let TMP_162 \def (\lambda (c1: C).(let +TMP_160 \def (S n) in (let TMP_161 \def (CHead x k x1) in (drop h TMP_160 c1 +TMP_161)))) in (let TMP_166 \def (\lambda (c1: C).(let TMP_163 \def (r k n) +in (let TMP_164 \def (lift h TMP_163 x1) in (let TMP_165 \def (CHead c k +TMP_164) in (csubc g c1 TMP_165))))) in (let TMP_167 \def (r k n) in (let +TMP_168 \def (lift h TMP_167 x1) in (let TMP_169 \def (CHead x2 k TMP_168) in +(let TMP_170 \def (drop_skip k h n x2 x H14 x1) in (let TMP_171 \def (r k n) +in (let TMP_172 \def (lift h TMP_171 x1) in (let TMP_173 \def (csubc_head g +x2 c H15 k TMP_172) in (ex_intro2 C TMP_162 TMP_166 TMP_169 TMP_170 +TMP_173))))))))))))) in (let TMP_175 \def (ex2_ind C TMP_150 TMP_151 TMP_159 +TMP_174 H13) in (eq_ind_r C TMP_140 TMP_147 TMP_175 e1 H11)))))))))))))))) in +(ex2_ind C TMP_131 TMP_132 TMP_139 TMP_176 H10)))))))) in (let TMP_266 \def +(\lambda (H10: (ex5_3 C T A (\lambda (_: C).(\lambda (_: T).(\lambda (_: +A).(eq K k (Bind Abbr))))) (\lambda (c1: C).(\lambda (v: T).(\lambda (_: +A).(eq C e1 (CHead c1 (Bind Abst) v))))) (\lambda (c1: C).(\lambda (_: +T).(\lambda (_: A).(csubc g c1 x0)))) (\lambda (c1: C).(\lambda (v: +T).(\lambda (a: A).(sc3 g (asucc g a) c1 v)))) (\lambda (_: C).(\lambda (_: +T).(\lambda (a: A).(sc3 g a x0 x1)))))).(let TMP_179 \def (\lambda (_: +C).(\lambda (_: T).(\lambda (_: A).(let TMP_178 \def (Bind Abbr) in (eq K k +TMP_178))))) in (let TMP_182 \def (\lambda (c1: C).(\lambda (v: T).(\lambda +(_: A).(let TMP_180 \def (Bind Abst) in (let TMP_181 \def (CHead c1 TMP_180 +v) in (eq C e1 TMP_181)))))) in (let TMP_183 \def (\lambda (c1: C).(\lambda +(_: T).(\lambda (_: A).(csubc g c1 x0)))) in (let TMP_185 \def (\lambda (c1: +C).(\lambda (v: T).(\lambda (a: A).(let TMP_184 \def (asucc g a) in (sc3 g +TMP_184 c1 v))))) in (let TMP_186 \def (\lambda (_: C).(\lambda (_: +T).(\lambda (a: A).(sc3 g a x0 x1)))) in (let TMP_188 \def (\lambda (c1: +C).(let TMP_187 \def (S n) in (drop h TMP_187 c1 e1))) in (let TMP_192 \def +(\lambda (c1: C).(let TMP_189 \def (r k n) in (let TMP_190 \def (lift h +TMP_189 x1) in (let TMP_191 \def (CHead c k TMP_190) in (csubc g c1 +TMP_191))))) in (let TMP_193 \def (ex2 C TMP_188 TMP_192) in (let TMP_265 +\def (\lambda (x2: C).(\lambda (x3: T).(\lambda (x4: A).(\lambda (H11: (eq K +k (Bind Abbr))).(\lambda (H12: (eq C e1 (CHead x2 (Bind Abst) x3))).(\lambda +(H13: (csubc g x2 x0)).(\lambda (H14: (sc3 g (asucc g x4) x2 x3)).(\lambda +(H15: (sc3 g x4 x0 x1)).(let TMP_194 \def (Bind Abst) in (let TMP_195 \def +(CHead x2 TMP_194 x3) in (let TMP_202 \def (\lambda (c0: C).(let TMP_197 \def +(\lambda (c1: C).(let TMP_196 \def (S n) in (drop h TMP_196 c1 c0))) in (let +TMP_201 \def (\lambda (c1: C).(let TMP_198 \def (r k n) in (let TMP_199 \def +(lift h TMP_198 x1) in (let TMP_200 \def (CHead c k TMP_199) in (csubc g c1 +TMP_200))))) in (ex2 C TMP_197 TMP_201)))) in (let TMP_208 \def (\lambda (k0: +K).