update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / wcpr0 / getl.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/wcpr0/getl.ma b/matita/matita/contribs/lambdadelta/basic_1/wcpr0/getl.ma
index 4eb36afbe06d94811e5b34a9f864414e86a9a092..2b43bb21ada932d75775c0059d32273b231b7b0e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/wcpr0/getl.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/wcpr0/getl.ma
@@ -18,663 +18,431 @@ include "basic_1/wcpr0/fwd.ma".
 
 include "basic_1/getl/props.ma".
 
-theorem wcpr0_drop:
+lemma wcpr0_drop:
  \forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to (\forall (h: 
 nat).(\forall (e1: C).(\forall (u1: T).(\forall (k: K).((drop h O c1 (CHead 
 e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(drop h O c2 
 (CHead e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda 
 (_: C).(\lambda (u2: T).(pr0 u1 u2)))))))))))
 \def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c1 c2)).(let TMP_5 \def 
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c1 c2)).(wcpr0_ind 
 (\lambda (c: C).(\lambda (c0: C).(\forall (h: nat).(\forall (e1: C).(\forall 
-(u1: T).(\forall (k: K).((drop h O 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 (drop h 
-O 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: (drop h O c (CHead e1 k u1))).(let TMP_7 \def (\lambda (e2: 
-C).(\lambda (u2: T).(let TMP_6 \def (CHead e2 k u2) in (drop h O 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_132 \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).((drop h O c3 
-(CHead e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(drop h O 
-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).((drop n O (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 (drop n O 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_67 \def (\lambda (e1: C).(\lambda 
-(u0: T).(\lambda (k0: K).(\lambda (H3: (drop O O (CHead c3 k u1) (CHead e1 k0 
-u0))).(let TMP_19 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow 
-c3 | (CHead c _ _) \Rightarrow c])) in (let TMP_20 \def (CHead c3 k u1) in 
-(let TMP_21 \def (CHead e1 k0 u0) in (let TMP_22 \def (CHead c3 k u1) in (let 
-TMP_23 \def (CHead e1 k0 u0) in (let TMP_24 \def (drop_gen_refl TMP_22 TMP_23 
-H3) in (let H4 \def (f_equal C C TMP_19 TMP_20 TMP_21 TMP_24) in (let TMP_25 
-\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow k | (CHead _ k1 _) 
-\Rightarrow k1])) in (let TMP_26 \def (CHead c3 k u1) in (let TMP_27 \def 
-(CHead e1 k0 u0) in (let TMP_28 \def (CHead c3 k u1) in (let TMP_29 \def 
-(CHead e1 k0 u0) in (let TMP_30 \def (drop_gen_refl TMP_28 TMP_29 H3) in (let 
-H5 \def (f_equal C K TMP_25 TMP_26 TMP_27 TMP_30) in (let TMP_31 \def 
-(\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead _ _ t) 
-\Rightarrow t])) in (let TMP_32 \def (CHead c3 k u1) in (let TMP_33 \def 
-(CHead e1 k0 u0) in (let TMP_34 \def (CHead c3 k u1) in (let TMP_35 \def 
-(CHead e1 k0 u0) in (let TMP_36 \def (drop_gen_refl TMP_34 TMP_35 H3) in (let 
-H6 \def (f_equal C T TMP_31 TMP_32 TMP_33 TMP_36) in (let TMP_65 \def 
-(\lambda (H7: (eq K k k0)).(\lambda (H8: (eq C c3 e1)).(let TMP_42 \def 
-(\lambda (k1: K).(let TMP_39 \def (\lambda (e2: C).(\lambda (u3: T).(let 
-TMP_37 \def (CHead c4 k u2) in (let TMP_38 \def (CHead e2 k1 u3) in (drop O O 
-TMP_37 TMP_38))))) in (let TMP_40 \def (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e1 e2))) in (let TMP_41 \def (\lambda (_: C).(\lambda (u3: T).(pr0 
-u0 u3))) in (ex3_2 C T TMP_39 TMP_40 TMP_41))))) in (let TMP_48 \def (\lambda 
-(t: T).(let TMP_45 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_43 \def 
-(CHead c4 k u2) in (let TMP_44 \def (CHead e2 k u3) in (drop O O TMP_43 
-TMP_44))))) in (let TMP_46 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 
-e2))) in (let TMP_47 \def (\lambda (_: C).(\lambda (u3: T).(pr0 t u3))) in 
-(ex3_2 C T TMP_45 TMP_46 TMP_47))))) in (let TMP_54 \def (\lambda (c: C).(let 
-TMP_51 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_49 \def (CHead c4 k 
-u2) in (let TMP_50 \def (CHead e2 k u3) in (drop O O TMP_49 TMP_50))))) in 
-(let TMP_52 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 c e2))) in (let 
-TMP_53 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in (ex3_2 C T 
-TMP_51 TMP_52 TMP_53))))) in (let TMP_57 \def (\lambda (e2: C).(\lambda (u3: 
-T).(let TMP_55 \def (CHead c4 k u2) in (let TMP_56 \def (CHead e2 k u3) in 
-(drop O O TMP_55 TMP_56))))) in (let TMP_58 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 c3 e2))) in (let TMP_59 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u1 u3))) in (let TMP_60 \def (CHead c4 k u2) in (let TMP_61 \def 
-(drop_refl TMP_60) in (let TMP_62 \def (ex3_2_intro C T TMP_57 TMP_58 TMP_59 
-c4 u2 TMP_61 H0 H2) in (let TMP_63 \def (eq_ind C c3 TMP_54 TMP_62 e1 H8) in 
-(let TMP_64 \def (eq_ind T u1 TMP_48 TMP_63 u0 H6) in (eq_ind K k TMP_42 
-TMP_64 k0 H7)))))))))))))) in (let TMP_66 \def (TMP_65 H5) in (TMP_66 
-H4)))))))))))))))))))))))))))) in (let TMP_74 \def (\lambda (k0: K).(\forall 
-(n: nat).(((\forall (e1: C).(\forall (u3: T).(\forall (k1: K).((drop n O 
-(CHead c3 k0 u1) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda 
-(u4: T).(drop n O (CHead c4 k0 u2) (CHead e2 k1 u4)))) (\lambda (e2: 
+(u1: T).(\forall (k: K).((drop h O c (CHead e1 k u1)) \to (ex3_2 C T (\lambda 
+(e2: C).(\lambda (u2: T).(drop h O 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: (drop h O c (CHead e1 k 
+u1))).(ex3_2_intro C T (\lambda (e2: C).(\lambda (u2: T).(drop h O 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).((drop h O c3 (CHead e1 k u1)) \to (ex3_2 C T (\lambda 
+(e2: C).(\lambda (u2: T).(drop h O 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).((drop n O (CHead c3 k u1) (CHead 
+e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O (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: (drop O O (CHead c3 k u1) 
+(CHead e1 k0 u0))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with 
+[(CSort _) \Rightarrow c3 | (CHead c _ _) \Rightarrow c])) (CHead c3 k u1) 
+(CHead e1 k0 u0) (drop_gen_refl (CHead c3 k u1) (CHead e1 k0 u0) H3)) in 
+((let H5 \def (f_equal C K (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow k | (CHead _ k1 _) \Rightarrow k1])) (CHead c3 k u1) (CHead e1 k0 
+u0) (drop_gen_refl (CHead c3 k u1) (CHead e1 k0 u0) H3)) in ((let H6 \def 
