-(u1: T).(\forall (k: K).((getl h c (CHead e1 k u1)) \to (let TMP_2 \def
-(\lambda (e2: C).(\lambda (u2: T).(let TMP_1 \def (CHead e2 k u2) in (getl h
-c0 TMP_1)))) in (let TMP_3 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1
-e2))) in (let TMP_4 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u1 u2))) in
-(ex3_2 C T TMP_2 TMP_3 TMP_4))))))))))) in (let TMP_12 \def (\lambda (c:
-C).(\lambda (h: nat).(\lambda (e1: C).(\lambda (u1: T).(\lambda (k:
-K).(\lambda (H0: (getl h c (CHead e1 k u1))).(let TMP_7 \def (\lambda (e2:
-C).(\lambda (u2: T).(let TMP_6 \def (CHead e2 k u2) in (getl h c TMP_6)))) in
-(let TMP_8 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let
-TMP_9 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u1 u2))) in (let TMP_10 \def
-(wcpr0_refl e1) in (let TMP_11 \def (pr0_refl u1) in (ex3_2_intro C T TMP_7
-TMP_8 TMP_9 e1 u1 H0 TMP_10 TMP_11)))))))))))) in (let TMP_175 \def (\lambda
-(c3: C).(\lambda (c4: C).(\lambda (H0: (wcpr0 c3 c4)).(\lambda (H1: ((\forall
-(h: nat).(\forall (e1: C).(\forall (u1: T).(\forall (k: K).((getl h c3 (CHead
-e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(getl h c4 (CHead
-e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
-C).(\lambda (u2: T).(pr0 u1 u2))))))))))).(\lambda (u1: T).(\lambda (u2:
-T).(\lambda (H2: (pr0 u1 u2)).(\lambda (k: K).(\lambda (h: nat).(let TMP_18
-\def (\lambda (n: nat).(\forall (e1: C).(\forall (u3: T).(\forall (k0:
-K).((getl n (CHead c3 k u1) (CHead e1 k0 u3)) \to (let TMP_15 \def (\lambda
-(e2: C).(\lambda (u4: T).(let TMP_13 \def (CHead c4 k u2) in (let TMP_14 \def
-(CHead e2 k0 u4) in (getl n TMP_13 TMP_14))))) in (let TMP_16 \def (\lambda
-(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_17 \def (\lambda (_:
-C).(\lambda (u4: T).(pr0 u3 u4))) in (ex3_2 C T TMP_15 TMP_16 TMP_17)))))))))
-in (let TMP_110 \def (\lambda (e1: C).(\lambda (u0: T).(\lambda (k0:
-K).(\lambda (H3: (getl O (CHead c3 k u1) (CHead e1 k0 u0))).(let TMP_24 \def
-(\lambda (k1: K).((clear (CHead c3 k1 u1) (CHead e1 k0 u0)) \to (let TMP_21
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_19 \def (CHead c4 k1 u2) in
-(let TMP_20 \def (CHead e2 k0 u3) in (getl O TMP_19 TMP_20))))) in (let
-TMP_22 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_23
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) in (ex3_2 C T TMP_21
-TMP_22 TMP_23)))))) in (let TMP_80 \def (\lambda (b: B).(\lambda (H4: (clear
-(CHead c3 (Bind b) u1) (CHead e1 k0 u0))).(let TMP_25 \def (\lambda (e:
-C).(match e with [(CSort _) \Rightarrow e1 | (CHead c _ _) \Rightarrow c]))
-in (let TMP_26 \def (CHead e1 k0 u0) in (let TMP_27 \def (Bind b) in (let
-TMP_28 \def (CHead c3 TMP_27 u1) in (let TMP_29 \def (CHead e1 k0 u0) in (let
-TMP_30 \def (clear_gen_bind b c3 TMP_29 u1 H4) in (let H5 \def (f_equal C C
-TMP_25 TMP_26 TMP_28 TMP_30) in (let TMP_31 \def (\lambda (e: C).(match e
-with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) in (let
-TMP_32 \def (CHead e1 k0 u0) in (let TMP_33 \def (Bind b) in (let TMP_34 \def
-(CHead c3 TMP_33 u1) in (let TMP_35 \def (CHead e1 k0 u0) in (let TMP_36 \def
-(clear_gen_bind b c3 TMP_35 u1 H4) in (let H6 \def (f_equal C K TMP_31 TMP_32
-TMP_34 TMP_36) in (let TMP_37 \def (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) in (let TMP_38 \def (CHead e1
-k0 u0) in (let TMP_39 \def (Bind b) in (let TMP_40 \def (CHead c3 TMP_39 u1)
-in (let TMP_41 \def (CHead e1 k0 u0) in (let TMP_42 \def (clear_gen_bind b c3
-TMP_41 u1 H4) in (let H7 \def (f_equal C T TMP_37 TMP_38 TMP_40 TMP_42) in
-(let TMP_78 \def (\lambda (H8: (eq K k0 (Bind b))).(\lambda (H9: (eq C e1
-c3)).(let TMP_43 \def (Bind b) in (let TMP_50 \def (\lambda (k1: K).(let