(\forall (h0: nat).((drop h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0 +k0 x1)) \to (\forall (e3: C).((csubc g e3 (CHead x0 k0 x1)) \to (let TMP_203 +\def (\lambda (c1: C).(drop h0 n c1 e3)) in (let TMP_207 \def (\lambda (c1: +C).(let TMP_204 \def (r k0 n) in (let TMP_205 \def (lift h TMP_204 x1) in +(let TMP_206 \def (CHead c k0 TMP_205) in (csubc g c1 TMP_206))))) in (ex2 C +TMP_203 TMP_207)))))))) in (let TMP_209 \def (Bind Abbr) in (let H16 \def +(eq_ind K k TMP_208 H8 TMP_209 H11) in (let TMP_211 \def (\lambda (k0: +K).(let TMP_210 \def (r k0 n) in (drop h TMP_210 c x0))) in (let TMP_212 \def +(Bind Abbr) in (let H17 \def (eq_ind K k TMP_211 H5 TMP_212 H11) in (let +TMP_213 \def (Bind Abbr) in (let TMP_222 \def (\lambda (k0: K).(let TMP_217 +\def (\lambda (c1: C).(let TMP_214 \def (S n) in (let TMP_215 \def (Bind +Abst) in (let TMP_216 \def (CHead x2 TMP_215 x3) in (drop h TMP_214 c1 +TMP_216))))) in (let TMP_221 \def (\lambda (c1: C).(let TMP_218 \def (r k0 n) +in (let TMP_219 \def (lift h TMP_218 x1) in (let TMP_220 \def (CHead c k0 +TMP_219) in (csubc g c1 TMP_220))))) in (ex2 C TMP_217 TMP_221)))) in (let +TMP_223 \def (Bind Abbr) in (let TMP_224 \def (r TMP_223 n) in (let H_x0 \def +(H x0 TMP_224 h H17 x2 H13) in (let H18 \def H_x0 in (let TMP_225 \def +(\lambda (c1: C).(drop h n c1 x2)) in (let TMP_226 \def (\lambda (c1: +C).(csubc g c1 c)) in (let TMP_230 \def (\lambda (c1: C).(let TMP_227 \def (S +n) in (let TMP_228 \def (Bind Abst) in (let TMP_229 \def (CHead x2 TMP_228 +x3) in (drop h TMP_227 c1 TMP_229))))) in (let TMP_236 \def (\lambda (c1: +C).(let TMP_231 \def (Bind Abbr) in (let TMP_232 \def (Bind Abbr) in (let +TMP_233 \def (r TMP_232 n) in (let TMP_234 \def (lift h TMP_233 x1) in (let +TMP_235 \def (CHead c TMP_231 TMP_234) in (csubc g c1 TMP_235))))))) in (let +TMP_237 \def (ex2 C TMP_230 TMP_236) in (let TMP_262 \def (\lambda (x: +C).(\lambda (H19: (drop h n x x2)).(\lambda (H20: (csubc g x c)).(let TMP_241 +\def (\lambda (c1: C).(let TMP_238 \def (S n) in (let TMP_239 \def (Bind +Abst) in (let TMP_240 \def (CHead x2 TMP_239 x3) in (drop h TMP_238 c1 +TMP_240))))) in (let TMP_247 \def (\lambda (c1: C).(let TMP_242 \def (Bind +Abbr) in (let TMP_243 \def (Bind Abbr) in (let TMP_244 \def (r TMP_243 n) in +(let TMP_245 \def (lift h TMP_244 x1) in (let TMP_246 \def (CHead c TMP_242 +TMP_245) in (csubc g c1 TMP_246))))))) in (let TMP_248 \def (Bind Abst) in +(let TMP_249 \def (lift h n x3) in (let TMP_250 \def (CHead x TMP_248 +TMP_249) in (let TMP_251 \def (drop_skip_bind h n x x2 H19 Abst x3) in (let +TMP_252 \def (lift h n x3) in (let TMP_253 \def (asucc g x4) in (let TMP_254 +\def (sc3_lift g TMP_253 x2 x3 H14 x h n H19) in (let TMP_255 \def (Bind +Abbr) in (let TMP_256 \def (r TMP_255 n) in (let TMP_257 \def (lift h TMP_256 +x1) in (let TMP_258 \def (Bind Abbr) in (let TMP_259 \def (r TMP_258 n) in +(let TMP_260 \def (sc3_lift g x4 x0 x1 H15 c