-k0 u0) (CHead c1 k u1))).(let TMP_40 \def (\lambda (e: C).(match e with
-[(CSort _) \Rightarrow c0 | (CHead c _ _) \Rightarrow c])) in (let TMP_41
-\def (CHead c0 k0 u0) in (let TMP_42 \def (CHead c1 k u1) in (let H5 \def
-(f_equal C C TMP_40 TMP_41 TMP_42 H4) in (let TMP_43 \def (\lambda (e:
-C).(match e with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1]))
-in (let TMP_44 \def (CHead c0 k0 u0) in (let TMP_45 \def (CHead c1 k u1) in
-(let H6 \def (f_equal C K TMP_43 TMP_44 TMP_45 H4) in (let TMP_46 \def
-(\lambda (e: C).(match e with [(CSort _) \Rightarrow u0 | (CHead _ _ t)
-\Rightarrow t])) in (let TMP_47 \def (CHead c0 k0 u0) in (let TMP_48 \def
-(CHead c1 k u1) in (let H7 \def (f_equal C T TMP_46 TMP_47 TMP_48 H4) in (let
-TMP_108 \def (\lambda (H8: (eq K k0 k)).(\lambda (H9: (eq C c0 c1)).(let
-TMP_58 \def (\lambda (k1: K).(let TMP_49 \def (CHead c2 k1 u2) in (let TMP_50
-\def (CHead c0 k1 u0) in (let TMP_51 \def (eq C TMP_49 TMP_50) in (let TMP_54
-\def (\lambda (c3: C).(\lambda (u3: T).(let TMP_52 \def (CHead c2 k1 u2) in
-(let TMP_53 \def (CHead c3 k u3) in (eq C TMP_52 TMP_53))))) in (let TMP_55
-\def (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3))) in (let TMP_56 \def
-(\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_57 \def (ex3_2 C T
-TMP_54 TMP_55 TMP_56) in (or TMP_51 TMP_57))))))))) in (let TMP_59 \def
-(\lambda (t: T).(pr0 t u2)) in (let H10 \def (eq_ind T u0 TMP_59 H3 u1 H7) in
-(let TMP_69 \def (\lambda (t: T).(let TMP_60 \def (CHead c2 k u2) in (let
-TMP_61 \def (CHead c0 k t) in (let TMP_62 \def (eq C TMP_60 TMP_61) in (let
-TMP_65 \def (\lambda (c3: C).(\lambda (u3: T).(let TMP_63 \def (CHead c2 k
-u2) in (let TMP_64 \def (CHead c3 k u3) in (eq C TMP_63 TMP_64))))) in (let
-TMP_66 \def (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3))) in (let TMP_67
-\def (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_68 \def
-(ex3_2 C T TMP_65 TMP_66 TMP_67) in (or TMP_62 TMP_68))))))))) in (let TMP_76
-\def (\lambda (c: C).((eq C c (CHead c1 k u1)) \to (let TMP_70 \def (eq C c2
-c) in (let TMP_72 \def (\lambda (c3: C).(\lambda (u3: T).(let TMP_71 \def
-(CHead c3 k u3) in (eq C c2 TMP_71)))) in (let TMP_73 \def (\lambda (c3:
-C).(\lambda (_: T).(wcpr0 c1 c3))) in (let TMP_74 \def (\lambda (_:
-C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_75 \def (ex3_2 C T TMP_72
-TMP_73 TMP_74) in (or TMP_70 TMP_75)))))))) in (let H11 \def (eq_ind C c0
-TMP_76 H2 c1 H9) in (let TMP_77 \def (\lambda (c: C).(wcpr0 c c2)) in (let
-H12 \def (eq_ind C c0 TMP_77 H1 c1 H9) in (let TMP_87 \def (\lambda (c:
-C).(let TMP_78 \def (CHead c2 k u2) in (let TMP_79 \def (CHead c k u1) in
-(let TMP_80 \def (eq C TMP_78 TMP_79) in (let TMP_83 \def (\lambda (c3:
-C).(\lambda (u3: T).(let TMP_81 \def (CHead c2 k u2) in (let TMP_82 \def
-(CHead c3 k u3) in (eq C TMP_81 TMP_82))))) in (let TMP_84 \def (\lambda (c3:
-C).(\lambda (_: T).(wcpr0 c1 c3))) in (let TMP_85 \def (\lambda (_:
-C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_86 \def (ex3_2 C T TMP_83
-TMP_84 TMP_85) in (or TMP_80 TMP_86))))))))) in (let TMP_88 \def (CHead c2 k
-u2) in (let TMP_89 \def (CHead c1 k u1) in (let TMP_90 \def (eq C TMP_88
-TMP_89) in (let TMP_93 \def (\lambda (c3: C).(\lambda (u3: T).(let TMP_91
-\def (CHead c2 k u2) in (let TMP_92 \def (CHead c3 k u3) in (eq C TMP_91
-TMP_92))))) in (let TMP_94 \def (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1
-c3))) in (let TMP_95 \def (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in
-(let TMP_96 \def (ex3_2 C T TMP_93 TMP_94 TMP_95) in (let TMP_99 \def
-(\lambda (c3: C).(\lambda (u3: T).(let TMP_97 \def (CHead c2 k u2) in (let
-TMP_98 \def (CHead c3 k u3) in (eq C TMP_97 TMP_98))))) in (let TMP_100 \def
-(\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3))) in (let TMP_101 \def
-(\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) in (let TMP_102 \def (CHead c2
-k u2) in (let TMP_103 \def (refl_equal C TMP_102) in (let TMP_104 \def
-(ex3_2_intro C T TMP_99 TMP_100 TMP_101 c2 u2 TMP_103 H12 H10) in (let
-TMP_105 \def (or_intror TMP_90 TMP_96 TMP_104) in (let TMP_106 \def (eq_ind_r
-C c1 TMP_87 TMP_105 c0 H9) in (let TMP_107 \def (eq_ind_r T u1 TMP_69 TMP_106
-u0 H7) in (eq_ind_r K k TMP_58 TMP_107 k0 H8)))))))))))))))))))))))))))) in
-(let TMP_109 \def (TMP_108 H6) in (TMP_109 H5)))))))))))))))))))))))) in
-(wcpr0_ind TMP_16 TMP_39 TMP_110 y x H0)))))) in (insert_eq C TMP_1 TMP_2
-TMP_9 TMP_111 H))))))))).