-TMP_47 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_44 \def (Bind b) in
-(let TMP_45 \def (CHead c4 TMP_44 u2) in (let TMP_46 \def (CHead e2 k1 u3) in
-(getl O TMP_45 TMP_46)))))) in (let TMP_48 \def (\lambda (e2: C).(\lambda (_:
-T).(wcpr0 e1 e2))) in (let TMP_49 \def (\lambda (_: C).(\lambda (u3: T).(pr0
-u0 u3))) in (ex3_2 C T TMP_47 TMP_48 TMP_49))))) in (let TMP_58 \def (\lambda
-(t: T).(let TMP_55 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_51 \def
-(Bind b) in (let TMP_52 \def (CHead c4 TMP_51 u2) in (let TMP_53 \def (Bind
-b) in (let TMP_54 \def (CHead e2 TMP_53 u3) in (getl O TMP_52 TMP_54)))))))
-in (let TMP_56 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let
-TMP_57 \def (\lambda (_: C).(\lambda (u3: T).(pr0 t u3))) in (ex3_2 C T
-TMP_55 TMP_56 TMP_57))))) in (let TMP_66 \def (\lambda (c: C).(let TMP_63
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_59 \def (Bind b) in (let
-TMP_60 \def (CHead c4 TMP_59 u2) in (let TMP_61 \def (Bind b) in (let TMP_62
-\def (CHead e2 TMP_61 u3) in (getl O TMP_60 TMP_62))))))) in (let TMP_64 \def
-(\lambda (e2: C).(\lambda (_: T).(wcpr0 c e2))) in (let TMP_65 \def (\lambda
-(_: C).(\lambda (u3: T).(pr0 u1 u3))) in (ex3_2 C T TMP_63 TMP_64 TMP_65)))))
-in (let TMP_71 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_67 \def (Bind
-b) in (let TMP_68 \def (CHead c4 TMP_67 u2) in (let TMP_69 \def (Bind b) in
-(let TMP_70 \def (CHead e2 TMP_69 u3) in (getl O TMP_68 TMP_70))))))) in (let
-TMP_72 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 c3 e2))) in (let TMP_73
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_74 \def
-(getl_refl b c4 u2) in (let TMP_75 \def (ex3_2_intro C T TMP_71 TMP_72 TMP_73
-c4 u2 TMP_74 H0 H2) in (let TMP_76 \def (eq_ind_r C c3 TMP_66 TMP_75 e1 H9)
-in (let TMP_77 \def (eq_ind_r T u1 TMP_58 TMP_76 u0 H7) in (eq_ind_r K TMP_43
-TMP_50 TMP_77 k0 H8)))))))))))))) in (let TMP_79 \def (TMP_78 H6) in (TMP_79
-H5)))))))))))))))))))))))))) in (let TMP_106 \def (\lambda (f: F).(\lambda
-(H4: (clear (CHead c3 (Flat f) u1) (CHead e1 k0 u0))).(let TMP_81 \def (CHead
-e1 k0 u0) in (let TMP_82 \def (drop_refl c3) in (let TMP_83 \def (CHead e1 k0
-u0) in (let TMP_84 \def (clear_gen_flat f c3 TMP_83 u1 H4) in (let TMP_85
-\def (getl_intro O c3 TMP_81 c3 TMP_82 TMP_84) in (let H5 \def (H1 O e1 u0 k0
-TMP_85) in (let TMP_87 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_86
-\def (CHead e2 k0 u3) in (getl O c4 TMP_86)))) in (let TMP_88 \def (\lambda
-(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_89 \def (\lambda (_:
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_93 \def (\lambda (e2:
-C).(\lambda (u3: T).(let TMP_90 \def (Flat f) in (let TMP_91 \def (CHead c4
-TMP_90 u2) in (let TMP_92 \def (CHead e2 k0 u3) in (getl O TMP_91
-TMP_92)))))) in (let TMP_94 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1
-e2))) in (let TMP_95 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) in
-(let TMP_96 \def (ex3_2 C T TMP_93 TMP_94 TMP_95) in (let TMP_105 \def
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl O c4 (CHead x0 k0
-x1))).(\lambda (H7: (wcpr0 e1 x0)).(\lambda (H8: (pr0 u0 x1)).(let TMP_100
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_97 \def (Flat f) in (let
-TMP_98 \def (CHead c4 TMP_97 u2) in (let TMP_99 \def (CHead e2 k0 u3) in
-(getl O TMP_98 TMP_99)))))) in (let TMP_101 \def (\lambda (e2: C).(\lambda
-(_: T).(wcpr0 e1 e2))) in (let TMP_102 \def (\lambda (_: C).(\lambda (u3:
-T).(pr0 u0 u3))) in (let TMP_103 \def (CHead x0 k0 x1) in (let TMP_104 \def
-(getl_flat c4 TMP_103 O H6 f u2) in (ex3_2_intro C T TMP_100 TMP_101 TMP_102
-x0 x1 TMP_104 H7 H8))))))))))) in (ex3_2_ind C T TMP_87 TMP_88 TMP_89 TMP_96