h TMP_259 H17) in (let TMP_261 +\def (csubc_abst g x c H20 TMP_252 x4 TMP_254 TMP_257 TMP_260) in (ex_intro2 +C TMP_241 TMP_247 TMP_250 TMP_251 TMP_261)))))))))))))))))))) in (let TMP_263 +\def (ex2_ind C TMP_225 TMP_226 TMP_237 TMP_262 H18) in (let TMP_264 \def +(eq_ind_r K TMP_213 TMP_222 TMP_263 k H11) in (eq_ind_r C TMP_195 TMP_202 +TMP_264 e1 H12)))))))))))))))))))))))))))))))) in (ex5_3_ind C T A TMP_179 +TMP_182 TMP_183 TMP_185 TMP_186 TMP_193 TMP_265 H10))))))))))) in (let +TMP_349 \def (\lambda (H10: (ex4_3 B C T (\lambda (_: B).(\lambda (c1: +C).(\lambda (v1: T).(eq C e1 (CHead c1 (Bind Void) v1))))) (\lambda (b: +B).(\lambda (_: C).(\lambda (_: T).(eq K k (Bind b))))) (\lambda (b: +B).(\lambda (_: C).(\lambda (_: T).(not (eq B b Void))))) (\lambda (_: +B).(\lambda (c1: C).(\lambda (_: T).(csubc g c1 x0)))))).(let TMP_269 \def +(\lambda (_: B).(\lambda (c1: C).(\lambda (v1: T).(let TMP_267 \def (Bind +Void) in (let TMP_268 \def (CHead c1 TMP_267 v1) in (eq C e1 TMP_268)))))) in +(let TMP_271 \def (\lambda (b: B).(\lambda (_: C).(\lambda (_: T).(let +TMP_270 \def (Bind b) in (eq K k TMP_270))))) in (let TMP_273 \def (\lambda +(b: B).(\lambda (_: C).(\lambda (_: T).(let TMP_272 \def (eq B b Void) in +(not TMP_272))))) in (let TMP_274 \def (\lambda (_: B).(\lambda (c1: +C).(\lambda (_: T).(csubc g c1 x0)))) in (let TMP_276 \def (\lambda (c1: +C).(let TMP_275 \def (S n) in (drop h TMP_275 c1 e1))) in (let TMP_280 \def +(\lambda (c1: C).(let TMP_277 \def (r k n) in (let TMP_278 \def (lift h +TMP_277 x1) in (let TMP_279 \def (CHead c k TMP_278) in (csubc g c1 +TMP_279))))) in (let TMP_281 \def (ex2 C TMP_276 TMP_280) in (let TMP_348 +\def (\lambda (x2: B).(\lambda (x3: C).(\lambda (x4: T).(\lambda (H11: (eq C +e1 (CHead x3 (Bind Void) x4))).(\lambda (H12: (eq K k (Bind x2))).(\lambda +(H13: (not (eq B x2 Void))).(\lambda (H14: (csubc g x3 x0)).(let TMP_282 \def +(Bind Void) in (let TMP_283 \def (CHead x3 TMP_282 x4) in (let TMP_290 \def +(\lambda (c0: C).(let TMP_285 \def (\lambda (c1: C).(let TMP_284 \def (S n) +in (drop h TMP_284 c1 c0))) in (let TMP_289 \def (\lambda (c1: C).(let +TMP_286 \def (r k n) in (let TMP_287 \def (lift h TMP_286 x1) in (let TMP_288 +\def (CHead c k TMP_287) in (csubc g c1 TMP_288))))) in (ex2 C TMP_285 +TMP_289)))) in (let TMP_296 \def (\lambda (k0: K).(\forall (h0: nat).((drop +h0 n (CHead c k0 (lift h (r k0 n) x1)) (CHead x0 k0 x1)) \to (\forall (e3: +C).((csubc g e3 (CHead x0 k0 x1)) \to (let TMP_291 \def (\lambda (c1: +C).(drop h0 n c1 e3)) in (let TMP_295 \def (\lambda (c1: C).(let TMP_292 \def +(r k0 n) in (let TMP_293 \def (lift h TMP_292 x1) in (let TMP_294 \def (CHead +c k0 TMP_293) in (csubc g c1 TMP_294))))) in (ex2 C TMP_291 TMP_295)))))))) +in (let TMP_297 \def (Bind x2) in (let H15 \def (eq_ind K k TMP_296 H8 +TMP_297 H12) in (let TMP_299 \def (\lambda (k0: K).