+k0 u0) (CHead c1 k u1))).(let H5 \def (f_equal C C (\lambda (e: C).(match e
+with [(CSort _) \Rightarrow c0 | (CHead c _ _) \Rightarrow c])) (CHead c0 k0
+u0) (CHead c1 k u1) H4) in ((let H6 \def (f_equal C K (\lambda (e: C).(match
+e with [(CSort _) \Rightarrow k0 | (CHead _ k1 _) \Rightarrow k1])) (CHead c0
+k0 u0) (CHead c1 k u1) H4) in ((let H7 \def (f_equal C T (\lambda (e:
+C).(match e with [(CSort _) \Rightarrow u0 | (CHead _ _ t) \Rightarrow t]))
+(CHead c0 k0 u0) (CHead c1 k u1) H4) in (\lambda (H8: (eq K k0 k)).(\lambda
+(H9: (eq C c0 c1)).(eq_ind_r K k (\lambda (k1: K).(or (eq C (CHead c2 k1 u2)
+(CHead c0 k1 u0)) (ex3_2 C T (\lambda (c3: C).(\lambda (u3: T).(eq C (CHead
+c2 k1 u2) (CHead c3 k u3)))) (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3)))
+(\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3)))))) (let H10 \def (eq_ind T u0
+(\lambda (t: T).(pr0 t u2)) H3 u1 H7) in (eq_ind_r T u1 (\lambda (t: T).(or
+(eq C (CHead c2 k u2) (CHead c0 k t)) (ex3_2 C T (\lambda (c3: C).(\lambda
+(u3: T).(eq C (CHead c2 k u2) (CHead c3 k u3)))) (\lambda (c3: C).(\lambda
+(_: T).(wcpr0 c1 c3))) (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3)))))) (let
+H11 \def (eq_ind C c0 (\lambda (c: C).((eq C c (CHead c1 k u1)) \to (or (eq C
+c2 c) (ex3_2 C T (\lambda (c3: C).(\lambda (u3: T).(eq C c2 (CHead c3 k
+u3)))) (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3))) (\lambda (_:
+C).(\lambda (u3: T).(pr0 u1 u3))))))) H2 c1 H9) in (let H12 \def (eq_ind C c0
+(\lambda (c: C).(wcpr0 c c2)) H1 c1 H9) in (eq_ind_r C c1 (\lambda (c: C).(or
+(eq C (CHead c2 k u2) (CHead c k u1)) (ex3_2 C T (\lambda (c3: C).(\lambda
+(u3: T).(eq C (CHead c2 k u2) (CHead c3 k u3)))) (\lambda (c3: C).(\lambda
+(_: T).(wcpr0 c1 c3))) (\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))))))
+(or_intror (eq C (CHead c2 k u2) (CHead c1 k u1)) (ex3_2 C T (\lambda (c3:
+C).(\lambda (u3: T).(eq C (CHead c2 k u2) (CHead c3 k u3)))) (\lambda (c3:
+C).(\lambda (_: T).(wcpr0 c1 c3))) (\lambda (_: C).(\lambda (u3: T).(pr0 u1
+u3)))) (ex3_2_intro C T (\lambda (c3: C).(\lambda (u3: T).(eq C (CHead c2 k
+u2) (CHead c3 k u3)))) (\lambda (c3: C).(\lambda (_: T).(wcpr0 c1 c3)))
+(\lambda (_: C).(\lambda (u3: T).(pr0 u1 u3))) c2 u2 (refl_equal C (CHead c2
+k u2)) H12 H10)) c0 H9))) u0 H7)) k0 H8)))) H6)) H5))))))))))) y x H0)))
+H))))).