-TMP_105 H5))))))))))))))))) in (let TMP_107 \def (CHead c3 k u1) in (let
-TMP_108 \def (CHead e1 k0 u0) in (let TMP_109 \def (getl_gen_O TMP_107
-TMP_108 H3) in (K_ind TMP_24 TMP_80 TMP_106 k TMP_109))))))))))) in (let
-TMP_117 \def (\lambda (k0: K).(\forall (n: nat).(((\forall (e1: C).(\forall
-(u3: T).(\forall (k1: K).((getl n (CHead c3 k0 u1) (CHead e1 k1 u3)) \to
-(ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c4 k0 u2) (CHead
-e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
-C).(\lambda (u4: T).(pr0 u3 u4))))))))) \to (\forall (e1: C).(\forall (u3:
-T).(\forall (k1: K).((getl (S n) (CHead c3 k0 u1) (CHead e1 k1 u3)) \to (let
-TMP_114 \def (\lambda (e2: C).(\lambda (u4: T).(let TMP_111 \def (S n) in
-(let TMP_112 \def (CHead c4 k0 u2) in (let TMP_113 \def (CHead e2 k1 u4) in
-(getl TMP_111 TMP_112 TMP_113)))))) in (let TMP_115 \def (\lambda (e2:
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_116 \def (\lambda (_:
-C).(\lambda (u4: T).(pr0 u3 u4))) in (ex3_2 C T TMP_114 TMP_115
-TMP_116))))))))))) in (let TMP_144 \def (\lambda (b: B).(\lambda (n:
+(u1: T).(\forall (k: K).((getl h c (CHead e1 k u1)) \to (ex3_2 C T (\lambda
+(e2: C).(\lambda (u2: T).(getl h c0 (CHead e2 k u2)))) (\lambda (e2:
+C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u2: T).(pr0 u1
+u2))))))))))) (\lambda (c: C).(\lambda (h: nat).(\lambda (e1: C).(\lambda
+(u1: T).(\lambda (k: K).(\lambda (H0: (getl h c (CHead e1 k
+u1))).(ex3_2_intro C T (\lambda (e2: C).(\lambda (u2: T).(getl h c (CHead e2
+k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
+C).(\lambda (u2: T).(pr0 u1 u2))) e1 u1 H0 (wcpr0_refl e1) (pr0_refl
+u1)))))))) (\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (wcpr0 c3
+c4)).(\lambda (H1: ((\forall (h: nat).(\forall (e1: C).(\forall (u1:
+T).(\forall (k: K).((getl h c3 (CHead e1 k u1)) \to (ex3_2 C T (\lambda (e2:
+C).(\lambda (u2: T).(getl h c4 (CHead e2 k u2)))) (\lambda (e2: C).(\lambda
+(_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u2: T).(pr0 u1
+u2))))))))))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H2: (pr0 u1
+u2)).(\lambda (k: K).(\lambda (h: nat).(nat_ind (\lambda (n: nat).(\forall
+(e1: C).(\forall (u3: T).(\forall (k0: K).((getl n (CHead c3 k u1) (CHead e1
+k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c4 k
+u2) (CHead e2 k0 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
+(\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))))))))) (\lambda (e1:
+C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H3: (getl O (CHead c3 k u1)
+(CHead e1 k0 u0))).(K_ind (\lambda (k1: K).((clear (CHead c3 k1 u1) (CHead e1
+k0 u0)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 k1
+u2) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
+(\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3)))))) (\lambda (b: B).(\lambda
+(H4: (clear (CHead c3 (Bind b) u1) (CHead e1 k0 u0))).(let H5 \def (f_equal C
+C (\lambda (e: C).(match e with [(CSort _) \Rightarrow e1 | (CHead c _ _)
+\Rightarrow c])) (CHead e1 k0 u0) (CHead c3 (Bind b) u1) (clear_gen_bind b c3
+(CHead e1 k0 u0) u1 H4)) in ((let H6 \def (f_equal C K (\lambda (e: C).(match
+e with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) (CHead e1
+k0 u0) (CHead c3 (Bind b) u1) (clear_gen_bind b c3 (CHead e1 k0 u0) u1 H4))
+in ((let H7 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u0 | (CHead _ _ t) \Rightarrow t])) (CHead e1 k0 u0) (CHead c3
+(Bind b) u1) (clear_gen_bind b c3 (CHead e1 k0 u0) u1 H4)) in (\lambda (H8:
+(eq K k0 (Bind b))).(\lambda (H9: (eq C e1 c3)).(eq_ind_r K (Bind b) (\lambda
+(k1: K).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 (Bind
+b) u2) (CHead e2 k1 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
