legacy_1, ground_1, and basic_1 recommitted without anticipation

[helm.git] / matita / matita / contribs / lambdadelta / basic_1 / csuba / clear.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_1/csuba/clear.ma b/matita/matita/contribs/lambdadelta/basic_1/csuba/clear.ma
index af8360519728d47317da499a3d00b38420c6ed9b..39936f41f951b08e0f289ba6bf7e90508978f9e3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_1/csuba/clear.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/csuba/clear.ma
@@ -24,84 +24,50 @@ theorem csuba_clear_conf:
 (\lambda (e2: C).(clear c2 e2))))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csuba g c1 
-c2)).(let TMP_3 \def (\lambda (c: C).(\lambda (c0: C).(\forall (e1: 
-C).((clear c e1) \to (let TMP_1 \def (\lambda (e2: C).(csuba g e1 e2)) in 
-(let TMP_2 \def (\lambda (e2: C).(clear c0 e2)) in (ex2 C TMP_1 TMP_2))))))) 
-in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear 
-(CSort n) e1)).(let TMP_4 \def (\lambda (e2: C).(csuba g e1 e2)) in (let 
-TMP_6 \def (\lambda (e2: C).(let TMP_5 \def (CSort n) in (clear TMP_5 e2))) 
-in (let TMP_7 \def (ex2 C TMP_4 TMP_6) in (clear_gen_sort e1 n H0 
-TMP_7))))))) in (let TMP_49 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda 
-(H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c3 e1) \to (ex2 
-C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4 
+c2)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).(\forall (e1: C).((clear c 
+e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c0 
+e2))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear (CSort n) 
+e1)).(clear_gen_sort e1 n H0 (ex2 C (\lambda (e2: C).(csuba g e1 e2)) 
+(\lambda (e2: C).(clear (CSort n) e2))))))) (\lambda (c3: C).(\lambda (c4: 
+C).(\lambda (H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c3 
+e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4 
 e2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (e1: C).(\lambda (H2: 
-(clear (CHead c3 k u) e1)).(let TMP_12 \def (\lambda (k0: K).((clear (CHead 
-c3 k0 u) e1) \to (let TMP_9 \def (\lambda (e2: C).(csuba g e1 e2)) in (let 
-TMP_11 \def (\lambda (e2: C).(let TMP_10 \def (CHead c4 k0 u) in (clear 
-TMP_10 e2))) in (ex2 C TMP_9 TMP_11))))) in (let TMP_33 \def (\lambda (b: 
-B).(\lambda (H3: (clear (CHead c3 (Bind b) u) e1)).(let TMP_13 \def (Bind b) 
-in (let TMP_14 \def (CHead c3 TMP_13 u) in (let TMP_19 \def (\lambda (c: 
-C).(let TMP_15 \def (\lambda (e2: C).(csuba g c e2)) in (let TMP_18 \def 
-(\lambda (e2: C).(let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead c4 
-TMP_16 u) in (clear TMP_17 e2)))) in (ex2 C TMP_15 TMP_18)))) in (let TMP_22 
-\def (\lambda (e2: C).(let TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c3 
