- \lambda (c: C).(let TMP_6 \def (\lambda (c0: C).(\forall (i: nat).(let TMP_3
-\def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_1 \def (Bind b)
-in (let TMP_2 \def (CHead e TMP_1 v) in (getl i c0 TMP_2)))))) in (let TMP_4
-\def (ex_3 C B T TMP_3) in (let TMP_5 \def (\forall (d: C).((getl i c0 d) \to
-(\forall (P: Prop).P))) in (or TMP_4 TMP_5)))))) in (let TMP_14 \def (\lambda
-(n: nat).(\lambda (i: nat).(let TMP_10 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_7 \def (CSort n) in (let TMP_8 \def (Bind b) in
-(let TMP_9 \def (CHead e TMP_8 v) in (getl i TMP_7 TMP_9))))))) in (let
-TMP_11 \def (ex_3 C B T TMP_10) in (let TMP_12 \def (\forall (d: C).((getl i
-(CSort n) d) \to (\forall (P: Prop).P))) in (let TMP_13 \def (\lambda (d:
-C).(\lambda (H: (getl i (CSort n) d)).(\lambda (P: Prop).(getl_gen_sort n i d
-H P)))) in (or_intror TMP_11 TMP_12 TMP_13))))))) in (let TMP_159 \def
-(\lambda (c0: C).(\lambda (H: ((\forall (i: nat).(or (ex_3 C B T (\lambda (e:
-C).(\lambda (b: B).(\lambda (v: T).(getl i c0 (CHead e (Bind b) v))))))
-(\forall (d: C).((getl i c0 d) \to (\forall (P: Prop).P))))))).(\lambda (k:
-K).(\lambda (t: T).(\lambda (i: nat).(let TMP_21 \def (\lambda (n: nat).(let
-TMP_18 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(let TMP_15 \def
-(CHead c0 k t) in (let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead e
-TMP_16 v) in (getl n TMP_15 TMP_17))))))) in (let TMP_19 \def (ex_3 C B T
-TMP_18) in (let TMP_20 \def (\forall (d: C).((getl n (CHead c0 k t) d) \to
-(\forall (P: Prop).P))) in (or TMP_19 TMP_20))))) in (let TMP_28 \def
-(\lambda (k0: K).(let TMP_25 \def (\lambda (e: C).(\lambda (b: B).(\lambda
-(v: T).(let TMP_22 \def (CHead c0 k0 t) in (let TMP_23 \def (Bind b) in (let
-TMP_24 \def (CHead e TMP_23 v) in (getl O TMP_22 TMP_24))))))) in (let TMP_26
-\def (ex_3 C B T TMP_25) in (let TMP_27 \def (\forall (d: C).((getl O (CHead
-c0 k0 t) d) \to (\forall (P: Prop).P))) in (or TMP_26 TMP_27))))) in (let
-TMP_43 \def (\lambda (b: B).(let TMP_33 \def (\lambda (e: C).(\lambda (b0:
-B).(\lambda (v: T).(let TMP_29 \def (Bind b) in (let TMP_30 \def (CHead c0
-TMP_29 t) in (let TMP_31 \def (Bind b0) in (let TMP_32 \def (CHead e TMP_31
-v) in (getl O TMP_30 TMP_32)))))))) in (let TMP_34 \def (ex_3 C B T TMP_33)
-in (let TMP_35 \def (\forall (d: C).((getl O (CHead c0 (Bind b) t) d) \to
-(\forall (P: Prop).P))) in (let TMP_40 \def (\lambda (e: C).(\lambda (b0:
-B).(\lambda (v: T).(let TMP_36 \def (Bind b) in (let TMP_37 \def (CHead c0
-TMP_36 t) in (let TMP_38 \def (Bind b0) in (let TMP_39 \def (CHead e TMP_38
-v) in (getl O TMP_37 TMP_39)))))))) in (let TMP_41 \def (getl_refl b c0 t) in
-(let TMP_42 \def (ex_3_intro C B T TMP_40 c0 b t TMP_41) in (or_introl TMP_34
-TMP_35 TMP_42)))))))) in (let TMP_101 \def (\lambda (f: F).(let H_x \def (H
-O) in (let H0 \def H_x in (let TMP_46 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_44 \def (Bind b) in (let TMP_45 \def (CHead e
-TMP_44 v) in (getl O c0 TMP_45)))))) in (let TMP_47 \def (ex_3 C B T TMP_46)
-in (let TMP_48 \def (\forall (d: C).((getl O c0 d) \to (\forall (P:
-Prop).P))) in (let TMP_53 \def (\lambda (e: C).(\lambda (b: B).(\lambda (v:
-T).(let TMP_49 \def (Flat f) in (let TMP_50 \def (CHead c0 TMP_49 t) in (let
-TMP_51 \def (Bind b) in (let TMP_52 \def (CHead e TMP_51 v) in (getl O TMP_50
-TMP_52)))))))) in (let TMP_54 \def (ex_3 C B T TMP_53) in (let TMP_55 \def
-(\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to (\forall (P: Prop).P)))
-in (let TMP_56 \def (or TMP_54 TMP_55) in (let TMP_85 \def (\lambda (H1:
-(ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl O c0 (CHead
-e (Bind b) v))))))).(let TMP_59 \def (\lambda (e: C).(\lambda (b: B).(\lambda
-(v: T).(let TMP_57 \def (Bind b) in (let TMP_58 \def (CHead e TMP_57 v) in
-(getl O c0 TMP_58)))))) in (let TMP_64 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_60 \def (Flat f) in (let TMP_61 \def (CHead c0
-TMP_60 t) in (let TMP_62 \def (Bind b) in (let TMP_63 \def (CHead e TMP_62 v)
-in (getl O TMP_61 TMP_63)))))))) in (let TMP_65 \def (ex_3 C B T TMP_64) in
-(let TMP_66 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to
-(\forall (P: Prop).P))) in (let TMP_67 \def (or TMP_65 TMP_66) in (let TMP_84
-\def (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl O
-c0 (CHead x0 (Bind x1) x2))).(let TMP_72 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_68 \def (Flat f) in (let TMP_69 \def (CHead c0
-TMP_68 t) in (let TMP_70 \def (Bind b) in (let TMP_71 \def (CHead e TMP_70 v)
-in (getl O TMP_69 TMP_71)))))))) in (let TMP_73 \def (ex_3 C B T TMP_72) in
-(let TMP_74 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to
-(\forall (P: Prop).P))) in (let TMP_79 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_75 \def (Flat f) in (let TMP_76 \def (CHead c0
-TMP_75 t) in (let TMP_77 \def (Bind b) in (let TMP_78 \def (CHead e TMP_77 v)
-in (getl O TMP_76 TMP_78)))))))) in (let TMP_80 \def (Bind x1) in (let TMP_81
-\def (CHead x0 TMP_80 x2) in (let TMP_82 \def (getl_flat c0 TMP_81 O H2 f t)
-in (let TMP_83 \def (ex_3_intro C B T TMP_79 x0 x1 x2 TMP_82) in (or_introl
-TMP_73 TMP_74 TMP_83))))))))))))) in (ex_3_ind C B T TMP_59 TMP_67 TMP_84
-H1)))))))) in (let TMP_100 \def (\lambda (H1: ((\forall (d: C).((getl O c0 d)
-\to (\forall (P: Prop).P))))).(let TMP_90 \def (\lambda (e: C).(\lambda (b:
-B).(\lambda (v: T).(let TMP_86 \def (Flat f) in (let TMP_87 \def (CHead c0
-TMP_86 t) in (let TMP_88 \def (Bind b) in (let TMP_89 \def (CHead e TMP_88 v)
-in (getl O TMP_87 TMP_89)))))))) in (let TMP_91 \def (ex_3 C B T TMP_90) in
-(let TMP_92 \def (\forall (d: C).((getl O (CHead c0 (Flat f) t) d) \to
-(\forall (P: Prop).P))) in (let TMP_99 \def (\lambda (d: C).(\lambda (H2:
-(getl O (CHead c0 (Flat f) t) d)).(\lambda (P: Prop).(let TMP_93 \def
-(drop_refl c0) in (let TMP_94 \def (Flat f) in (let TMP_95 \def (CHead c0
-TMP_94 t) in (let TMP_96 \def (getl_gen_O TMP_95 d H2) in (let TMP_97 \def
-(clear_gen_flat f c0 d t TMP_96) in (let TMP_98 \def (getl_intro O c0 d c0
-TMP_93 TMP_97) in (H1 d TMP_98 P)))))))))) in (or_intror TMP_91 TMP_92
-TMP_99)))))) in (or_ind TMP_47 TMP_48 TMP_56 TMP_85 TMP_100 H0)))))))))))))
-in (let TMP_102 \def (K_ind TMP_28 TMP_43 TMP_101 k) in (let TMP_158 \def
-(\lambda (n: nat).(\lambda (_: (or (ex_3 C B T (\lambda (e: C).(\lambda (b: