-(f: F).(\lambda (H: (csubt g (CHead e1 (Flat f) v) c2)).(let TMP_1 \def (Flat
-f) in (let TMP_2 \def (CHead e1 TMP_1 v) in (let TMP_3 \def (\lambda (c:
-C).(csubt g c c2)) in (let TMP_8 \def (\lambda (_: C).(let TMP_6 \def
-(\lambda (e2: C).(let TMP_4 \def (Flat f) in (let TMP_5 \def (CHead e2 TMP_4
-v) in (eq C c2 TMP_5)))) in (let TMP_7 \def (\lambda (e2: C).(csubt g e1 e2))
-in (ex2 C TMP_6 TMP_7)))) in (let TMP_96 \def (\lambda (y: C).(\lambda (H0:
-(csubt g y c2)).(let TMP_13 \def (\lambda (c: C).(\lambda (c0: C).((eq C c
-(CHead e1 (Flat f) v)) \to (let TMP_11 \def (\lambda (e2: C).(let TMP_9 \def
-(Flat f) in (let TMP_10 \def (CHead e2 TMP_9 v) in (eq C c0 TMP_10)))) in
-(let TMP_12 \def (\lambda (e2: C).(csubt g e1 e2)) in (ex2 C TMP_11
-TMP_12)))))) in (let TMP_24 \def (\lambda (n: nat).(\lambda (H1: (eq C (CSort
-n) (CHead e1 (Flat f) v))).(let TMP_14 \def (CSort n) in (let TMP_15 \def
-(\lambda (ee: C).(match ee with [(CSort _) \Rightarrow True | (CHead _ _ _)
-\Rightarrow False])) in (let TMP_16 \def (Flat f) in (let TMP_17 \def (CHead
-e1 TMP_16 v) in (let H2 \def (eq_ind C TMP_14 TMP_15 I TMP_17 H1) in (let
-TMP_21 \def (\lambda (e2: C).(let TMP_18 \def (CSort n) in (let TMP_19 \def
-(Flat f) in (let TMP_20 \def (CHead e2 TMP_19 v) in (eq C TMP_18 TMP_20)))))
-in (let TMP_22 \def (\lambda (e2: C).(csubt g e1 e2)) in (let TMP_23 \def
-(ex2 C TMP_21 TMP_22) in (False_ind TMP_23 H2))))))))))) in (let TMP_69 \def
-(\lambda (c1: C).(\lambda (c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda
-(H2: (((eq C c1 (CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3
-(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (k:
-K).(\lambda (u: T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Flat f)
-v))).(let TMP_25 \def (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1
-| (CHead c _ _) \Rightarrow c])) in (let TMP_26 \def (CHead c1 k u) in (let
-TMP_27 \def (Flat f) in (let TMP_28 \def (CHead e1 TMP_27 v) in (let H4 \def
-(f_equal C C TMP_25 TMP_26 TMP_28 H3) in (let TMP_29 \def (\lambda (e:
-C).(match e with [(CSort _) \Rightarrow k | (CHead _ k0 _) \Rightarrow k0]))
-in (let TMP_30 \def (CHead c1 k u) in (let TMP_31 \def (Flat f) in (let
-TMP_32 \def (CHead e1 TMP_31 v) in (let H5 \def (f_equal C K TMP_29 TMP_30
-TMP_32 H3) in (let TMP_33 \def (\lambda (e: C).(match e with [(CSort _)
-\Rightarrow u | (CHead _ _ t) \Rightarrow t])) in (let TMP_34 \def (CHead c1
-k u) in (let TMP_35 \def (Flat f) in (let TMP_36 \def (CHead e1 TMP_35 v) in
-(let H6 \def (f_equal C T TMP_33 TMP_34 TMP_36 H3) in (let TMP_67 \def
-(\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1 e1)).(let TMP_42 \def
-(\lambda (t: T).(let TMP_40 \def (\lambda (e2: C).(let TMP_37 \def (CHead c3
-k t) in (let TMP_38 \def (Flat f) in (let TMP_39 \def (CHead e2 TMP_38 v) in
-(eq C TMP_37 TMP_39))))) in (let TMP_41 \def (\lambda (e2: C).(csubt g e1
-e2)) in (ex2 C TMP_40 TMP_41)))) in (let TMP_43 \def (Flat f) in (let TMP_49
-\def (\lambda (k0: K).(let TMP_47 \def (\lambda (e2: C).(let TMP_44 \def
-(CHead c3 k0 v) in (let TMP_45 \def (Flat f) in (let TMP_46 \def (CHead e2
-TMP_45 v) in (eq C TMP_44 TMP_46))))) in (let TMP_48 \def (\lambda (e2:
-C).(csubt g e1 e2)) in (ex2 C TMP_47 TMP_48)))) in (let TMP_54 \def (\lambda