(let TMP_298 \def (r k0 n) +in (drop h TMP_298 c x0))) in (let TMP_300 \def (Bind x2) in (let H16 \def +(eq_ind K k TMP_299 H5 TMP_300 H12) in (let TMP_301 \def (Bind x2) in (let +TMP_310 \def (\lambda (k0: K).(let TMP_305 \def (\lambda (c1: C).(let TMP_302 +\def (S n) in (let TMP_303 \def (Bind Void) in (let TMP_304 \def (CHead x3 +TMP_303 x4) in (drop h TMP_302 c1 TMP_304))))) in (let TMP_309 \def (\lambda +(c1: C).(let TMP_306 \def (r k0 n) in (let TMP_307 \def (lift h TMP_306 x1) +in (let TMP_308 \def (CHead c k0 TMP_307) in (csubc g c1 TMP_308))))) in (ex2 +C TMP_305 TMP_309)))) in (let TMP_311 \def (Bind x2) in (let TMP_312 \def (r +TMP_311 n) in (let H_x0 \def (H x0 TMP_312 h H16 x3 H14) in (let H17 \def +H_x0 in (let TMP_313 \def (\lambda (c1: C).(drop h n c1 x3)) in (let TMP_314 +\def (\lambda (c1: C).(csubc g c1 c)) in (let TMP_318 \def (\lambda (c1: +C).(let TMP_315 \def (S n) in (let TMP_316 \def (Bind Void) in (let TMP_317 +\def (CHead x3 TMP_316 x4) in (drop h TMP_315 c1 TMP_317))))) in (let TMP_324 +\def (\lambda (c1: C).(let TMP_319 \def (Bind x2) in (let TMP_320 \def (Bind +x2) in (let TMP_321 \def (r TMP_320 n) in (let TMP_322 \def (lift h TMP_321 +x1) in (let TMP_323 \def (CHead c TMP_319 TMP_322) in (csubc g c1 +TMP_323))))))) in (let TMP_325 \def (ex2 C TMP_318 TMP_324) in (let TMP_345 +\def (\lambda (x: C).(\lambda (H18: (drop h n x x3)).(\lambda (H19: (csubc g +x c)).(let TMP_329 \def (\lambda (c1: C).(let TMP_326 \def (S n) in (let +TMP_327 \def (Bind Void) in (let TMP_328 \def (CHead x3 TMP_327 x4) in (drop +h TMP_326 c1 TMP_328))))) in (let TMP_335 \def (\lambda (c1: C).(let TMP_330 +\def (Bind x2) in (let TMP_331 \def (Bind x2) in (let TMP_332 \def (r TMP_331 +n) in (let TMP_333 \def (lift h TMP_332 x1) in (let TMP_334 \def (CHead c +TMP_330 TMP_333) in (csubc g c1 TMP_334))))))) in (let TMP_336 \def (Bind +Void) in (let TMP_337 \def (lift h n x4) in (let TMP_338 \def (CHead x +TMP_336 TMP_337) in (let TMP_339 \def (drop_skip_bind h n x x3 H18 Void x4) +in (let TMP_340 \def (lift h n x4) in (let TMP_341 \def (Bind x2) in (let +TMP_342 \def (r TMP_341 n) in (let TMP_343 \def (lift h TMP_342 x1) in (let +TMP_344 \def (csubc_void g x c H19 x2 H13 TMP_340 TMP_343) in (ex_intro2 C +TMP_329 TMP_335 TMP_338 TMP_339 TMP_344))))))))))))))) in (let TMP_346 \def +(ex2_ind C TMP_313 TMP_314 TMP_325 TMP_345 H17) in (let TMP_347 \def +(eq_ind_r K TMP_301 TMP_310 TMP_346 k H12) in (eq_ind_r C TMP_283 TMP_290 +TMP_347 e1 H11))))))))))))))))))))))))))))))) in (ex4_3_ind B C T TMP_269 +TMP_271 TMP_273 TMP_274 TMP_281 TMP_348 H10)))))))))) in (let TMP_350 \def +(or3_ind TMP_103 TMP_113 TMP_122 TMP_129 TMP_177 TMP_266 TMP_349 H9) in +(eq_ind_r T TMP_94 TMP_99 TMP_350 t +H4)))))))))))))))))))))))))))))))))))))))))) in (let TMP_352 \def +(drop_gen_skip_l c e2 t h n k H1) in (ex3_2_ind C T TMP_69 TMP_72 TMP_74 +TMP_79 TMP_351 TMP_352))))))))))))))) in (nat_ind TMP_34 TMP_67 TMP_353 +d)))))))))) in (C_ind TMP_3 TMP_30 TMP_354 c2))))).