-TMP_20 u) in (csuba g TMP_21 e2)))) in (let TMP_25 \def (\lambda (e2: C).(let 
-TMP_23 \def (Bind b) in (let TMP_24 \def (CHead c4 TMP_23 u) in (clear TMP_24 
-e2)))) in (let TMP_26 \def (Bind b) in (let TMP_27 \def (CHead c4 TMP_26 u) 
-in (let TMP_28 \def (Bind b) in (let TMP_29 \def (csuba_head g c3 c4 H0 
-TMP_28 u) in (let TMP_30 \def (clear_bind b c4 u) in (let TMP_31 \def 
-(ex_intro2 C TMP_22 TMP_25 TMP_27 TMP_29 TMP_30) in (let TMP_32 \def 
-(clear_gen_bind b c3 e1 u H3) in (eq_ind_r C TMP_14 TMP_19 TMP_31 e1 
-TMP_32))))))))))))))) in (let TMP_48 \def (\lambda (f: F).(\lambda (H3: 
-(clear (CHead c3 (Flat f) u) e1)).(let TMP_34 \def (clear_gen_flat f c3 e1 u 
-H3) in (let H4 \def (H1 e1 TMP_34) in (let TMP_35 \def (\lambda (e2: 
-C).(csuba g e1 e2)) in (let TMP_36 \def (\lambda (e2: C).(clear c4 e2)) in 
-(let TMP_37 \def (\lambda (e2: C).(csuba g e1 e2)) in (let TMP_40 \def 
-(\lambda (e2: C).(let TMP_38 \def (Flat f) in (let TMP_39 \def (CHead c4 
-TMP_38 u) in (clear TMP_39 e2)))) in (let TMP_41 \def (ex2 C TMP_37 TMP_40) 
-in (let TMP_47 \def (\lambda (x: C).(\lambda (H5: (csuba g e1 x)).(\lambda 
-(H6: (clear c4 x)).(let TMP_42 \def (\lambda (e2: C).(csuba g e1 e2)) in (let 
-TMP_45 \def (\lambda (e2: C).(let TMP_43 \def (Flat f) in (let TMP_44 \def 
-(CHead c4 TMP_43 u) in (clear TMP_44 e2)))) in (let TMP_46 \def (clear_flat 
-c4 x H6 f u) in (ex_intro2 C TMP_42 TMP_45 x H5 TMP_46))))))) in (ex2_ind C 
-TMP_35 TMP_36 TMP_41 TMP_47 H4))))))))))) in (K_ind TMP_12 TMP_33 TMP_48 k 
-H2)))))))))))) in (let TMP_69 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda 
-(H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c3 e1) \to (ex2 
-C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear c4 
-e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1: 
-T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: (clear (CHead c3 (Bind 
-Void) u1) e1)).(let TMP_50 \def (Bind Void) in (let TMP_51 \def (CHead c3 
-TMP_50 u1) in (let TMP_56 \def (\lambda (c: C).(let TMP_52 \def (\lambda (e2: 
-C).(csuba g c e2)) in (let TMP_55 \def (\lambda (e2: C).(let TMP_53 \def 
-(Bind b) in (let TMP_54 \def (CHead c4 TMP_53 u2) in (clear TMP_54 e2)))) in 
-(ex2 C TMP_52 TMP_55)))) in (let TMP_59 \def (\lambda (e2: C).(let TMP_57 
-\def (Bind Void) in (let TMP_58 \def (CHead c3 TMP_57 u1) in (csuba g TMP_58 
-e2)))) in (let TMP_62 \def (\lambda (e2: C).(let TMP_60 \def (Bind b) in (let 
-TMP_61 \def (CHead c4 TMP_60 u2) in (clear TMP_61 e2)))) in (let TMP_63 \def 
-(Bind b) in (let TMP_64 \def (CHead c4 TMP_63 u2) in (let TMP_65 \def 
-(csuba_void g c3 c4 H0 b H2 u1 u2) in (let TMP_66 \def (clear_bind b c4 u2) 
-in (let TMP_67 \def (ex_intro2 C TMP_59 TMP_62 TMP_64 TMP_65 TMP_66) in (let 
-TMP_68 \def (clear_gen_bind Void c3 e1 u1 H3) in (eq_ind_r C TMP_51 TMP_56 
-TMP_67 e1 TMP_68)))))))))))))))))))))) in (let TMP_89 \def (\lambda (c3: 
+(clear (CHead c3 k u) e1)).(K_ind (\lambda (k0: K).((clear (CHead c3 k0 u) 
+e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear 
+(CHead c4 k0 u) e2))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c3 (Bind 
+b) u) e1)).(eq_ind_r C (CHead c3 (Bind b) u) (\lambda (c: C).(ex2 C (\lambda 
+(e2: C).(csuba g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) u) e2)))) 
+(ex_intro2 C (\lambda (e2: C).(csuba g (CHead c3 (Bind b) u) e2)) (\lambda 
+(e2: C).(clear (CHead c4 (Bind b) u) e2)) (CHead c4 (Bind b) u) (csuba_head g 
+c3 c4 H0 (Bind b) u) (clear_bind b c4 u)) e1 (clear_gen_bind b c3 e1 u H3)))) 
+(\lambda (f: F).(\lambda (H3: (clear (CHead c3 (Flat f) u) e1)).(let H4 \def 
+(H1 e1 (clear_gen_flat f c3 e1 u H3)) in (ex2_ind C (\lambda (e2: C).(csuba g 
+e1 e2)) (\lambda (e2: C).(clear c4 e2)) (ex2 C (\lambda (e2: C).(csuba g e1 
+e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f) u) e2))) (\lambda (x: 
+C).(\lambda (H5: (csuba g e1 x)).(\lambda (H6: (clear c4 x)).(ex_intro2 C 
+(\lambda (e2: C).(csuba g e1 e2)) (\lambda (e2: C).(clear (CHead c4 (Flat f) 
+u) e2)) x H5 (clear_flat c4 x H6 f u))))) H4)))) k H2))))))))) (\lambda (c3: 
 C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall 
 (e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) (\lambda 
-(e2: C).(clear c4 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H2: 
-(arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u 
-a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c3 (Bind Abst) t) e1)).(let 
-TMP_70 \def (Bind Abst) in (let TMP_71 \def (CHead c3 TMP_70 t) in (let 
-TMP_76 \def (\lambda (c: C).(let TMP_72 \def (\lambda (e2: C).(csuba g c e2)) 
-in (let TMP_75 \def (\lambda (e2: C).(let TMP_73 \def (Bind Abbr) in (let 
-TMP_74 \def (CHead c4 TMP_73 u) in (clear TMP_74 e2)))) in (ex2 C TMP_72 
-TMP_75)))) in (let TMP_79 \def (\lambda (e2: C).(let TMP_77 \def (Bind Abst) 
-in (let TMP_78 \def (CHead c3 TMP_77 t) in (csuba g TMP_78 e2)))) in (let 
-TMP_82 \def (\lambda (e2: C).(let TMP_80 \def (Bind Abbr) in (let TMP_81 \def 
-(CHead c4 TMP_80 u) in (clear TMP_81 e2)))) in (let TMP_83 \def (Bind Abbr) 
-in (let TMP_84 \def (CHead c4 TMP_83 u) in (let TMP_85 \def (csuba_abst g c3 
-c4 H0 t a H2 u H3) in (let TMP_86 \def (clear_bind Abbr c4 u) in (let TMP_87 
-\def (ex_intro2 C TMP_79 TMP_82 TMP_84 TMP_85 TMP_86) in (let TMP_88 \def 
-(clear_gen_bind Abst c3 e1 t H4) in (eq_ind_r C TMP_71 TMP_76 TMP_87 e1 
-TMP_88))))))))))))))))))))))) in (csuba_ind g TMP_3 TMP_8 TMP_49 TMP_69 
-TMP_89 c1 c2 H))))))))).
+(e2: C).(clear c4 e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b 
+Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: 
+(clear (CHead c3 (Bind Void) u1) e1)).(eq_ind_r C (CHead c3 (Bind Void) u1) 
+(\lambda (c: C).(ex2 C (\lambda (e2: C).(csuba g c e2)) (\lambda (e2: 
+C).(clear (CHead c4 (Bind b) u2) e2)))) (ex_intro2 C (\lambda (e2: C).(csuba 
+g (CHead c3 (Bind Void) u1) e2)) (\lambda (e2: C).(clear (CHead c4 (Bind b) 
+u2) e2)) (CHead c4 (Bind b) u2) (csuba_void g c3 c4 H0 b H2 u1 u2) 
+(clear_bind b c4 u2)) e1 (clear_gen_bind Void c3 e1 u1 H3)))))))))))) 
+(\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: 
+((\forall (e1: C).((clear c3 e1) \to (ex2 C (\lambda (e2: C).(csuba g e1 e2)) 
+(\lambda (e2: C).(clear c4 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda 
+(H2: (arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u 
+a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c3 (Bind Abst) t) 
+e1)).(eq_ind_r C (CHead c3 (Bind Abst) t) (\lambda (c: C).(ex2 C (\lambda 
+(e2: C).(csuba g c e2)) (\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u) 
+e2)))) (ex_intro2 C (\lambda (e2: C).(csuba g (CHead c3 (Bind Abst) t) e2)) 
+(\lambda (e2: C).(clear (CHead c4 (Bind Abbr) u) e2)) (CHead c4 (Bind Abbr) 
+u) (csuba_abst g c3 c4 H0 t a H2 u H3) (clear_bind Abbr c4 u)) e1 
+(clear_gen_bind Abst c3 e1 t H4))))))))))))) c1 c2 H)))).
 
 theorem csuba_clear_trans:
  \forall (g: G).(\forall (c1: C).(\forall (c2: C).((csuba g c2 c1) \to 
@@ -109,82 +75,48 @@ theorem csuba_clear_trans:
 (\lambda (e2: C).(clear c2 e2))))))))
 \def
  \lambda (g: G).(\lambda (c1: C).(\lambda (c2: C).(\lambda (H: (csuba g c2 
-c1)).(let TMP_3 \def (\lambda (c: C).(\lambda (c0: C).(\forall (e1: 
-C).((clear c0 e1) \to (let TMP_1 \def (\lambda (e2: C).(csuba g e2 e1)) in 
-(let TMP_2 \def (\lambda (e2: C).(clear c e2)) in (ex2 C TMP_1 TMP_2))))))) 
-in (let TMP_8 \def (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear 
-(CSort n) e1)).(let TMP_4 \def (\lambda (e2: C).(csuba g e2 e1)) in (let 
-TMP_6 \def (\lambda (e2: C).(let TMP_5 \def (CSort n) in (clear TMP_5 e2))) 
-in (let TMP_7 \def (ex2 C TMP_4 TMP_6) in (clear_gen_sort e1 n H0 
-TMP_7))))))) in (let TMP_49 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda 
-(H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c4 e1) \to (ex2 
-C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3 
+c1)).(csuba_ind g (\lambda (c: C).(\lambda (c0: C).(\forall (e1: C).((clear 
+c0 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c 
+e2))))))) (\lambda (n: nat).(\lambda (e1: C).(\lambda (H0: (clear (CSort n) 
+e1)).(clear_gen_sort e1 n H0 (ex2 C (\lambda (e2: C).(csuba g e2 e1)) 
+(\lambda (e2: C).(clear (CSort n) e2))))))) (\lambda (c3: C).(\lambda (c4: 
+C).(\lambda (H0: (csuba g c3 c4)).(\lambda (H1: ((\forall (e1: C).((clear c4 
+e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3 
 e2))))))).(\lambda (k: K).(\lambda (u: T).(\lambda (e1: C).(\lambda (H2: 
-(clear (CHead c4 k u) e1)).(let TMP_12 \def (\lambda (k0: K).((clear (CHead 
-c4 k0 u) e1) \to (let TMP_9 \def (\lambda (e2: C).(csuba g e2 e1)) in (let 
-TMP_11 \def (\lambda (e2: C).(let TMP_10 \def (CHead c3 k0 u) in (clear 
-TMP_10 e2))) in (ex2 C TMP_9 TMP_11))))) in (let TMP_33 \def (\lambda (b: 
-B).(\lambda (H3: (clear (CHead c4 (Bind b) u) e1)).(let TMP_13 \def (Bind b) 
-in (let TMP_14 \def (CHead c4 TMP_13 u) in (let TMP_19 \def (\lambda (c: 
-C).(let TMP_15 \def (\lambda (e2: C).(csuba g e2 c)) in (let TMP_18 \def 
-(\lambda (e2: C).(let TMP_16 \def (Bind b) in (let TMP_17 \def (CHead c3 
-TMP_16 u) in (clear TMP_17 e2)))) in (ex2 C TMP_15 TMP_18)))) in (let TMP_22 
-\def (\lambda (e2: C).(let TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c4 
-TMP_20 u) in (csuba g e2 TMP_21)))) in (let TMP_25 \def (\lambda (e2: C).(let 
-TMP_23 \def (Bind b) in (let TMP_24 \def (CHead c3 TMP_23 u) in (clear TMP_24 
-e2)))) in (let TMP_26 \def (Bind b) in (let TMP_27 \def (CHead c3 TMP_26 u) 
-in (let TMP_28 \def (Bind b) in (let TMP_29 \def (csuba_head g c3 c4 H0 
-TMP_28 u) in (let TMP_30 \def (clear_bind b c3 u) in (let TMP_31 \def 
-(ex_intro2 C TMP_22 TMP_25 TMP_27 TMP_29 TMP_30) in (let TMP_32 \def 
-(clear_gen_bind b c4 e1 u H3) in (eq_ind_r C TMP_14 TMP_19 TMP_31 e1 
-TMP_32))))))))))))))) in (let TMP_48 \def (\lambda (f: F).(\lambda (H3: 
-(clear (CHead c4 (Flat f) u) e1)).(let TMP_34 \def (clear_gen_flat f c4 e1 u 
-H3) in (let H4 \def (H1 e1 TMP_34) in (let TMP_35 \def (\lambda (e2: 
-C).(csuba g e2 e1)) in (let TMP_36 \def (\lambda (e2: C).(clear c3 e2)) in 
-(let TMP_37 \def (\lambda (e2: C).(csuba g e2 e1)) in (let TMP_40 \def 
-(\lambda (e2: C).(let TMP_38 \def (Flat f) in (let TMP_39 \def (CHead c3 
-TMP_38 u) in (clear TMP_39 e2)))) in (let TMP_41 \def (ex2 C TMP_37 TMP_40) 
-in (let TMP_47 \def (\lambda (x: C).(\lambda (H5: (csuba g x e1)).(\lambda 
-(H6: (clear c3 x)).(let TMP_42 \def (\lambda (e2: C).(csuba g e2 e1)) in (let 
-TMP_45 \def (\lambda (e2: C).(let TMP_43 \def (Flat f) in (let TMP_44 \def 
-(CHead c3 TMP_43 u) in (clear TMP_44 e2)))) in (let TMP_46 \def (clear_flat 
-c3 x H6 f u) in (ex_intro2 C TMP_42 TMP_45 x H5 TMP_46))))))) in (ex2_ind C 
-TMP_35 TMP_36 TMP_41 TMP_47 H4))))))))))) in (K_ind TMP_12 TMP_33 TMP_48 k 
-H2)))))))))))) in (let TMP_69 \def (\lambda (c3: C).(\lambda (c4: C).(\lambda 
-(H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear c4 e1) \to (ex2 
-C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear c3 
-e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b Void))).(\lambda (u1: 
-T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: (clear (CHead c4 (Bind b) 
-u2) e1)).(let TMP_50 \def (Bind b) in (let TMP_51 \def (CHead c4 TMP_50 u2) 
-in (let TMP_56 \def (\lambda (c: C).(let TMP_52 \def (\lambda (e2: C).(csuba 
-g e2 c)) in (let TMP_55 \def (\lambda (e2: C).(let TMP_53 \def (Bind Void) in 
-(let TMP_54 \def (CHead c3 TMP_53 u1) in (clear TMP_54 e2)))) in (ex2 C 
-TMP_52 TMP_55)))) in (let TMP_59 \def (\lambda (e2: C).(let TMP_57 \def (Bind 
-b) in (let TMP_58 \def (CHead c4 TMP_57 u2) in (csuba g e2 TMP_58)))) in (let 
-TMP_62 \def (\lambda (e2: C).(let TMP_60 \def (Bind Void) in (let TMP_61 \def 
-(CHead c3 TMP_60 u1) in (clear TMP_61 e2)))) in (let TMP_63 \def (Bind Void) 
-in (let TMP_64 \def (CHead c3 TMP_63 u1) in (let TMP_65 \def (csuba_void g c3 
-c4 H0 b H2 u1 u2) in (let TMP_66 \def (clear_bind Void c3 u1) in (let TMP_67 
-\def (ex_intro2 C TMP_59 TMP_62 TMP_64 TMP_65 TMP_66) in (let TMP_68 \def 
-(clear_gen_bind b c4 e1 u2 H3) in (eq_ind_r C TMP_51 TMP_56 TMP_67 e1 
-TMP_68)))))))))))))))))))))) in (let TMP_89 \def (\lambda (c3: C).(\lambda 
-(c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall (e1: C).((clear 
-c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear 
-c3 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda (H2: (arity g c3 t 
-(asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u a)).(\lambda (e1: 
-C).(\lambda (H4: (clear (CHead c4 (Bind Abbr) u) e1)).(let TMP_70 \def (Bind 
-Abbr) in (let TMP_71 \def (CHead c4 TMP_70 u) in (let TMP_76 \def (\lambda 
-(c: C).(let TMP_72 \def (\lambda (e2: C).(csuba g e2 c)) in (let TMP_75 \def 
-(\lambda (e2: C).(let TMP_73 \def (Bind Abst) in (let TMP_74 \def (CHead c3 
-TMP_73 t) in (clear TMP_74 e2)))) in (ex2 C TMP_72 TMP_75)))) in (let TMP_79 
-\def (\lambda (e2: C).(let TMP_77 \def (Bind Abbr) in (let TMP_78 \def (CHead 
-c4 TMP_77 u) in (csuba g e2 TMP_78)))) in (let TMP_82 \def (\lambda (e2: 
-C).(let TMP_80 \def (Bind Abst) in (let TMP_81 \def (CHead c3 TMP_80 t) in 
-(clear TMP_81 e2)))) in (let TMP_83 \def (Bind Abst) in (let TMP_84 \def 
-(CHead c3 TMP_83 t) in (let TMP_85 \def (csuba_abst g c3 c4 H0 t a H2 u H3) 
-in (let TMP_86 \def (clear_bind Abst c3 t) in (let TMP_87 \def (ex_intro2 C 
-TMP_79 TMP_82 TMP_84 TMP_85 TMP_86) in (let TMP_88 \def (clear_gen_bind Abbr 
-c4 e1 u H4) in (eq_ind_r C TMP_71 TMP_76 TMP_87 e1 
-TMP_88))))))))))))))))))))))) in (csuba_ind g TMP_3 TMP_8 TMP_49 TMP_69 
-TMP_89 c2 c1 H))))))))).
+(clear (CHead c4 k u) e1)).(K_ind (\lambda (k0: K).((clear (CHead c4 k0 u) 
+e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear 
+(CHead c3 k0 u) e2))))) (\lambda (b: B).(\lambda (H3: (clear (CHead c4 (Bind 
+b) u) e1)).(eq_ind_r C (CHead c4 (Bind b) u) (\lambda (c: C).(ex2 C (\lambda 
+(e2: C).(csuba g e2 c)) (\lambda (e2: C).(clear (CHead c3 (Bind b) u) e2)))) 
+(ex_intro2 C (\lambda (e2: C).(csuba g e2 (CHead c4 (Bind b) u))) (\lambda 
+(e2: C).(clear (CHead c3 (Bind b) u) e2)) (CHead c3 (Bind b) u) (csuba_head g 
+c3 c4 H0 (Bind b) u) (clear_bind b c3 u)) e1 (clear_gen_bind b c4 e1 u H3)))) 
+(\lambda (f: F).(\lambda (H3: (clear (CHead c4 (Flat f) u) e1)).(let H4 \def 
+(H1 e1 (clear_gen_flat f c4 e1 u H3)) in (ex2_ind C (\lambda (e2: C).(csuba g 
+e2 e1)) (\lambda (e2: C).(clear c3 e2)) (ex2 C (\lambda (e2: C).(csuba g e2 
+e1)) (\lambda (e2: C).(clear (CHead c3 (Flat f) u) e2))) (\lambda (x: 
+C).(\lambda (H5: (csuba g x e1)).(\lambda (H6: (clear c3 x)).(ex_intro2 C 
+(\lambda (e2: C).(csuba g e2 e1)) (\lambda (e2: C).(clear (CHead c3 (Flat f) 
+u) e2)) x H5 (clear_flat c3 x H6 f u))))) H4)))) k H2))))))))) (\lambda (c3: 
+C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: ((\forall 
+(e1: C).((clear c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) (\lambda 
+(e2: C).(clear c3 e2))))))).(\lambda (b: B).(\lambda (H2: (not (eq B b 
+Void))).(\lambda (u1: T).(\lambda (u2: T).(\lambda (e1: C).(\lambda (H3: 
+(clear (CHead c4 (Bind b) u2) e1)).(eq_ind_r C (CHead c4 (Bind b) u2) 
+(\lambda (c: C).(ex2 C (\lambda (e2: C).(csuba g e2 c)) (\lambda (e2: 
+C).(clear (CHead c3 (Bind Void) u1) e2)))) (ex_intro2 C (\lambda (e2: 
+C).(csuba g e2 (CHead c4 (Bind b) u2))) (\lambda (e2: C).(clear (CHead c3 
+(Bind Void) u1) e2)) (CHead c3 (Bind Void) u1) (csuba_void g c3 c4 H0 b H2 u1 
+u2) (clear_bind Void c3 u1)) e1 (clear_gen_bind b c4 e1 u2 H3)))))))))))) 
+(\lambda (c3: C).(\lambda (c4: C).(\lambda (H0: (csuba g c3 c4)).(\lambda (_: 
+((\forall (e1: C).((clear c4 e1) \to (ex2 C (\lambda (e2: C).(csuba g e2 e1)) 
+(\lambda (e2: C).(clear c3 e2))))))).(\lambda (t: T).(\lambda (a: A).(\lambda 
+(H2: (arity g c3 t (asucc g a))).(\lambda (u: T).(\lambda (H3: (arity g c4 u 
+a)).(\lambda (e1: C).(\lambda (H4: (clear (CHead c4 (Bind Abbr) u) 
+e1)).(eq_ind_r C (CHead c4 (Bind Abbr) u) (\lambda (c: C).(ex2 C (\lambda 
+(e2: C).(csuba g e2 c)) (\lambda (e2: C).(clear (CHead c3 (Bind Abst) t) 
+e2)))) (ex_intro2 C (\lambda (e2: C).(csuba g e2 (CHead c4 (Bind Abbr) u))) 
+(\lambda (e2: C).(clear (CHead c3 (Bind Abst) t) e2)) (CHead c3 (Bind Abst) 
+t) (csuba_abst g c3 c4 H0 t a H2 u H3) (clear_bind Abst c3 t)) e1 
+(clear_gen_bind Abbr c4 e1 u H4))))))))))))) c2 c1 H)))).