-(c: C).((eq C c (CHead e1 (Flat f) v)) \to (let TMP_52 \def (\lambda (e2:
-C).(let TMP_50 \def (Flat f) in (let TMP_51 \def (CHead e2 TMP_50 v) in (eq C
-c3 TMP_51)))) in (let TMP_53 \def (\lambda (e2: C).(csubt g e1 e2)) in (ex2 C
-TMP_52 TMP_53))))) in (let H9 \def (eq_ind C c1 TMP_54 H2 e1 H8) in (let
-TMP_55 \def (\lambda (c: C).(csubt g c c3)) in (let H10 \def (eq_ind C c1
-TMP_55 H1 e1 H8) in (let TMP_60 \def (\lambda (e2: C).(let TMP_56 \def (Flat
-f) in (let TMP_57 \def (CHead c3 TMP_56 v) in (let TMP_58 \def (Flat f) in
-(let TMP_59 \def (CHead e2 TMP_58 v) in (eq C TMP_57 TMP_59)))))) in (let
-TMP_61 \def (\lambda (e2: C).(csubt g e1 e2)) in (let TMP_62 \def (Flat f) in
-(let TMP_63 \def (CHead c3 TMP_62 v) in (let TMP_64 \def (refl_equal C
-TMP_63) in (let TMP_65 \def (ex_intro2 C TMP_60 TMP_61 c3 TMP_64 H10) in (let
-TMP_66 \def (eq_ind_r K TMP_43 TMP_49 TMP_65 k H7) in (eq_ind_r T v TMP_42
-TMP_66 u H6))))))))))))))))) in (let TMP_68 \def (TMP_67 H5) in (TMP_68
-H4))))))))))))))))))))))))) in (let TMP_82 \def (\lambda (c1: C).(\lambda
-(c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1 (CHead e1 (Flat
-f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda
-(e2: C).(csubt g e1 e2)))))).(\lambda (b: B).(\lambda (_: (not (eq B b
-Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C (CHead c1 (Bind
-Void) u1) (CHead e1 (Flat f) v))).(let TMP_70 \def (Bind Void) in (let TMP_71
-\def (CHead c1 TMP_70 u1) in (let TMP_72 \def (\lambda (ee: C).(match ee with
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind
-_) \Rightarrow True | (Flat _) \Rightarrow False])])) in (let TMP_73 \def
-(Flat f) in (let TMP_74 \def (CHead e1 TMP_73 v) in (let H5 \def (eq_ind C
-TMP_71 TMP_72 I TMP_74 H4) in (let TMP_79 \def (\lambda (e2: C).(let TMP_75
-\def (Bind b) in (let TMP_76 \def (CHead c3 TMP_75 u2) in (let TMP_77 \def
-(Flat f) in (let TMP_78 \def (CHead e2 TMP_77 v) in (eq C TMP_76 TMP_78))))))
-in (let TMP_80 \def (\lambda (e2: C).(csubt g e1 e2)) in (let TMP_81 \def
-(ex2 C TMP_79 TMP_80) in (False_ind TMP_81 H5))))))))))))))))))) in (let
-TMP_95 \def (\lambda (c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1
-c3)).(\lambda (_: (((eq C c1 (CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2:
-C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1
-e2)))))).(\lambda (u: T).(\lambda (t: T).(\lambda (_: (ty3 g c1 u
-t)).(\lambda (_: (ty3 g c3 u t)).(\lambda (H5: (eq C (CHead c1 (Bind Abst) t)
-(CHead e1 (Flat f) v))).(let TMP_83 \def (Bind Abst) in (let TMP_84 \def
-(CHead c1 TMP_83 t) in (let TMP_85 \def (\lambda (ee: C).(match ee with
-[(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind
-_) \Rightarrow True | (Flat _) \Rightarrow False])])) in (let TMP_86 \def
-(Flat f) in (let TMP_87 \def (CHead e1 TMP_86 v) in (let H6 \def (eq_ind C
-TMP_84 TMP_85 I TMP_87 H5) in (let TMP_92 \def (\lambda (e2: C).(let TMP_88
-\def (Bind Abbr) in (let TMP_89 \def (CHead c3 TMP_88 u) in (let TMP_90 \def
-(Flat f) in (let TMP_91 \def (CHead e2 TMP_90 v) in (eq C TMP_89 TMP_91))))))
-in (let TMP_93 \def (\lambda (e2: C).(csubt g e1 e2)) in (let TMP_94 \def
-(ex2 C TMP_92 TMP_93) in (False_ind TMP_94 H6))))))))))))))))))) in
-(csubt_ind g TMP_13 TMP_24 TMP_69 TMP_82 TMP_95 y c2 H0)))))))) in (insert_eq
-C TMP_2 TMP_3 TMP_8 TMP_96 H))))))))))).
+(f: F).(\lambda (H: (csubt g (CHead e1 (Flat f) v) c2)).(insert_eq C (CHead
+e1 (Flat f) v) (\lambda (c: C).(csubt g c c2)) (\lambda (_: C).(ex2 C
+(\lambda (e2: C).(eq C c2 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g
+e1 e2)))) (\lambda (y: C).(\lambda (H0: (csubt g y c2)).(csubt_ind g (\lambda
+(c: C).(\lambda (c0: C).((eq C c (CHead e1 (Flat f) v)) \to (ex2 C (\lambda
+(e2: C).(eq C c0 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1
+e2)))))) (\lambda (n: nat).(\lambda (H1: (eq C (CSort n) (CHead e1 (Flat f)
+v))).(let H2 \def (eq_ind C (CSort n) (\lambda (ee: C).(match ee with [(CSort
+_) \Rightarrow True | (CHead _ _ _) \Rightarrow False])) I (CHead e1 (Flat f)
+v) H1) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CSort n) (CHead e2 (Flat
+f) v))) (\lambda (e2: C).(csubt g e1 e2))) H2)))) (\lambda (c1: C).(\lambda
+(c3: C).(\lambda (H1: (csubt g c1 c3)).(\lambda (H2: (((eq C c1 (CHead e1
+(Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v)))
+(\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (k: K).(\lambda (u:
+T).(\lambda (H3: (eq C (CHead c1 k u) (CHead e1 (Flat f) v))).(let H4 \def
+(f_equal C C (\lambda (e: C).(match e with [(CSort _) \Rightarrow c1 | (CHead
+c _ _) \Rightarrow c])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in ((let H5
+\def (f_equal C K (\lambda (e: C).(match e with [(CSort _) \Rightarrow k |
+(CHead _ k0 _) \Rightarrow k0])) (CHead c1 k u) (CHead e1 (Flat f) v) H3) in
+((let H6 \def (f_equal C T (\lambda (e: C).(match e with [(CSort _)
+\Rightarrow u | (CHead _ _ t) \Rightarrow t])) (CHead c1 k u) (CHead e1 (Flat
+f) v) H3) in (\lambda (H7: (eq K k (Flat f))).(\lambda (H8: (eq C c1
+e1)).(eq_ind_r T v (\lambda (t: T).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k
+t) (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))) (eq_ind_r K
+(Flat f) (\lambda (k0: K).(ex2 C (\lambda (e2: C).(eq C (CHead c3 k0 v)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))) (let H9 \def
+(eq_ind C c1 (\lambda (c: C).((eq C c (CHead e1 (Flat f) v)) \to (ex2 C
+(\lambda (e2: C).(eq C c3 (CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g
+e1 e2))))) H2 e1 H8) in (let H10 \def (eq_ind C c1 (\lambda (c: C).(csubt g c
+c3)) H1 e1 H8) in (ex_intro2 C (\lambda (e2: C).(eq C (CHead c3 (Flat f) v)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)) c3 (refl_equal C
+(CHead c3 (Flat f) v)) H10))) k H7) u H6)))) H5)) H4))))))))) (\lambda (c1:
+C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C c1
+(CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2 (Flat
+f) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (b: B).(\lambda (_:
+(not (eq B b Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (H4: (eq C
+(CHead c1 (Bind Void) u1) (CHead e1 (Flat f) v))).(let H5 \def (eq_ind C
+(CHead c1 (Bind Void) u1) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e1 (Flat f) v)
+H4) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind b) u2) (CHead
+e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))) H5))))))))))) (\lambda
+(c1: C).(\lambda (c3: C).(\lambda (_: (csubt g c1 c3)).(\lambda (_: (((eq C
+c1 (CHead e1 (Flat f) v)) \to (ex2 C (\lambda (e2: C).(eq C c3 (CHead e2
+(Flat f) v))) (\lambda (e2: C).(csubt g e1 e2)))))).(\lambda (u: T).(\lambda
+(t: T).(\lambda (_: (ty3 g c1 u t)).(\lambda (_: (ty3 g c3 u t)).(\lambda
+(H5: (eq C (CHead c1 (Bind Abst) t) (CHead e1 (Flat f) v))).(let H6 \def
+(eq_ind C (CHead c1 (Bind Abst) t) (\lambda (ee: C).(match ee with [(CSort _)
+\Rightarrow False | (CHead _ k _) \Rightarrow (match k with [(Bind _)
+\Rightarrow True | (Flat _) \Rightarrow False])])) I (CHead e1 (Flat f) v)
+H5) in (False_ind (ex2 C (\lambda (e2: C).(eq C (CHead c3 (Bind Abbr) u)
+(CHead e2 (Flat f) v))) (\lambda (e2: C).(csubt g e1 e2))) H6))))))))))) y c2
+H0))) H)))))).