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u1 | (CHead 
+_ _ t) \Rightarrow t])) (CHead c3 k u1) (CHead e1 k0 u0) (drop_gen_refl 
+(CHead c3 k u1) (CHead e1 k0 u0) H3)) in (\lambda (H7: (eq K k k0)).(\lambda 
+(H8: (eq C c3 e1)).(eq_ind K k (\lambda (k1: K).(ex3_2 C T (\lambda (e2: 
+C).(\lambda (u3: T).(drop O O (CHead c4 k u2) (CHead e2 k1 u3)))) (\lambda 
+(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 
+u0 u3))))) (eq_ind T u1 (\lambda (t: T).(ex3_2 C T (\lambda (e2: C).(\lambda 
+(u3: T).(drop O O (CHead c4 k u2) (CHead e2 k u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: C).(\lambda (u3: T).(pr0 t 
+u3))))) (eq_ind C c3 (\lambda (c: C).(ex3_2 C T (\lambda (e2: C).(\lambda 
+(u3: T).(drop O O (CHead c4 k u2) (CHead e2 k 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).(drop O O (CHead 
+c4 k u2) (CHead e2 k u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 c3 e2))) 
+(\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) c4 u2 (drop_refl (CHead c4 k 
+u2)) H0 H2) e1 H8) u0 H6) k0 H7)))) H5)) H4)))))) (K_ind (\lambda (k0: 
+K).(\forall (n: nat).(((\forall (e1: C).(\forall (u3: T).(\forall (k1: 
+K).((drop n O (CHead c3 k0 u1) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u4: T).(drop n O (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).((drop 
+(S n) O (CHead c3 k0 u1) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u4: T).(drop (S n) O (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).((drop n O (CHead c3 
+(Bind b) u1) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: 
+T).(drop n O (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))))))))) \to (\forall (e1: C).(\forall (u3: T).(\forall (k1: K).((drop (S 
-n) O (CHead c3 k0 u1) (CHead e1 k1 u3)) \to (let TMP_71 \def (\lambda (e2: 
-C).(\lambda (u4: T).(let TMP_68 \def (S n) in (let TMP_69 \def (CHead c4 k0 
-u2) in (let TMP_70 \def (CHead e2 k1 u4) in (drop TMP_68 O TMP_69 
-TMP_70)))))) in (let TMP_72 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 
-e2))) in (let TMP_73 \def (\lambda (_: C).(\lambda (u4: T).(pr0 u3 u4))) in 
-(ex3_2 C T TMP_71 TMP_72 TMP_73))))))))))) in (let TMP_101 \def (\lambda (b: 
-B).(\lambda (n: nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall 
-(k0: K).((drop n O (CHead c3 (Bind b) u1) (CHead e1 k0 u3)) \to (ex3_2 C T 
-(\lambda (e2: C).(\lambda (u4: T).(drop n O (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: (drop (S n) O (CHead c3 (Bind b) u1) (CHead 
-e1 k0 u0))).(let TMP_75 \def (Bind b) in (let TMP_76 \def (CHead e1 k0 u0) in 
-(let TMP_77 \def (drop_gen_drop TMP_75 c3 TMP_76 u1 n H4) in (let H5 \def (H1 
-n e1 u0 k0 TMP_77) in (let TMP_79 \def (\lambda (e2: C).(\lambda (u3: T).(let 
-TMP_78 \def (CHead e2 k0 u3) in (drop n O c4 TMP_78)))) in (let TMP_80 \def 
-(\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_81 \def (\lambda 
-(_: C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_86 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_82 \def (S n) in (let TMP_83 \def (Bind b) in 
-(let TMP_84 \def (CHead c4 TMP_83 u2) in (let TMP_85 \def (CHead e2 k0 u3) in 
-(drop TMP_82 O TMP_84 TMP_85))))))) in (let TMP_87 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_88 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_89 \def (ex3_2 C T TMP_86 
-TMP_87 TMP_88) in (let TMP_100 \def (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (drop n O c4 (CHead x0 k0 x1))).(\lambda (H7: (wcpr0 e1 
-x0)).(\lambda (H8: (pr0 u0 x1)).(let TMP_94 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_90 \def (S n) in (let TMP_91 \def (Bind b) in (let TMP_92 
-\def (CHead c4 TMP_91 u2) in (let TMP_93 \def (CHead e2 k0 u3) in (drop 
-TMP_90 O TMP_92 TMP_93))))))) in (let TMP_95 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 e1 e2))) in (let TMP_96 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u0 u3))) in (let TMP_97 \def (Bind b) in (let TMP_98 \def (CHead x0 
-k0 x1) in (let TMP_99 \def (drop_drop TMP_97 n c4 TMP_98 H6 u2) in 
-(ex3_2_intro C T TMP_94 TMP_95 TMP_96 x0 x1 TMP_99 H7 H8)))))))))))) in 
-(ex3_2_ind C T TMP_79 TMP_80 TMP_81 TMP_89 TMP_100 H5)))))))))))))))))))) in 
-(let TMP_130 \def (\lambda (f: F).(\lambda (n: nat).(\lambda (_: ((\forall 
-(e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c3 (Flat f) u1) 
-(CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O 
-(CHead c4 (Flat f) 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: 
-(drop (S n) O (CHead c3 (Flat f) u1) (CHead e1 k0 u0))).(let TMP_102 \def (S 
-n) in (let TMP_103 \def (Flat f) in (let TMP_104 \def (CHead e1 k0 u0) in 
-(let TMP_105 \def (drop_gen_drop TMP_103 c3 TMP_104 u1 n H4) in (let H5 \def 
-(H1 TMP_102 e1 u0 k0 TMP_105) in (let TMP_108 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_106 \def (S n) in (let TMP_107 \def (CHead e2 k0 u3) in 
-(drop TMP_106 O c4 TMP_107))))) in (let TMP_109 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_110 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_115 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_111 \def (S n) in (let TMP_112 \def (Flat f) in 
-(let TMP_113 \def (CHead c4 TMP_112 u2) in (let TMP_114 \def (CHead e2 k0 u3) 
-in (drop TMP_111 O TMP_113 TMP_114))))))) in (let TMP_116 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_117 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_118 \def (ex3_2 C T TMP_115 
-TMP_116 TMP_117) in (let TMP_129 \def (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (drop (S n) O c4 (CHead x0 k0 x1))).(\lambda (H7: (wcpr0 e1 
-x0)).(\lambda (H8: (pr0 u0 x1)).(let TMP_123 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_119 \def (S n) in (let TMP_120 \def (Flat f) in (let TMP_121 
-\def (CHead c4 TMP_120 u2) in (let TMP_122 \def (CHead e2 k0 u3) in (drop 
-TMP_119 O TMP_121 TMP_122))))))) in (let TMP_124 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_125 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_126 \def (Flat f) in (let 
-TMP_127 \def (CHead x0 k0 x1) in (let TMP_128 \def (drop_drop TMP_126 n c4 
-TMP_127 H6 u2) in (ex3_2_intro C T TMP_123 TMP_124 TMP_125 x0 x1 TMP_128 H7 
-H8)))))))))))) in (ex3_2_ind C T TMP_108 TMP_109 TMP_110 TMP_118 TMP_129 
-H5))))))))))))))))))))) in (let TMP_131 \def (K_ind TMP_74 TMP_101 TMP_130 k) 
-in (nat_ind TMP_18 TMP_67 TMP_131 h)))))))))))))))) in (wcpr0_ind TMP_5 
-TMP_12 TMP_132 c1 c2 H)))))).
+(drop (S n) O (CHead c3 (Bind b) u1) (CHead e1 k0 u0))).(let H5 \def (H1 n e1 
+u0 k0 (drop_gen_drop (Bind b) c3 (CHead e1 k0 u0) u1 n H4)) in (ex3_2_ind C T 
+(\lambda (e2: C).(\lambda (u3: T).(drop n 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).(drop (S n) O (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: (drop n 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).(drop (S n) O (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 (drop_drop (Bind b) n c4 (CHead x0 k0 x1) H6 u2) 
+H7 H8)))))) H5))))))))) (\lambda (f: F).(\lambda (n: nat).(\lambda (_: 
+((\forall (e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c3 
+(Flat f) u1) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: 
+T).(drop n O (CHead c4 (Flat f) 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: 
+(drop (S n) O (CHead c3 (Flat f) u1) (CHead e1 k0 u0))).(let H5 \def (H1 (S 
+n) e1 u0 k0 (drop_gen_drop (Flat f) c3 (CHead e1 k0 u0) u1 n H4)) in 
+(ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(drop (S n) 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).(drop (S n) 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: (drop (S n) 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).(drop (S n) 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 (drop_drop 
+(Flat f) n c4 (CHead x0 k0 x1) H6 u2) H7 H8)))))) H5))))))))) k) h)))))))))) 
+c1 c2 H))).
 
-theorem wcpr0_drop_back:
+lemma wcpr0_drop_back:
  \forall (c1: C).(\forall (c2: C).((wcpr0 c2 c1) \to (\forall (h: 
 nat).(\forall (e1: C).(\forall (u1: T).(\forall (k: K).((drop h O c1 (CHead 
 e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(drop h O c2 
 (CHead e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda 
 (_: C).(\lambda (u2: T).(pr0 u2 u1)))))))))))
 \def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c2 c1)).(let TMP_5 \def 
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c2 c1)).(wcpr0_ind 
 (\lambda (c: C).(\lambda (c0: C).(\forall (h: nat).(\forall (e1: C).(\forall 
-(u1: T).(\forall (k: K).((drop h O c0 (CHead e1 k u1)) \to (let TMP_2 \def 
-(\lambda (e2: C).(\lambda (u2: T).(let TMP_1 \def (CHead e2 k u2) in (drop h 
-O c TMP_1)))) in (let TMP_3 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
-e1))) in (let TMP_4 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u2 u1))) 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: (drop h O c (CHead e1 k u1))).(let TMP_7 \def (\lambda (e2: 
-C).(\lambda (u2: T).(let TMP_6 \def (CHead e2 k u2) in (drop h O c TMP_6)))) 
-in (let TMP_8 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let 
-TMP_9 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u2 u1))) 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_132 \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).((drop h O c4 
-(CHead e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(drop h O 
-c3 (CHead e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
-(\lambda (_: C).(\lambda (u2: T).(pr0 u2 u1))))))))))).(\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).((drop n O (CHead c4 k u2) (CHead e1 k0 u3)) \to (let 
-TMP_15 \def (\lambda (e2: C).(\lambda (u4: T).(let TMP_13 \def (CHead c3 k 
-u1) in (let TMP_14 \def (CHead e2 k0 u4) in (drop n O TMP_13 TMP_14))))) in 
-(let TMP_16 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let 
-TMP_17 \def (\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))) in (ex3_2 C T 
-TMP_15 TMP_16 TMP_17))))))))) in (let TMP_67 \def (\lambda (e1: C).(\lambda 
-(u0: T).(\lambda (k0: K).(\lambda (H3: (drop O O (CHead c4 k u2) (CHead e1 k0 
-u0))).(let TMP_19 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow 
-c4 | (CHead c _ _) \Rightarrow c])) in (let TMP_20 \def (CHead c4 k u2) in 
-(let TMP_21 \def (CHead e1 k0 u0) in (let TMP_22 \def (CHead c4 k u2) in (let 
-TMP_23 \def (CHead e1 k0 u0) in (let TMP_24 \def (drop_gen_refl TMP_22 TMP_23 
-H3) in (let H4 \def (f_equal C C TMP_19 TMP_20 TMP_21 TMP_24) in (let TMP_25 
-\def (\lambda (e: C).(match e with [(CSort _) \Rightarrow k | (CHead _ k1 _) 
-\Rightarrow k1])) in (let TMP_26 \def (CHead c4 k u2) in (let TMP_27 \def 
-(CHead e1 k0 u0) in (let TMP_28 \def (CHead c4 k u2) in (let TMP_29 \def 
-(CHead e1 k0 u0) in (let TMP_30 \def (drop_gen_refl TMP_28 TMP_29 H3) in (let 
-H5 \def (f_equal C K TMP_25 TMP_26 TMP_27 TMP_30) in (let TMP_31 \def 
-(\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | (CHead _ _ t) 
-\Rightarrow t])) in (let TMP_32 \def (CHead c4 k u2) in (let TMP_33 \def 
-(CHead e1 k0 u0) in (let TMP_34 \def (CHead c4 k u2) in (let TMP_35 \def 
-(CHead e1 k0 u0) in (let TMP_36 \def (drop_gen_refl TMP_34 TMP_35 H3) in (let 
-H6 \def (f_equal C T TMP_31 TMP_32 TMP_33 TMP_36) in (let TMP_65 \def 
-(\lambda (H7: (eq K k k0)).(\lambda (H8: (eq C c4 e1)).(let TMP_42 \def 
-(\lambda (k1: K).(let TMP_39 \def (\lambda (e2: C).(\lambda (u3: T).(let 
-TMP_37 \def (CHead c3 k u1) in (let TMP_38 \def (CHead e2 k1 u3) in (drop O O 
-TMP_37 TMP_38))))) in (let TMP_40 \def (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e2 e1))) in (let TMP_41 \def (\lambda (_: C).(\lambda (u3: T).(pr0 
-u3 u0))) in (ex3_2 C T TMP_39 TMP_40 TMP_41))))) in (let TMP_48 \def (\lambda 
-(t: T).(let TMP_45 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_43 \def 
-(CHead c3 k u1) in (let TMP_44 \def (CHead e2 k u3) in (drop O O TMP_43 
-TMP_44))))) in (let TMP_46 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
-e1))) in (let TMP_47 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 t))) in 
-(ex3_2 C T TMP_45 TMP_46 TMP_47))))) in (let TMP_54 \def (\lambda (c: C).(let 
-TMP_51 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_49 \def (CHead c3 k 
-u1) in (let TMP_50 \def (CHead e2 k u3) in (drop O O TMP_49 TMP_50))))) in 
-(let TMP_52 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 c))) in (let 
-TMP_53 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u2))) in (ex3_2 C T 
-TMP_51 TMP_52 TMP_53))))) in (let TMP_57 \def (\lambda (e2: C).(\lambda (u3: 
-T).(let TMP_55 \def (CHead c3 k u1) in (let TMP_56 \def (CHead e2 k u3) in 
-(drop O O TMP_55 TMP_56))))) in (let TMP_58 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 e2 c4))) in (let TMP_59 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u3 u2))) in (let TMP_60 \def (CHead c3 k u1) in (let TMP_61 \def 
-(drop_refl TMP_60) in (let TMP_62 \def (ex3_2_intro C T TMP_57 TMP_58 TMP_59 
-c3 u1 TMP_61 H0 H2) in (let TMP_63 \def (eq_ind C c4 TMP_54 TMP_62 e1 H8) in 
-(let TMP_64 \def (eq_ind T u2 TMP_48 TMP_63 u0 H6) in (eq_ind K k TMP_42 
-TMP_64 k0 H7)))))))))))))) in (let TMP_66 \def (TMP_65 H5) in (TMP_66 
-H4)))))))))))))))))))))))))))) in (let TMP_74 \def (\lambda (k0: K).(\forall 
+(u1: T).(\forall (k: K).((drop h O c0 (CHead e1 k u1)) \to (ex3_2 C T 
+(\lambda (e2: C).(\lambda (u2: T).(drop h O c (CHead e2 k u2)))) (\lambda 
+(e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u2: T).(pr0 
+u2 u1))))))))))) (\lambda (c: C).(\lambda (h: nat).(\lambda (e1: C).(\lambda 
+(u1: T).(\lambda (k: K).(\lambda (H0: (drop h O c (CHead e1 k 
+u1))).(ex3_2_intro C T (\lambda (e2: C).(\lambda (u2: T).(drop h O c (CHead 
+e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u2: T).(pr0 u2 u1))) 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).((drop h O c4 (CHead e1 k u1)) \to (ex3_2 C T (\lambda 
+(e2: C).(\lambda (u2: T).(drop h O c3 (CHead e2 k u2)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u2: T).(pr0 u2 
+u1))))))))))).(\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).((drop n O (CHead c4 k u2) (CHead 
+e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O (CHead 
+c3 k u1) (CHead e2 k0 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
+(\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))))))))) (\lambda (e1: 
+C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H3: (drop O O (CHead c4 k u2) 
+(CHead e1 k0 u0))).(let H4 \def (f_equal C C (\lambda (e: C).(match e with 
+[(CSort _) \Rightarrow c4 | (CHead c _ _) \Rightarrow c])) (CHead c4 k u2) 
+(CHead e1 k0 u0) (drop_gen_refl (CHead c4 k u2) (CHead e1 k0 u0) H3)) in 
+((let H5 \def (f_equal C K (\lambda (e: C).(match e with [(CSort _) 
+\Rightarrow k | (CHead _ k1 _) \Rightarrow k1])) (CHead c4 k u2) (CHead e1 k0 
+u0) (drop_gen_refl (CHead c4 k u2) (CHead e1 k0 u0) H3)) in ((let H6 \def 
+(f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow u2 | (CHead 
+_ _ t) \Rightarrow t])) (CHead c4 k u2) (CHead e1 k0 u0) (drop_gen_refl 
+(CHead c4 k u2) (CHead e1 k0 u0) H3)) in (\lambda (H7: (eq K k k0)).(\lambda 
+(H8: (eq C c4 e1)).(eq_ind K k (\lambda (k1: K).(ex3_2 C T (\lambda (e2: 
+C).(\lambda (u3: T).(drop O O (CHead c3 k u1) (CHead e2 k1 u3)))) (\lambda 
+(e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 
+u3 u0))))) (eq_ind T u2 (\lambda (t: T).(ex3_2 C T (\lambda (e2: C).(\lambda 
+(u3: T).(drop O O (CHead c3 k u1) (CHead e2 k u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 
+t))))) (eq_ind C c4 (\lambda (c: C).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: 
+T).(drop O O (CHead c3 k u1) (CHead e2 k u3)))) (\lambda (e2: C).(\lambda (_: 
+T).(wcpr0 e2 c))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u2))))) 
+(ex3_2_intro C T (\lambda (e2: C).(\lambda (u3: T).(drop O O (CHead c3 k u1) 
+(CHead e2 k u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 c4))) (\lambda 
+(_: C).(\lambda (u3: T).(pr0 u3 u2))) c3 u1 (drop_refl (CHead c3 k u1)) H0 
+H2) e1 H8) u0 H6) k0 H7)))) H5)) H4)))))) (K_ind (\lambda (k0: K).(\forall 
 (n: nat).(((\forall (e1: C).(\forall (u3: T).(\forall (k1: K).((drop n O 
 (CHead c4 k0 u2) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda 
 (u4: T).(drop n O (CHead c3 k0 u1) (CHead e2 k1 u4)))) (\lambda (e2: 
 C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 
 u3))))))))) \to (\forall (e1: C).(\forall (u3: T).(\forall (k1: K).((drop (S 
-n) O (CHead c4 k0 u2) (CHead e1 k1 u3)) \to (let TMP_71 \def (\lambda (e2: 
-C).(\lambda (u4: T).(let TMP_68 \def (S n) in (let TMP_69 \def (CHead c3 k0 
-u1) in (let TMP_70 \def (CHead e2 k1 u4) in (drop TMP_68 O TMP_69 
-TMP_70)))))) in (let TMP_72 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
-e1))) in (let TMP_73 \def (\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))) in 
-(ex3_2 C T TMP_71 TMP_72 TMP_73))))))))))) in (let TMP_101 \def (\lambda (b: 
-B).(\lambda (n: nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall 
-(k0: K).((drop n O (CHead c4 (Bind b) u2) (CHead e1 k0 u3)) \to (ex3_2 C T 
-(\lambda (e2: C).(\lambda (u4: T).(drop n O (CHead c3 (Bind b) u1) (CHead e2 
-k0 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
-C).(\lambda (u4: T).(pr0 u4 u3)))))))))).(\lambda (e1: C).(\lambda (u0: 
-T).(\lambda (k0: K).(\lambda (H4: (drop (S n) O (CHead c4 (Bind b) u2) (CHead 
-e1 k0 u0))).(let TMP_75 \def (Bind b) in (let TMP_76 \def (CHead e1 k0 u0) in 
-(let TMP_77 \def (drop_gen_drop TMP_75 c4 TMP_76 u2 n H4) in (let H5 \def (H1 
-n e1 u0 k0 TMP_77) in (let TMP_79 \def (\lambda (e2: C).(\lambda (u3: T).(let 
-TMP_78 \def (CHead e2 k0 u3) in (drop n O c3 TMP_78)))) in (let TMP_80 \def 
-(\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_81 \def (\lambda 
-(_: C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_86 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_82 \def (S n) in (let TMP_83 \def (Bind b) in 
-(let TMP_84 \def (CHead c3 TMP_83 u1) in (let TMP_85 \def (CHead e2 k0 u3) in 
-(drop TMP_82 O TMP_84 TMP_85))))))) in (let TMP_87 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_88 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_89 \def (ex3_2 C T TMP_86 
-TMP_87 TMP_88) in (let TMP_100 \def (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (drop n O c3 (CHead x0 k0 x1))).(\lambda (H7: (wcpr0 x0 
-e1)).(\lambda (H8: (pr0 x1 u0)).(let TMP_94 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_90 \def (S n) in (let TMP_91 \def (Bind b) in (let TMP_92 
-\def (CHead c3 TMP_91 u1) in (let TMP_93 \def (CHead e2 k0 u3) in (drop 
-TMP_90 O TMP_92 TMP_93))))))) in (let TMP_95 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 e2 e1))) in (let TMP_96 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u3 u0))) in (let TMP_97 \def (Bind b) in (let TMP_98 \def (CHead x0 
-k0 x1) in (let TMP_99 \def (drop_drop TMP_97 n c3 TMP_98 H6 u1) in 
-(ex3_2_intro C T TMP_94 TMP_95 TMP_96 x0 x1 TMP_99 H7 H8)))))))))))) in 
-(ex3_2_ind C T TMP_79 TMP_80 TMP_81 TMP_89 TMP_100 H5)))))))))))))))))))) in 
-(let TMP_130 \def (\lambda (f: F).(\lambda (n: nat).(\lambda (_: ((\forall 
-(e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c4 (Flat f) u2) 
-(CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(drop n O 
-(CHead c3 (Flat f) u1) (CHead e2 k0 u4)))) (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 
+n) O (CHead c4 k0 u2) (CHead e1 k1 u3)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u4: T).(drop (S n) O (CHead c3 k0 u1) (CHead e2 k1 u4)))) 
+(\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda 
+(u4: T).(pr0 u4 u3))))))))))) (\lambda (b: B).(\lambda (n: nat).(\lambda (_: 
+((\forall (e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c4 
+(Bind b) u2) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: 
+T).(drop n O (CHead c3 (Bind b) u1) (CHead e2 k0 u4)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 
 u3)))))))))).(\lambda (e1: C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H4: 
-(drop (S n) O (CHead c4 (Flat f) u2) (CHead e1 k0 u0))).(let TMP_102 \def (S 
-n) in (let TMP_103 \def (Flat f) in (let TMP_104 \def (CHead e1 k0 u0) in 
-(let TMP_105 \def (drop_gen_drop TMP_103 c4 TMP_104 u2 n H4) in (let H5 \def 
-(H1 TMP_102 e1 u0 k0 TMP_105) in (let TMP_108 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_106 \def (S n) in (let TMP_107 \def (CHead e2 k0 u3) in 
-(drop TMP_106 O c3 TMP_107))))) in (let TMP_109 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_110 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_115 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_111 \def (S n) in (let TMP_112 \def (Flat f) in 
-(let TMP_113 \def (CHead c3 TMP_112 u1) in (let TMP_114 \def (CHead e2 k0 u3) 
-in (drop TMP_111 O TMP_113 TMP_114))))))) in (let TMP_116 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_117 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_118 \def (ex3_2 C T TMP_115 
-TMP_116 TMP_117) in (let TMP_129 \def (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (drop (S n) O c3 (CHead x0 k0 x1))).(\lambda (H7: (wcpr0 x0 
-e1)).(\lambda (H8: (pr0 x1 u0)).(let TMP_123 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_119 \def (S n) in (let TMP_120 \def (Flat f) in (let TMP_121 
-\def (CHead c3 TMP_120 u1) in (let TMP_122 \def (CHead e2 k0 u3) in (drop 
-TMP_119 O TMP_121 TMP_122))))))) in (let TMP_124 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_125 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_126 \def (Flat f) in (let 
-TMP_127 \def (CHead x0 k0 x1) in (let TMP_128 \def (drop_drop TMP_126 n c3 
-TMP_127 H6 u1) in (ex3_2_intro C T TMP_123 TMP_124 TMP_125 x0 x1 TMP_128 H7 
-H8)))))))))))) in (ex3_2_ind C T TMP_108 TMP_109 TMP_110 TMP_118 TMP_129 
-H5))))))))))))))))))))) in (let TMP_131 \def (K_ind TMP_74 TMP_101 TMP_130 k) 
-in (nat_ind TMP_18 TMP_67 TMP_131 h)))))))))))))))) in (wcpr0_ind TMP_5 
-TMP_12 TMP_132 c2 c1 H)))))).
+(drop (S n) O (CHead c4 (Bind b) u2) (CHead e1 k0 u0))).(let H5 \def (H1 n e1 
+u0 k0 (drop_gen_drop (Bind b) c4 (CHead e1 k0 u0) u2 n H4)) in (ex3_2_ind C T 
+(\lambda (e2: C).(\lambda (u3: T).(drop n O c3 (CHead e2 k0 u3)))) (\lambda 
+(e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 
+u3 u0))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(drop (S n) O (CHead c3 
+(Bind b) u1) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
+e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0)))) (\lambda (x0: 
+C).(\lambda (x1: T).(\lambda (H6: (drop n O c3 (CHead x0 k0 x1))).(\lambda 
+(H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 u0)).(ex3_2_intro C T (\lambda (e2: 
+C).(\lambda (u3: T).(drop (S n) O (CHead c3 (Bind b) u1) (CHead e2 k0 u3)))) 
+(\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda 
+(u3: T).(pr0 u3 u0))) x0 x1 (drop_drop (Bind b) n c3 (CHead x0 k0 x1) H6 u1) 
+H7 H8)))))) H5))))))))) (\lambda (f: F).(\lambda (n: nat).(\lambda (_: 
+((\forall (e1: C).(\forall (u3: T).(\forall (k0: K).((drop n O (CHead c4 
+(Flat f) u2) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: 
+T).(drop n O (CHead c3 (Flat f) u1) (CHead e2 k0 u4)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 
+u3)))))))))).(\lambda (e1: C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H4: 
+(drop (S n) O (CHead c4 (Flat f) u2) (CHead e1 k0 u0))).(let H5 \def (H1 (S 
+n) e1 u0 k0 (drop_gen_drop (Flat f) c4 (CHead e1 k0 u0) u2 n H4)) in 
+(ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(drop (S n) O c3 (CHead e2 
+k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u3: T).(pr0 u3 u0))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3: 
+T).(drop (S n) O (CHead c3 (Flat f) u1) (CHead e2 k0 u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 
+u0)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (drop (S n) O c3 
+(CHead x0 k0 x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 
+u0)).(ex3_2_intro C T (\lambda (e2: C).(\lambda (u3: T).(drop (S n) O (CHead 
+c3 (Flat f) u1) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 
+e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) x0 x1 (drop_drop 
+(Flat f) n c3 (CHead x0 k0 x1) H6 u1) H7 H8)))))) H5))))))))) k) h)))))))))) 
+c2 c1 H))).
 
-theorem wcpr0_getl:
+lemma wcpr0_getl:
  \forall (c1: C).(\forall (c2: C).((wcpr0 c1 c2) \to (\forall (h: 
 nat).(\forall (e1: C).(\forall (u1: T).(\forall (k: K).((getl h c1 (CHead e1 
 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(getl h c2 (CHead e2 
 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) (\lambda (_: 
 C).(\lambda (u2: T).(pr0 u1 u2)))))))))))
 \def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c1 c2)).(let TMP_5 \def 
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c1 c2)).(wcpr0_ind 
 (\lambda (c: C).(\lambda (c0: C).(\forall (h: nat).(\forall (e1: C).(\forall 
-(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: 
 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)))) 
+n (CHead c3 (Flat f) u1) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u4: T).(getl n (CHead c4 (Flat f) 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 
-TMP_118 \def (Bind b) in (let TMP_119 \def (CHead e1 k0 u0) in (let TMP_120 
-\def (getl_gen_S TMP_118 c3 TMP_119 u1 n H4) in (let H5 \def (H1 n e1 u0 k0 
-TMP_120) in (let TMP_122 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_121 
-\def (CHead e2 k0 u3) in (getl n c4 TMP_121)))) in (let TMP_123 \def (\lambda 
-(e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_124 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_129 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_125 \def (S n) in (let TMP_126 \def (Bind b) in 
-(let TMP_127 \def (CHead c4 TMP_126 u2) in (let TMP_128 \def (CHead e2 k0 u3) 
-in (getl TMP_125 TMP_127 TMP_128))))))) in (let TMP_130 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_131 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_132 \def (ex3_2 C T TMP_129 
-TMP_130 TMP_131) in (let TMP_143 \def (\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)).(let TMP_137 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_133 \def (S n) in (let TMP_134 \def (Bind b) in (let TMP_135 
-\def (CHead c4 TMP_134 u2) in (let TMP_136 \def (CHead e2 k0 u3) in (getl 
-TMP_133 TMP_135 TMP_136))))))) in (let TMP_138 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 e1 e2))) in (let TMP_139 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u0 u3))) in (let TMP_140 \def (Bind b) in (let TMP_141 \def (CHead x0 
-k0 x1) in (let TMP_142 \def (getl_head TMP_140 n c4 TMP_141 H6 u2) in 
-(ex3_2_intro C T TMP_137 TMP_138 TMP_139 x0 x1 TMP_142 H7 H8)))))))))))) in 
-(ex3_2_ind C T TMP_122 TMP_123 TMP_124 TMP_132 TMP_143 H5)))))))))))))))))))) 
-in (let TMP_173 \def (\lambda (f: F).(\lambda (n: nat).(\lambda (_: ((\forall 
-(e1: C).(\forall (u3: T).(\forall (k0: K).((getl n (CHead c3 (Flat f) u1) 
-(CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n 
-(CHead c4 (Flat f) 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 (Flat f) u1) (CHead e1 k0 u0))).(let TMP_145 \def (S n) 
-in (let TMP_146 \def (Flat f) in (let TMP_147 \def (CHead e1 k0 u0) in (let 
-TMP_148 \def (getl_gen_S TMP_146 c3 TMP_147 u1 n H4) in (let H5 \def (H1 
-TMP_145 e1 u0 k0 TMP_148) in (let TMP_151 \def (\lambda (e2: C).(\lambda (u3: 
-T).(let TMP_149 \def (S n) in (let TMP_150 \def (CHead e2 k0 u3) in (getl 
-TMP_149 c4 TMP_150))))) in (let TMP_152 \def (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e1 e2))) in (let TMP_153 \def (\lambda (_: C).(\lambda (u3: T).(pr0 
-u0 u3))) in (let TMP_158 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_154 
-\def (S n) in (let TMP_155 \def (Flat f) in (let TMP_156 \def (CHead c4 
-TMP_155 u2) in (let TMP_157 \def (CHead e2 k0 u3) in (getl TMP_154 TMP_156 
-TMP_157))))))) in (let TMP_159 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 
-e1 e2))) in (let TMP_160 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) 
-in (let TMP_161 \def (ex3_2 C T TMP_158 TMP_159 TMP_160) in (let TMP_172 \def 
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl (S n) c4 (CHead x0 k0 
-x1))).(\lambda (H7: (wcpr0 e1 x0)).(\lambda (H8: (pr0 u0 x1)).(let TMP_166 
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_162 \def (S n) in (let 
-TMP_163 \def (Flat f) in (let TMP_164 \def (CHead c4 TMP_163 u2) in (let 
-TMP_165 \def (CHead e2 k0 u3) in (getl TMP_162 TMP_164 TMP_165))))))) in (let 
-TMP_167 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e1 e2))) in (let TMP_168 
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u0 u3))) in (let TMP_169 \def 
-(Flat f) in (let TMP_170 \def (CHead x0 k0 x1) in (let TMP_171 \def 
-(getl_head TMP_169 n c4 TMP_170 H6 u2) in (ex3_2_intro C T TMP_166 TMP_167 
-TMP_168 x0 x1 TMP_171 H7 H8)))))))))))) in (ex3_2_ind C T TMP_151 TMP_152 
-TMP_153 TMP_161 TMP_172 H5))))))))))))))))))))) in (let TMP_174 \def (K_ind 
-TMP_117 TMP_144 TMP_173 k) in (nat_ind TMP_18 TMP_110 TMP_174 
-h)))))))))))))))) in (wcpr0_ind TMP_5 TMP_12 TMP_175 c1 c2 H)))))).
+K).(\lambda (H4: (getl (S n) (CHead c3 (Flat f) u1) (CHead e1 k0 u0))).(let 
+H5 \def (H1 (S n) e1 u0 k0 (getl_gen_S (Flat f) c3 (CHead e1 k0 u0) u1 n H4)) 
+in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl (S 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 (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 (S 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 
+(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_head (Flat 
+f) n c4 (CHead x0 k0 x1) H6 u2) H7 H8)))))) H5))))))))) k) h)))))))))) c1 c2 
+H))).
 
-theorem wcpr0_getl_back:
+lemma wcpr0_getl_back:
  \forall (c1: C).(\forall (c2: C).((wcpr0 c2 c1) \to (\forall (h: 
 nat).(\forall (e1: C).(\forall (u1: T).(\forall (k: K).((getl h c1 (CHead e1 
 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(getl h c2 (CHead e2 
 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
 C).(\lambda (u2: T).(pr0 u2 u1)))))))))))
 \def
- \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c2 c1)).(let TMP_5 \def 
+ \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c2 c1)).(wcpr0_ind 
 (\lambda (c: C).(\lambda (c0: C).(\forall (h: nat).(\forall (e1: C).(\forall 
-(u1: T).(\forall (k: K).((getl h c0 (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 
-c TMP_1)))) in (let TMP_3 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
-e1))) in (let TMP_4 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u2 u1))) 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 e2 e1))) in (let 
-TMP_9 \def (\lambda (_: C).(\lambda (u2: T).(pr0 u2 u1))) 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 c4 (CHead 
-e1 k u1)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u2: T).(getl h c3 (CHead 
-e2 k u2)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
-C).(\lambda (u2: T).(pr0 u2 u1))))))))))).(\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 c4 k u2) (CHead e1 k0 u3)) \to (let TMP_15 \def (\lambda 
-(e2: C).(\lambda (u4: T).(let TMP_13 \def (CHead c3 k u1) 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 e2 e1))) in (let TMP_17 \def (\lambda (_: 
-C).(\lambda (u4: T).(pr0 u4 u3))) 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 c4 k u2) (CHead e1 k0 u0))).(let TMP_24 \def 
-(\lambda (k1: K).((clear (CHead c4 k1 u2) (CHead e1 k0 u0)) \to (let TMP_21 
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_19 \def (CHead c3 k1 u1) 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 e2 e1))) in (let TMP_23 
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) in (ex3_2 C T TMP_21 
-TMP_22 TMP_23)))))) in (let TMP_80 \def (\lambda (b: B).(\lambda (H4: (clear 
-(CHead c4 (Bind b) u2) (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 c4 TMP_27 u2) in (let TMP_29 \def (CHead e1 k0 u0) in (let 
-TMP_30 \def (clear_gen_bind b c4 TMP_29 u2 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 c4 TMP_33 u2) in (let TMP_35 \def (CHead e1 k0 u0) in (let TMP_36 \def 
-(clear_gen_bind b c4 TMP_35 u2 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 c4 TMP_39 u2) 
-in (let TMP_41 \def (CHead e1 k0 u0) in (let TMP_42 \def (clear_gen_bind b c4 
-TMP_41 u2 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 
-c4)).(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 c3 TMP_44 u1) 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 e2 e1))) in (let TMP_49 \def (\lambda (_: C).(\lambda (u3: T).(pr0 
-u3 u0))) 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 c3 TMP_51 u1) 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 e2 e1))) in (let 
-TMP_57 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 t))) 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 c3 TMP_59 u1) 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 e2 c))) in (let TMP_65 \def (\lambda 
-(_: C).(\lambda (u3: T).(pr0 u3 u2))) 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 c3 TMP_67 u1) 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 e2 c4))) in (let TMP_73 
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u2))) in (let TMP_74 \def 
-(getl_refl b c3 u1) in (let TMP_75 \def (ex3_2_intro C T TMP_71 TMP_72 TMP_73 
-c3 u1 TMP_74 H0 H2) in (let TMP_76 \def (eq_ind_r C c4 TMP_66 TMP_75 e1 H9) 
-in (let TMP_77 \def (eq_ind_r T u2 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 c4 (Flat f) u2) (CHead e1 k0 u0))).(let TMP_81 \def (CHead 
-e1 k0 u0) in (let TMP_82 \def (drop_refl c4) in (let TMP_83 \def (CHead e1 k0 
-u0) in (let TMP_84 \def (clear_gen_flat f c4 TMP_83 u2 H4) in (let TMP_85 
-\def (getl_intro O c4 TMP_81 c4 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 c3 TMP_86)))) in (let TMP_88 \def (\lambda 
-(e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_89 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_93 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_90 \def (Flat f) in (let TMP_91 \def (CHead c3 
-TMP_90 u1) 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 e2 
-e1))) in (let TMP_95 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) 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 c3 (CHead x0 k0 
-x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 u0)).(let TMP_100 
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_97 \def (Flat f) in (let 
-TMP_98 \def (CHead c3 TMP_97 u1) 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 e2 e1))) in (let TMP_102 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u3 u0))) in (let TMP_103 \def (CHead x0 k0 x1) in (let TMP_104 \def 
-(getl_flat c3 TMP_103 O H6 f u1) 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 c4 k u2) 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 c4 k0 u2) (CHead e1 k1 u3)) \to 
-(ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c3 k0 u1) (CHead 
-e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
-C).(\lambda (u4: T).(pr0 u4 u3))))))))) \to (\forall (e1: C).(\forall (u3: 
-T).(\forall (k1: K).((getl (S n) (CHead c4 k0 u2) (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 c3 k0 u1) 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 e2 e1))) in (let TMP_116 \def (\lambda (_: 
-C).(\lambda (u4: T).(pr0 u4 u3))) 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 c0 (CHead e1 k u1)) \to (ex3_2 C T (\lambda 
+(e2: C).(\lambda (u2: T).(getl h c (CHead e2 k u2)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u2: T).(pr0 u2 
+u1))))))))))) (\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 e2 e1))) (\lambda (_: 
+C).(\lambda (u2: T).(pr0 u2 u1))) 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 c4 (CHead e1 k u1)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u2: T).(getl h c3 (CHead e2 k u2)))) (\lambda (e2: C).(\lambda 
+(_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u2: T).(pr0 u2 
+u1))))))))))).(\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 c4 k u2) (CHead e1 
+k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c3 k 
+u1) (CHead e2 k0 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
+(\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))))))))) (\lambda (e1: 
+C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H3: (getl O (CHead c4 k u2) 
+(CHead e1 k0 u0))).(K_ind (\lambda (k1: K).((clear (CHead c4 k1 u2) (CHead e1 
+k0 u0)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 k1 
+u1) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
+(\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0)))))) (\lambda (b: B).(\lambda 
+(H4: (clear (CHead c4 (Bind b) u2) (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 c4 (Bind b) u2) (clear_gen_bind b c4 
+(CHead e1 k0 u0) u2 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 c4 (Bind b) u2) (clear_gen_bind b c4 (CHead e1 k0 u0) u2 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 c4 
+(Bind b) u2) (clear_gen_bind b c4 (CHead e1 k0 u0) u2 H4)) in (\lambda (H8: 
+(eq K k0 (Bind b))).(\lambda (H9: (eq C e1 c4)).(eq_ind_r K (Bind b) (\lambda 
+(k1: K).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 (Bind 
+b) u1) (CHead e2 k1 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
+(\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))))) (eq_ind_r T u2 (\lambda (t: 
+T).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 (Bind b) 
+u1) (CHead e2 (Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
+e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 t))))) (eq_ind_r C c4 (\lambda 
+(c: C).(ex3_2 C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 (Bind 
+b) u1) (CHead e2 (Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
+c))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u2))))) (ex3_2_intro C T 
+(\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 (Bind b) u1) (CHead e2 
+(Bind b) u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 c4))) (\lambda (_: 
+C).(\lambda (u3: T).(pr0 u3 u2))) c3 u1 (getl_refl b c3 u1) H0 H2) e1 H9) u0 
+H7) k0 H8)))) H6)) H5)))) (\lambda (f: F).(\lambda (H4: (clear (CHead c4 
+(Flat f) u2) (CHead e1 k0 u0))).(let H5 \def (H1 O e1 u0 k0 (getl_intro O c4 
+(CHead e1 k0 u0) c4 (drop_refl c4) (clear_gen_flat f c4 (CHead e1 k0 u0) u2 
+H4))) in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl O c3 (CHead 
+e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u3: T).(pr0 u3 u0))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3: 
+T).(getl O (CHead c3 (Flat f) u1) (CHead e2 k0 u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 
+u0)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl O c3 (CHead x0 
+k0 x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 u0)).(ex3_2_intro 
+C T (\lambda (e2: C).(\lambda (u3: T).(getl O (CHead c3 (Flat f) u1) (CHead 
+e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u3: T).(pr0 u3 u0))) x0 x1 (getl_flat c3 (CHead x0 k0 x1) O H6 f 
+u1) H7 H8)))))) H5)))) k (getl_gen_O (CHead c4 k u2) (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 c4 k0 u2) (CHead e1 k1 
+u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c3 k0 
+u1) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) 
+(\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))))))))) \to (\forall (e1: 
+C).(\forall (u3: T).(\forall (k1: K).((getl (S n) (CHead c4 k0 u2) (CHead e1 
+k1 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl (S n) (CHead 
+c3 k0 u1) (CHead e2 k1 u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
+e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 u3))))))))))) (\lambda (b: 
+B).(\lambda (n: nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall 
+(k0: K).((getl n (CHead c4 (Bind b) u2) (CHead e1 k0 u3)) \to (ex3_2 C T 
+(\lambda (e2: C).(\lambda (u4: T).(getl n (CHead c3 (Bind b) u1) (CHead e2 k0 
+u4)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u4: T).(pr0 u4 u3)))))))))).(\lambda (e1: C).(\lambda (u0: 
+T).(\lambda (k0: K).(\lambda (H4: (getl (S n) (CHead c4 (Bind b) u2) (CHead 
+e1 k0 u0))).(let H5 \def (H1 n e1 u0 k0 (getl_gen_S (Bind b) c4 (CHead e1 k0 
+u0) u2 n H4)) in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl n c3 
+(CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda 
+(_: C).(\lambda (u3: T).(pr0 u3 u0))) (ex3_2 C T (\lambda (e2: C).(\lambda 
+(u3: T).(getl (S n) (CHead c3 (Bind b) u1) (CHead e2 k0 u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 
+u0)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl n c3 (CHead x0 
+k0 x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 u0)).(ex3_2_intro 
+C T (\lambda (e2: C).(\lambda (u3: T).(getl (S n) (CHead c3 (Bind b) u1) 
+(CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda 
+(_: C).(\lambda (u3: T).(pr0 u3 u0))) x0 x1 (getl_head (Bind b) n c3 (CHead 
+x0 k0 x1) H6 u1) H7 H8)))))) H5))))))))) (\lambda (f: F).(\lambda (n: 
 nat).(\lambda (_: ((\forall (e1: C).(\forall (u3: T).(\forall (k0: K).((getl 
-n (CHead c4 (Bind b) u2) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: 
-C).(\lambda (u4: T).(getl n (CHead c3 (Bind b) u1) (CHead e2 k0 u4)))) 
+n (CHead c4 (Flat f) u2) (CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: 
+C).(\lambda (u4: T).(getl n (CHead c3 (Flat f) u1) (CHead e2 k0 u4)))) 
 (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda 
 (u4: T).(pr0 u4 u3)))))))))).(\lambda (e1: C).(\lambda (u0: T).(\lambda (k0: 
-K).(\lambda (H4: (getl (S n) (CHead c4 (Bind b) u2) (CHead e1 k0 u0))).(let 
-TMP_118 \def (Bind b) in (let TMP_119 \def (CHead e1 k0 u0) in (let TMP_120 
-\def (getl_gen_S TMP_118 c4 TMP_119 u2 n H4) in (let H5 \def (H1 n e1 u0 k0 
-TMP_120) in (let TMP_122 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_121 
-\def (CHead e2 k0 u3) in (getl n c3 TMP_121)))) in (let TMP_123 \def (\lambda 
-(e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_124 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_129 \def (\lambda (e2: 
-C).(\lambda (u3: T).(let TMP_125 \def (S n) in (let TMP_126 \def (Bind b) in 
-(let TMP_127 \def (CHead c3 TMP_126 u1) in (let TMP_128 \def (CHead e2 k0 u3) 
-in (getl TMP_125 TMP_127 TMP_128))))))) in (let TMP_130 \def (\lambda (e2: 
-C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_131 \def (\lambda (_: 
-C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_132 \def (ex3_2 C T TMP_129 
-TMP_130 TMP_131) in (let TMP_143 \def (\lambda (x0: C).(\lambda (x1: 
-T).(\lambda (H6: (getl n c3 (CHead x0 k0 x1))).(\lambda (H7: (wcpr0 x0 
-e1)).(\lambda (H8: (pr0 x1 u0)).(let TMP_137 \def (\lambda (e2: C).(\lambda 
-(u3: T).(let TMP_133 \def (S n) in (let TMP_134 \def (Bind b) in (let TMP_135 
-\def (CHead c3 TMP_134 u1) in (let TMP_136 \def (CHead e2 k0 u3) in (getl 
-TMP_133 TMP_135 TMP_136))))))) in (let TMP_138 \def (\lambda (e2: C).(\lambda 
-(_: T).(wcpr0 e2 e1))) in (let TMP_139 \def (\lambda (_: C).(\lambda (u3: 
-T).(pr0 u3 u0))) in (let TMP_140 \def (Bind b) in (let TMP_141 \def (CHead x0 
-k0 x1) in (let TMP_142 \def (getl_head TMP_140 n c3 TMP_141 H6 u1) in 
-(ex3_2_intro C T TMP_137 TMP_138 TMP_139 x0 x1 TMP_142 H7 H8)))))))))))) in 
-(ex3_2_ind C T TMP_122 TMP_123 TMP_124 TMP_132 TMP_143 H5)))))))))))))))))))) 
-in (let TMP_173 \def (\lambda (f: F).(\lambda (n: nat).(\lambda (_: ((\forall 
-(e1: C).(\forall (u3: T).(\forall (k0: K).((getl n (CHead c4 (Flat f) u2) 
-(CHead e1 k0 u3)) \to (ex3_2 C T (\lambda (e2: C).(\lambda (u4: T).(getl n 
-(CHead c3 (Flat f) u1) (CHead e2 k0 u4)))) (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u4: T).(pr0 u4 
-u3)))))))))).(\lambda (e1: C).(\lambda (u0: T).(\lambda (k0: K).(\lambda (H4: 
-(getl (S n) (CHead c4 (Flat f) u2) (CHead e1 k0 u0))).(let TMP_145 \def (S n) 
-in (let TMP_146 \def (Flat f) in (let TMP_147 \def (CHead e1 k0 u0) in (let 
-TMP_148 \def (getl_gen_S TMP_146 c4 TMP_147 u2 n H4) in (let H5 \def (H1 
-TMP_145 e1 u0 k0 TMP_148) in (let TMP_151 \def (\lambda (e2: C).(\lambda (u3: 
-T).(let TMP_149 \def (S n) in (let TMP_150 \def (CHead e2 k0 u3) in (getl 
-TMP_149 c3 TMP_150))))) in (let TMP_152 \def (\lambda (e2: C).(\lambda (_: 
-T).(wcpr0 e2 e1))) in (let TMP_153 \def (\lambda (_: C).(\lambda (u3: T).(pr0 
-u3 u0))) in (let TMP_158 \def (\lambda (e2: C).(\lambda (u3: T).(let TMP_154 
-\def (S n) in (let TMP_155 \def (Flat f) in (let TMP_156 \def (CHead c3 
-TMP_155 u1) in (let TMP_157 \def (CHead e2 k0 u3) in (getl TMP_154 TMP_156 
-TMP_157))))))) in (let TMP_159 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 
-e2 e1))) in (let TMP_160 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) 
-in (let TMP_161 \def (ex3_2 C T TMP_158 TMP_159 TMP_160) in (let TMP_172 \def 
-(\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl (S n) c3 (CHead x0 k0 
-x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 u0)).(let TMP_166 
-\def (\lambda (e2: C).(\lambda (u3: T).(let TMP_162 \def (S n) in (let 
-TMP_163 \def (Flat f) in (let TMP_164 \def (CHead c3 TMP_163 u1) in (let 
-TMP_165 \def (CHead e2 k0 u3) in (getl TMP_162 TMP_164 TMP_165))))))) in (let 
-TMP_167 \def (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) in (let TMP_168 
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) in (let TMP_169 \def 
-(Flat f) in (let TMP_170 \def (CHead x0 k0 x1) in (let TMP_171 \def 
-(getl_head TMP_169 n c3 TMP_170 H6 u1) in (ex3_2_intro C T TMP_166 TMP_167 
-TMP_168 x0 x1 TMP_171 H7 H8)))))))))))) in (ex3_2_ind C T TMP_151 TMP_152 
-TMP_153 TMP_161 TMP_172 H5))))))))))))))))))))) in (let TMP_174 \def (K_ind 
-TMP_117 TMP_144 TMP_173 k) in (nat_ind TMP_18 TMP_110 TMP_174 
-h)))))))))))))))) in (wcpr0_ind TMP_5 TMP_12 TMP_175 c2 c1 H)))))).
+K).(\lambda (H4: (getl (S n) (CHead c4 (Flat f) u2) (CHead e1 k0 u0))).(let 
+H5 \def (H1 (S n) e1 u0 k0 (getl_gen_S (Flat f) c4 (CHead e1 k0 u0) u2 n H4)) 
+in (ex3_2_ind C T (\lambda (e2: C).(\lambda (u3: T).(getl (S n) c3 (CHead e2 
+k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: 
+C).(\lambda (u3: T).(pr0 u3 u0))) (ex3_2 C T (\lambda (e2: C).(\lambda (u3: 
+T).(getl (S n) (CHead c3 (Flat f) u1) (CHead e2 k0 u3)))) (\lambda (e2: 
+C).(\lambda (_: T).(wcpr0 e2 e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 
+u0)))) (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl (S n) c3 (CHead 
+x0 k0 x1))).(\lambda (H7: (wcpr0 x0 e1)).(\lambda (H8: (pr0 x1 
+u0)).(ex3_2_intro C T (\lambda (e2: C).(\lambda (u3: T).(getl (S n) (CHead c3 
+(Flat f) u1) (CHead e2 k0 u3)))) (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 
+e1))) (\lambda (_: C).(\lambda (u3: T).(pr0 u3 u0))) x0 x1 (getl_head (Flat 
+f) n c3 (CHead x0 k0 x1) H6 u1) H7 H8)))))) H5))))))))) k) h)))))))))) c2 c1 
+H))).