+(\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))))) (eq_ind_r T u1 (\lambda (t:
+T).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 (Bind b)
+u2) (CHead e2 (Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1
+e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 t u3))))) (eq_ind_r C c3 (\lambda
+(c: C).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 (Bind
+b) u2) (CHead e2 (Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 c
+e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))))) (ex3_2_intro C T
+(\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 (Bind b) u2) (CHead e2
+(Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 c3 e2))) (\lambda (_:
+C).(\lambda (u3: T).(pr0 u1 u3))) c4 u2 (getl_refl b c4 u2) H0 H2) e1 H9) u0
+H7) k0 H8)))) H6)) H5)))) (\lambda (f: F).(\lambda (H4: (clear (CHead c3
+(Flat f) u1) (CHead e1 k0 u0))).(let H5 \def (H1 O e1 u0 k0 (getl_intro O c3
+(CHead e1 k0 u0) c3 (drop_refl c3) (clear_gen_flat f c3 (CHead e1 k0 u0) u1
+H4))) in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl O c4 (CHead
+e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
+C).(\lambda (u3: T).(pr0 u0 u3))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3:
+T).(getl O (CHead c4 (Flat f) u2) (CHead e2 k0 u3)))) (\lambda (e2:
+C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u0
+u3)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl O c4 (CHead x0
+k0 x1))).(\lambda (H7: (wcpr0 e1 x0)).(\lambda (H8: (pr0 u0 x1)).(ex3_2_intro
+C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c4 (Flat f) u2) (CHead
+e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
+C).(\lambda (u3: T).(pr0 u0 u3))) x0 x1 (getl_flat c4 (CHead x0 k0 x1) O H6 f
+u2) H7 H8)))))) H5)))) k (getl_gen_O (CHead c3 k u1) (CHead e1 k0 u0)
+H3)))))) (K_ind (\lambda (k0: K).(\forall (n: nat).(((\forall (e1:
+C).(\forall (u3: T).(\forall (k1: K).((getl n (CHead c3 k0 u1) (CHead e1 k1
+u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c4 k0
+u2) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2)))
+(\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))))))))) \to (\forall (e1:
+C).(\forall (u3: T).(\forall (k1: K).((getl (S n) (CHead c3 k0 u1) (CHead e1
+k1 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl (S n) (CHead
+c4 k0 u2) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1
+e2))) (\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))))))))))) (\lambda (b:
+B).(\lambda (n: nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall
+(k0: K).((getl n (CHead c3 (Bind b) u1) (CHead e1 k0 u3)) \to (ex3_2 C T
+(\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c4 (Bind b) u2) (CHead e2 k0
+u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_:
+C).(\lambda (u4: T).(pr0 u3 u4)))))))))).(\lambda (e1: C).(\lambda (u0:
+T).(\lambda (k0: K).(\lambda (H4: (getl (S n) (CHead c3 (Bind b) u1) (CHead
+e1 k0 u0))).(let H5 \def (H1 n e1 u0 k0 (getl_gen_S (Bind b) c3 (CHead e1 k0
+u0) u1 n H4)) in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl n c4
+(CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda
+(_: C).(\lambda (u3: T).(pr0 u0 u3))) (ex3_2 C T (\lambda (e2: C).(\lambda
+(u3: T).(getl (S n) (CHead c4 (Bind b) u2) (CHead e2 k0 u3)))) (\lambda (e2:
+C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 u0
+u3)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl n c4 (CHead x0
+k0 x1))).(\lambda (H7: (wcpr0 e1 x0)).(\lambda (H8: (pr0 u0 x1)).(ex3_2_intro
+C T (\lambda (e2: C).(\lambda (u3: T).(getl (S n) (CHead c4 (Bind b) u2)
+(CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda
+(_: C).(\lambda (u3: T).(pr0 u0 u3))) x0 x1 (getl_head (Bind b) n c4 (CHead
+x0 k0 x1) H6 u2) H7 H8)))))) H5))))))))) (\lambda (f: F).(\lambda (n: