X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2FT%2Fdec.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_1%2FT%2Fdec.ma;h=e8e7ed885debc48cabb3ecdf08aabc3c85a64921;hb=9c954a9a843ebb1bf189536df4e14f77132ed1cf;hp=a088c40e3bb410629eb0c8e932c9aca9ecce0b8a;hpb=e51d01099c08e9945ea093da6fcac353db7ca23c;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_1/T/dec.ma b/matita/matita/contribs/lambdadelta/basic_1/T/dec.ma
index a088c40e3..e8e7ed885 100644
--- a/matita/matita/contribs/lambdadelta/basic_1/T/dec.ma
+++ b/matita/matita/contribs/lambdadelta/basic_1/T/dec.ma
@@ -14,433 +14,656 @@
 
 (* This file was automatically generated: do not edit *********************)
 
-include "Basic-1/T/defs.ma".
+include "basic_1/T/fwd.ma".
 
 theorem terms_props__bind_dec:
  \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) ((eq B b1 b2) \to (\forall 
 (P: Prop).P))))
 \def
- \lambda (b1: B).(B_ind (\lambda (b: B).(\forall (b2: B).(or (eq B b b2) ((eq 
-B b b2) \to (\forall (P: Prop).P))))) (\lambda (b2: B).(B_ind (\lambda (b: 
-B).(or (eq B Abbr b) ((eq B Abbr b) \to (\forall (P: Prop).P)))) (or_introl 
-(eq B Abbr Abbr) ((eq B Abbr Abbr) \to (\forall (P: Prop).P)) (refl_equal B 
-Abbr)) (or_intror (eq B Abbr Abst) ((eq B Abbr Abst) \to (\forall (P: 
-Prop).P)) (\lambda (H: (eq B Abbr Abst)).(\lambda (P: Prop).(let H0 \def 
-(eq_ind B Abbr (\lambda (ee: B).(match ee in B return (\lambda (_: B).Prop) 
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow 
-False])) I Abst H) in (False_ind P H0))))) (or_intror (eq B Abbr Void) ((eq B 
-Abbr Void) \to (\forall (P: Prop).P)) (\lambda (H: (eq B Abbr Void)).(\lambda 
-(P: Prop).(let H0 \def (eq_ind B Abbr (\lambda (ee: B).(match ee in B return 
-(\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False | 
-Void \Rightarrow False])) I Void H) in (False_ind P H0))))) b2)) (\lambda 
-(b2: B).(B_ind (\lambda (b: B).(or (eq B Abst b) ((eq B Abst b) \to (\forall 
-(P: Prop).P)))) (or_intror (eq B Abst Abbr) ((eq B Abst Abbr) \to (\forall 
-(P: Prop).P)) (\lambda (H: (eq B Abst Abbr)).(\lambda (P: Prop).(let H0 \def 
-(eq_ind B Abst (\lambda (ee: B).(match ee in B return (\lambda (_: B).Prop) 
-with [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow 
-False])) I Abbr H) in (False_ind P H0))))) (or_introl (eq B Abst Abst) ((eq B 
-Abst Abst) \to (\forall (P: Prop).P)) (refl_equal B Abst)) (or_intror (eq B 
-Abst Void) ((eq B Abst Void) \to (\forall (P: Prop).P)) (\lambda (H: (eq B 
-Abst Void)).(\lambda (P: Prop).(let H0 \def (eq_ind B Abst (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | 
-Abst \Rightarrow True | Void \Rightarrow False])) I Void H) in (False_ind P 
-H0))))) b2)) (\lambda (b2: B).(B_ind (\lambda (b: B).(or (eq B Void b) ((eq B 
-Void b) \to (\forall (P: Prop).P)))) (or_intror (eq B Void Abbr) ((eq B Void 
-Abbr) \to (\forall (P: Prop).P)) (\lambda (H: (eq B Void Abbr)).(\lambda (P: 
-Prop).(let H0 \def (eq_ind B Void (\lambda (ee: B).(match ee in B return 
-(\lambda (_: B).Prop) with [Abbr \Rightarrow False | Abst \Rightarrow False | 
-Void \Rightarrow True])) I Abbr H) in (False_ind P H0))))) (or_intror (eq B 
-Void Abst) ((eq B Void Abst) \to (\forall (P: Prop).P)) (\lambda (H: (eq B 
-Void Abst)).(\lambda (P: Prop).(let H0 \def (eq_ind B Void (\lambda (ee: 
-B).(match ee in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow False | 
-Abst \Rightarrow False | Void \Rightarrow True])) I Abst H) in (False_ind P 
-H0))))) (or_introl (eq B Void Void) ((eq B Void Void) \to (\forall (P: 
-Prop).P)) (refl_equal B Void)) b2)) b1).
-(* COMMENTS
-Initial nodes: 559
-END *)
+ \lambda (b1: B).(let TMP_61 \def (\lambda (b: B).(\forall (b2: B).(let 
+TMP_60 \def (eq B b b2) in (let TMP_59 \def ((eq B b b2) \to (\forall (P: 
+Prop).P)) in (or TMP_60 TMP_59))))) in (let TMP_58 \def (\lambda (b2: B).(let 
+TMP_57 \def (\lambda (b: B).(let TMP_56 \def (eq B Abbr b) in (let TMP_55 
+\def ((eq B Abbr b) \to (\forall (P: Prop).P)) in (or TMP_56 TMP_55)))) in 
+(let TMP_53 \def (eq B Abbr Abbr) in (let TMP_52 \def ((eq B Abbr Abbr) \to 
+(\forall (P: Prop).P)) in (let TMP_51 \def (refl_equal B Abbr) in (let TMP_54 
+\def (or_introl TMP_53 TMP_52 TMP_51) in (let TMP_49 \def (eq B Abbr Abst) in 
+(let TMP_48 \def ((eq B Abbr Abst) \to (\forall (P: Prop).P)) in (let TMP_47 
+\def (\lambda (H: (eq B Abbr Abst)).(\lambda (P: Prop).(let TMP_46 \def 
+(\lambda (ee: B).(match ee in B with [Abbr \Rightarrow True | Abst 
+\Rightarrow False | Void \Rightarrow False])) in (let H0 \def (eq_ind B Abbr 
+TMP_46 I Abst H) in (False_ind P H0))))) in (let TMP_50 \def (or_intror 
+TMP_49 TMP_48 TMP_47) in (let TMP_44 \def (eq B Abbr Void) in (let TMP_43 
+\def ((eq B Abbr Void) \to (\forall (P: Prop).P)) in (let TMP_42 \def 
+(\lambda (H: (eq B Abbr Void)).(\lambda (P: Prop).(let TMP_41 \def (\lambda 
+(ee: B).(match ee in B with [Abbr \Rightarrow True | Abst \Rightarrow False | 
+Void \Rightarrow False])) in (let H0 \def (eq_ind B Abbr TMP_41 I Void H) in 
+(False_ind P H0))))) in (let TMP_45 \def (or_intror TMP_44 TMP_43 TMP_42) in 
+(B_ind TMP_57 TMP_54 TMP_50 TMP_45 b2))))))))))))))) in (let TMP_40 \def 
+(\lambda (b2: B).(let TMP_39 \def (\lambda (b: B).(let TMP_38 \def (eq B Abst 
+b) in (let TMP_37 \def ((eq B Abst b) \to (\forall (P: Prop).P)) in (or 
+TMP_38 TMP_37)))) in (let TMP_35 \def (eq B Abst Abbr) in (let TMP_34 \def 
+((eq B Abst Abbr) \to (\forall (P: Prop).P)) in (let TMP_33 \def (\lambda (H: 
+(eq B Abst Abbr)).(\lambda (P: Prop).(let TMP_32 \def (\lambda (ee: B).(match 
+ee in B with [Abbr \Rightarrow False | Abst \Rightarrow True | Void 
+\Rightarrow False])) in (let H0 \def (eq_ind B Abst TMP_32 I Abbr H) in 
+(False_ind P H0))))) in (let TMP_36 \def (or_intror TMP_35 TMP_34 TMP_33) in 
+(let TMP_30 \def (eq B Abst Abst) in (let TMP_29 \def ((eq B Abst Abst) \to 
+(\forall (P: Prop).P)) in (let TMP_28 \def (refl_equal B Abst) in (let TMP_31 
+\def (or_introl TMP_30 TMP_29 TMP_28) in (let TMP_26 \def (eq B Abst Void) in 
+(let TMP_25 \def ((eq B Abst Void) \to (\forall (P: Prop).P)) in (let TMP_24 
+\def (\lambda (H: (eq B Abst Void)).(\lambda (P: Prop).(let TMP_23 \def 
+(\lambda (ee: B).(match ee in B with [Abbr \Rightarrow False | Abst 
+\Rightarrow True | Void \Rightarrow False])) in (let H0 \def (eq_ind B Abst 
+TMP_23 I Void H) in (False_ind P H0))))) in (let TMP_27 \def (or_intror 
+TMP_26 TMP_25 TMP_24) in (B_ind TMP_39 TMP_36 TMP_31 TMP_27 b2))))))))))))))) 
+in (let TMP_22 \def (\lambda (b2: B).(let TMP_21 \def (\lambda (b: B).(let 
+TMP_20 \def (eq B Void b) in (let TMP_19 \def ((eq B Void b) \to (\forall (P: 
+Prop).P)) in (or TMP_20 TMP_19)))) in (let TMP_17 \def (eq B Void Abbr) in 
+(let TMP_16 \def ((eq B Void Abbr) \to (\forall (P: Prop).P)) in (let TMP_15 
+\def (\lambda (H: (eq B Void Abbr)).(\lambda (P: Prop).(let TMP_14 \def 
+(\lambda (ee: B).(match ee in B with [Abbr \Rightarrow False | Abst 
+\Rightarrow False | Void \Rightarrow True])) in (let H0 \def (eq_ind B Void 
+TMP_14 I Abbr H) in (False_ind P H0))))) in (let TMP_18 \def (or_intror 
+TMP_17 TMP_16 TMP_15) in (let TMP_12 \def (eq B Void Abst) in (let TMP_11 
+\def ((eq B Void Abst) \to (\forall (P: Prop).P)) in (let TMP_10 \def 
+(\lambda (H: (eq B Void Abst)).(\lambda (P: Prop).(let TMP_9 \def (\lambda 
+(ee: B).(match ee in B with [Abbr \Rightarrow False | Abst \Rightarrow False 
+| Void \Rightarrow True])) in (let H0 \def (eq_ind B Void TMP_9 I Abst H) in 
+(False_ind P H0))))) in (let TMP_13 \def (or_intror TMP_12 TMP_11 TMP_10) in 
+(let TMP_7 \def (eq B Void Void) in (let TMP_6 \def ((eq B Void Void) \to 
+(\forall (P: Prop).P)) in (let TMP_5 \def (refl_equal B Void) in (let TMP_8 
+\def (or_introl TMP_7 TMP_6 TMP_5) in (B_ind TMP_21 TMP_18 TMP_13 TMP_8 
+b2))))))))))))))) in (B_ind TMP_61 TMP_58 TMP_40 TMP_22 b1))))).
 
 theorem bind_dec_not:
  \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) (not (eq B b1 b2))))
 \def
  \lambda (b1: B).(\lambda (b2: B).(let H_x \def (terms_props__bind_dec b1 b2) 
-in (let H \def H_x in (or_ind (eq B b1 b2) ((eq B b1 b2) \to (\forall (P: 
-Prop).P)) (or (eq B b1 b2) ((eq B b1 b2) \to False)) (\lambda (H0: (eq B b1 
-b2)).(or_introl (eq B b1 b2) ((eq B b1 b2) \to False) H0)) (\lambda (H0: 
-(((eq B b1 b2) \to (\forall (P: Prop).P)))).(or_intror (eq B b1 b2) ((eq B b1 
-b2) \to False) (\lambda (H1: (eq B b1 b2)).(H0 H1 False)))) H)))).
-(* COMMENTS
-Initial nodes: 131
-END *)
+in (let H \def H_x in (let TMP_73 \def (eq B b1 b2) in (let TMP_72 \def ((eq 
+B b1 b2) \to (\forall (P: Prop).P)) in (let TMP_70 \def (eq B b1 b2) in (let 
+TMP_69 \def ((eq B b1 b2) \to False) in (let TMP_71 \def (or TMP_70 TMP_69) 
+in (let TMP_68 \def (\lambda (H0: (eq B b1 b2)).(let TMP_67 \def (eq B b1 b2) 
+in (let TMP_66 \def ((eq B b1 b2) \to False) in (or_introl TMP_67 TMP_66 
+H0)))) in (let TMP_65 \def (\lambda (H0: (((eq B b1 b2) \to (\forall (P: 
+Prop).P)))).(let TMP_64 \def (eq B b1 b2) in (let TMP_63 \def ((eq B b1 b2) 
+\to False) in (let TMP_62 \def (\lambda (H1: (eq B b1 b2)).(H0 H1 False)) in 
+(or_intror TMP_64 TMP_63 TMP_62))))) in (or_ind TMP_73 TMP_72 TMP_71 TMP_68 
+TMP_65 H))))))))))).
 
 theorem terms_props__flat_dec:
  \forall (f1: F).(\forall (f2: F).(or (eq F f1 f2) ((eq F f1 f2) \to (\forall 
 (P: Prop).P))))
 \def
- \lambda (f1: F).(F_ind (\lambda (f: F).(\forall (f2: F).(or (eq F f f2) ((eq 
-F f f2) \to (\forall (P: Prop).P))))) (\lambda (f2: F).(F_ind (\lambda (f: 
-F).(or (eq F Appl f) ((eq F Appl f) \to (\forall (P: Prop).P)))) (or_introl 
-(eq F Appl Appl) ((eq F Appl Appl) \to (\forall (P: Prop).P)) (refl_equal F 
-Appl)) (or_intror (eq F Appl Cast) ((eq F Appl Cast) \to (\forall (P: 
-Prop).P)) (\lambda (H: (eq F Appl Cast)).(\lambda (P: Prop).(let H0 \def 
-(eq_ind F Appl (\lambda (ee: F).(match ee in F return (\lambda (_: F).Prop) 
-with [Appl \Rightarrow True | Cast \Rightarrow False])) I Cast H) in 
-(False_ind P H0))))) f2)) (\lambda (f2: F).(F_ind (\lambda (f: F).(or (eq F 
-Cast f) ((eq F Cast f) \to (\forall (P: Prop).P)))) (or_intror (eq F Cast 
-Appl) ((eq F Cast Appl) \to (\forall (P: Prop).P)) (\lambda (H: (eq F Cast 
-Appl)).(\lambda (P: Prop).(let H0 \def (eq_ind F Cast (\lambda (ee: F).(match 
-ee in F return (\lambda (_: F).Prop) with [Appl \Rightarrow False | Cast 
-\Rightarrow True])) I Appl H) in (False_ind P H0))))) (or_introl (eq F Cast 
-Cast) ((eq F Cast Cast) \to (\forall (P: Prop).P)) (refl_equal F Cast)) f2)) 
-f1).
-(* COMMENTS
-Initial nodes: 263
-END *)
+ \lambda (f1: F).(let TMP_102 \def (\lambda (f: F).(\forall (f2: F).(let 
+TMP_101 \def (eq F f f2) in (let TMP_100 \def ((eq F f f2) \to (\forall (P: 
+Prop).P)) in (or TMP_101 TMP_100))))) in (let TMP_99 \def (\lambda (f2: 
+F).(let TMP_98 \def (\lambda (f: F).(let TMP_97 \def (eq F Appl f) in (let 
+TMP_96 \def ((eq F Appl f) \to (\forall (P: Prop).P)) in (or TMP_97 
+TMP_96)))) in (let TMP_94 \def (eq F Appl Appl) in (let TMP_93 \def ((eq F 
+Appl Appl) \to (\forall (P: Prop).P)) in (let TMP_92 \def (refl_equal F Appl) 
+in (let TMP_95 \def (or_introl TMP_94 TMP_93 TMP_92) in (let TMP_90 \def (eq 
+F Appl Cast) in (let TMP_89 \def ((eq F Appl Cast) \to (\forall (P: Prop).P)) 
+in (let TMP_88 \def (\lambda (H: (eq F Appl Cast)).(\lambda (P: Prop).(let 
+TMP_87 \def (\lambda (ee: F).(match ee in F with [Appl \Rightarrow True | 
+Cast \Rightarrow False])) in (let H0 \def (eq_ind F Appl TMP_87 I Cast H) in 
+(False_ind P H0))))) in (let TMP_91 \def (or_intror TMP_90 TMP_89 TMP_88) in 
+(F_ind TMP_98 TMP_95 TMP_91 f2))))))))))) in (let TMP_86 \def (\lambda (f2: 
+F).(let TMP_85 \def (\lambda (f: F).(let TMP_84 \def (eq F Cast f) in (let 
+TMP_83 \def ((eq F Cast f) \to (\forall (P: Prop).P)) in (or TMP_84 
+TMP_83)))) in (let TMP_81 \def (eq F Cast Appl) in (let TMP_80 \def ((eq F 
+Cast Appl) \to (\forall (P: Prop).P)) in (let TMP_79 \def (\lambda (H: (eq F 
+Cast Appl)).(\lambda (P: Prop).(let TMP_78 \def (\lambda (ee: F).(match ee in 
+F with [Appl \Rightarrow False | Cast \Rightarrow True])) in (let H0 \def 
+(eq_ind F Cast TMP_78 I Appl H) in (False_ind P H0))))) in (let TMP_82 \def 
+(or_intror TMP_81 TMP_80 TMP_79) in (let TMP_76 \def (eq F Cast Cast) in (let 
+TMP_75 \def ((eq F Cast Cast) \to (\forall (P: Prop).P)) in (let TMP_74 \def 
+(refl_equal F Cast) in (let TMP_77 \def (or_introl TMP_76 TMP_75 TMP_74) in 
+(F_ind TMP_85 TMP_82 TMP_77 f2))))))))))) in (F_ind TMP_102 TMP_99 TMP_86 
+f1)))).
 
 theorem terms_props__kind_dec:
  \forall (k1: K).(\forall (k2: K).(or (eq K k1 k2) ((eq K k1 k2) \to (\forall 
 (P: Prop).P))))
 \def
- \lambda (k1: K).(K_ind (\lambda (k: K).(\forall (k2: K).(or (eq K k k2) ((eq 
-K k k2) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda (k2: K).(K_ind 
-(\lambda (k: K).(or (eq K (Bind b) k) ((eq K (Bind b) k) \to (\forall (P: 
-Prop).P)))) (\lambda (b0: B).(let H_x \def (terms_props__bind_dec b b0) in 
-(let H \def H_x in (or_ind (eq B b b0) ((eq B b b0) \to (\forall (P: 
-Prop).P)) (or (eq K (Bind b) (Bind b0)) ((eq K (Bind b) (Bind b0)) \to 
-(\forall (P: Prop).P))) (\lambda (H0: (eq B b b0)).(eq_ind B b (\lambda (b1: 
-B).(or (eq K (Bind b) (Bind b1)) ((eq K (Bind b) (Bind b1)) \to (\forall (P: 
-Prop).P)))) (or_introl (eq K (Bind b) (Bind b)) ((eq K (Bind b) (Bind b)) \to 
-(\forall (P: Prop).P)) (refl_equal K (Bind b))) b0 H0)) (\lambda (H0: (((eq B 
-b b0) \to (\forall (P: Prop).P)))).(or_intror (eq K (Bind b) (Bind b0)) ((eq 
-K (Bind b) (Bind b0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq K (Bind b) 
-(Bind b0))).(\lambda (P: Prop).(let H2 \def (f_equal K B (\lambda (e: 
-K).(match e in K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | 
-(Flat _) \Rightarrow b])) (Bind b) (Bind b0) H1) in (let H3 \def (eq_ind_r B 
-b0 (\lambda (b1: B).((eq B b b1) \to (\forall (P0: Prop).P0))) H0 b H2) in 
-(H3 (refl_equal B b) P))))))) H)))) (\lambda (f: F).(or_intror (eq K (Bind b) 
-(Flat f)) ((eq K (Bind b) (Flat f)) \to (\forall (P: Prop).P)) (\lambda (H: 
-(eq K (Bind b) (Flat f))).(\lambda (P: Prop).(let H0 \def (eq_ind K (Bind b) 
-(\lambda (ee: K).(match ee in K return (\lambda (_: K).Prop) with [(Bind _) 
-\Rightarrow True | (Flat _) \Rightarrow False])) I (Flat f) H) in (False_ind 
-P H0)))))) k2))) (\lambda (f: F).(\lambda (k2: K).(K_ind (\lambda (k: K).(or 
-(eq K (Flat f) k) ((eq K (Flat f) k) \to (\forall (P: Prop).P)))) (\lambda 
-(b: B).(or_intror (eq K (Flat f) (Bind b)) ((eq K (Flat f) (Bind b)) \to 
-(\forall (P: Prop).P)) (\lambda (H: (eq K (Flat f) (Bind b))).(\lambda (P: 
-Prop).(let H0 \def (eq_ind K (Flat f) (\lambda (ee: K).(match ee in K return 
-(\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow 
-True])) I (Bind b) H) in (False_ind P H0)))))) (\lambda (f0: F).(let H_x \def 
-(terms_props__flat_dec f f0) in (let H \def H_x in (or_ind (eq F f f0) ((eq F 
-f f0) \to (\forall (P: Prop).P)) (or (eq K (Flat f) (Flat f0)) ((eq K (Flat 
-f) (Flat f0)) \to (\forall (P: Prop).P))) (\lambda (H0: (eq F f f0)).(eq_ind 
-F f (\lambda (f1: F).(or (eq K (Flat f) (Flat f1)) ((eq K (Flat f) (Flat f1)) 
-\to (\forall (P: Prop).P)))) (or_introl (eq K (Flat f) (Flat f)) ((eq K (Flat 
-f) (Flat f)) \to (\forall (P: Prop).P)) (refl_equal K (Flat f))) f0 H0)) 
-(\lambda (H0: (((eq F f f0) \to (\forall (P: Prop).P)))).(or_intror (eq K 
-(Flat f) (Flat f0)) ((eq K (Flat f) (Flat f0)) \to (\forall (P: Prop).P)) 
-(\lambda (H1: (eq K (Flat f) (Flat f0))).(\lambda (P: Prop).(let H2 \def 
-(f_equal K F (\lambda (e: K).(match e in K return (\lambda (_: K).F) with 
-[(Bind _) \Rightarrow f | (Flat f1) \Rightarrow f1])) (Flat f) (Flat f0) H1) 
-in (let H3 \def (eq_ind_r F f0 (\lambda (f1: F).((eq F f f1) \to (\forall 
-(P0: Prop).P0))) H0 f H2) in (H3 (refl_equal F f) P))))))) H)))) k2))) k1).
-(* COMMENTS
-Initial nodes: 799
-END *)
+ \lambda (k1: K).(let TMP_197 \def (\lambda (k: K).(\forall (k2: K).(let 
+TMP_196 \def (eq K k k2) in (let TMP_195 \def ((eq K k k2) \to (\forall (P: 
+Prop).P)) in (or TMP_196 TMP_195))))) in (let TMP_194 \def (\lambda (b: 
+B).(\lambda (k2: K).(let TMP_193 \def (\lambda (k: K).(let TMP_191 \def (Bind 
+b) in (let TMP_192 \def (eq K TMP_191 k) in (let TMP_190 \def ((eq K (Bind b) 
+k) \to (\forall (P: Prop).P)) in (or TMP_192 TMP_190))))) in (let TMP_189 
+\def (\lambda (b0: B).(let H_x \def (terms_props__bind_dec b b0) in (let H 
+\def H_x in (let TMP_188 \def (eq B b b0) in (let TMP_187 \def ((eq B b b0) 
+\to (\forall (P: Prop).P)) in (let TMP_184 \def (Bind b) in (let TMP_183 \def 
+(Bind b0) in (let TMP_185 \def (eq K TMP_184 TMP_183) in (let TMP_182 \def 
+((eq K (Bind b) (Bind b0)) \to (\forall (P: Prop).P)) in (let TMP_186 \def 
+(or TMP_185 TMP_182) in (let TMP_181 \def (\lambda (H0: (eq B b b0)).(let 
+TMP_180 \def (\lambda (b1: B).(let TMP_178 \def (Bind b) in (let TMP_177 \def 
+(Bind b1) in (let TMP_179 \def (eq K TMP_178 TMP_177) in (let TMP_176 \def 
+((eq K (Bind b) (Bind b1)) \to (\forall (P: Prop).P)) in (or TMP_179 
+TMP_176)))))) in (let TMP_173 \def (Bind b) in (let TMP_172 \def (Bind b) in 
+(let TMP_174 \def (eq K TMP_173 TMP_172) in (let TMP_171 \def ((eq K (Bind b) 
+(Bind b)) \to (\forall (P: Prop).P)) in (let TMP_169 \def (Bind b) in (let 
+TMP_170 \def (refl_equal K TMP_169) in (let TMP_175 \def (or_introl TMP_174 
+TMP_171 TMP_170) in (eq_ind B b TMP_180 TMP_175 b0 H0)))))))))) in (let 
+TMP_168 \def (\lambda (H0: (((eq B b b0) \to (\forall (P: Prop).P)))).(let 
+TMP_166 \def (Bind b) in (let TMP_165 \def (Bind b0) in (let TMP_167 \def (eq 
+K TMP_166 TMP_165) in (let TMP_164 \def ((eq K (Bind b) (Bind b0)) \to 
+(\forall (P: Prop).P)) in (let TMP_163 \def (\lambda (H1: (eq K (Bind b) 
+(Bind b0))).(\lambda (P: Prop).(let TMP_160 \def (\lambda (e: K).(match e in 
+K with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])) in (let TMP_159 
+\def (Bind b) in (let TMP_158 \def (Bind b0) in (let H2 \def (f_equal K B 
+TMP_160 TMP_159 TMP_158 H1) in (let TMP_161 \def (\lambda (b1: B).((eq B b 
+b1) \to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r B b0 TMP_161 H0 b 
+H2) in (let TMP_162 \def (refl_equal B b) in (H3 TMP_162 P)))))))))) in 
+(or_intror TMP_167 TMP_164 TMP_163))))))) in (or_ind TMP_188 TMP_187 TMP_186 
+TMP_181 TMP_168 H))))))))))))) in (let TMP_157 \def (\lambda (f: F).(let 
+TMP_155 \def (Bind b) in (let TMP_154 \def (Flat f) in (let TMP_156 \def (eq 
+K TMP_155 TMP_154) in (let TMP_153 \def ((eq K (Bind b) (Flat f)) \to 
+(\forall (P: Prop).P)) in (let TMP_152 \def (\lambda (H: (eq K (Bind b) (Flat 
+f))).(\lambda (P: Prop).(let TMP_151 \def (Bind b) in (let TMP_150 \def 
+(\lambda (ee: K).(match ee in K with [(Bind _) \Rightarrow True | (Flat _) 
+\Rightarrow False])) in (let TMP_149 \def (Flat f) in (let H0 \def (eq_ind K 
+TMP_151 TMP_150 I TMP_149 H) in (False_ind P H0))))))) in (or_intror TMP_156 
+TMP_153 TMP_152))))))) in (K_ind TMP_193 TMP_189 TMP_157 k2)))))) in (let 
+TMP_148 \def (\lambda (f: F).(\lambda (k2: K).(let TMP_147 \def (\lambda (k: 
+K).(let TMP_145 \def (Flat f) in (let TMP_146 \def (eq K TMP_145 k) in (let 
+TMP_144 \def ((eq K (Flat f) k) \to (\forall (P: Prop).P)) in (or TMP_146 
+TMP_144))))) in (let TMP_143 \def (\lambda (b: B).(let TMP_141 \def (Flat f) 
+in (let TMP_140 \def (Bind b) in (let TMP_142 \def (eq K TMP_141 TMP_140) in 
+(let TMP_139 \def ((eq K (Flat f) (Bind b)) \to (\forall (P: Prop).P)) in 
+(let TMP_138 \def (\lambda (H: (eq K (Flat f) (Bind b))).(\lambda (P: 
+Prop).(let TMP_137 \def (Flat f) in (let TMP_136 \def (\lambda (ee: K).(match 
+ee in K with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])) in 
+(let TMP_135 \def (Bind b) in (let H0 \def (eq_ind K TMP_137 TMP_136 I 
+TMP_135 H) in (False_ind P H0))))))) in (or_intror TMP_142 TMP_139 
+TMP_138))))))) in (let TMP_134 \def (\lambda (f0: F).(let H_x \def 
+(terms_props__flat_dec f f0) in (let H \def H_x in (let TMP_133 \def (eq F f 
+f0) in (let TMP_132 \def ((eq F f f0) \to (\forall (P: Prop).P)) in (let 
+TMP_129 \def (Flat f) in (let TMP_128 \def (Flat f0) in (let TMP_130 \def (eq 
+K TMP_129 TMP_128) in (let TMP_127 \def ((eq K (Flat f) (Flat f0)) \to 
+(\forall (P: Prop).P)) in (let TMP_131 \def (or TMP_130 TMP_127) in (let 
+TMP_126 \def (\lambda (H0: (eq F f f0)).(let TMP_125 \def (\lambda (f1: 
+F).(let TMP_123 \def (Flat f) in (let TMP_122 \def (Flat f1) in (let TMP_124 
+\def (eq K TMP_123 TMP_122) in (let TMP_121 \def ((eq K (Flat f) (Flat f1)) 
+\to (\forall (P: Prop).P)) in (or TMP_124 TMP_121)))))) in (let TMP_118 \def 
+(Flat f) in (let TMP_117 \def (Flat f) in (let TMP_119 \def (eq K TMP_118 
+TMP_117) in (let TMP_116 \def ((eq K (Flat f) (Flat f)) \to (\forall (P: 
+Prop).P)) in (let TMP_114 \def (Flat f) in (let TMP_115 \def (refl_equal K 
+TMP_114) in (let TMP_120 \def (or_introl TMP_119 TMP_116 TMP_115) in (eq_ind 
+F f TMP_125 TMP_120 f0 H0)))))))))) in (let TMP_113 \def (\lambda (H0: (((eq 
+F f f0) \to (\forall (P: Prop).P)))).(let TMP_111 \def (Flat f) in (let 
+TMP_110 \def (Flat f0) in (let TMP_112 \def (eq K TMP_111 TMP_110) in (let 
+TMP_109 \def ((eq K (Flat f) (Flat f0)) \to (\forall (P: Prop).P)) in (let 
+TMP_108 \def (\lambda (H1: (eq K (Flat f) (Flat f0))).(\lambda (P: Prop).(let 
+TMP_105 \def (\lambda (e: K).(match e in K with [(Bind _) \Rightarrow f | 
+(Flat f1) \Rightarrow f1])) in (let TMP_104 \def (Flat f) in (let TMP_103 
+\def (Flat f0) in (let H2 \def (f_equal K F TMP_105 TMP_104 TMP_103 H1) in 
+(let TMP_106 \def (\lambda (f1: F).((eq F f f1) \to (\forall (P0: Prop).P0))) 
+in (let H3 \def (eq_ind_r F f0 TMP_106 H0 f H2) in (let TMP_107 \def 
+(refl_equal F f) in (H3 TMP_107 P)))))))))) in (or_intror TMP_112 TMP_109 
+TMP_108))))))) in (or_ind TMP_133 TMP_132 TMP_131 TMP_126 TMP_113 
+H))))))))))))) in (K_ind TMP_147 TMP_143 TMP_134 k2)))))) in (K_ind TMP_197 
+TMP_194 TMP_148 k1)))).
 
 theorem term_dec:
  \forall (t1: T).(\forall (t2: T).(or (eq T t1 t2) ((eq T t1 t2) \to (\forall 
 (P: Prop).P))))
 \def
- \lambda (t1: T).(T_ind (\lambda (t: T).(\forall (t2: T).(or (eq T t t2) ((eq 
-T t t2) \to (\forall (P: Prop).P))))) (\lambda (n: nat).(\lambda (t2: 
-T).(T_ind (\lambda (t: T).(or (eq T (TSort n) t) ((eq T (TSort n) t) \to 
-(\forall (P: Prop).P)))) (\lambda (n0: nat).(let H_x \def (nat_dec n n0) in 
-(let H \def H_x in (or_ind (eq nat n n0) ((eq nat n n0) \to (\forall (P: 
-Prop).P)) (or (eq T (TSort n) (TSort n0)) ((eq T (TSort n) (TSort n0)) \to 
-(\forall (P: Prop).P))) (\lambda (H0: (eq nat n n0)).(eq_ind nat n (\lambda 
-(n1: nat).(or (eq T (TSort n) (TSort n1)) ((eq T (TSort n) (TSort n1)) \to 
-(\forall (P: Prop).P)))) (or_introl (eq T (TSort n) (TSort n)) ((eq T (TSort 
-n) (TSort n)) \to (\forall (P: Prop).P)) (refl_equal T (TSort n))) n0 H0)) 
-(\lambda (H0: (((eq nat n n0) \to (\forall (P: Prop).P)))).(or_intror (eq T 
-(TSort n) (TSort n0)) ((eq T (TSort n) (TSort n0)) \to (\forall (P: Prop).P)) 
-(\lambda (H1: (eq T (TSort n) (TSort n0))).(\lambda (P: Prop).(let H2 \def 
-(f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with 
-[(TSort n1) \Rightarrow n1 | (TLRef _) \Rightarrow n | (THead _ _ _) 
-\Rightarrow n])) (TSort n) (TSort n0) H1) in (let H3 \def (eq_ind_r nat n0 
-(\lambda (n1: nat).((eq nat n n1) \to (\forall (P0: Prop).P0))) H0 n H2) in 
-(H3 (refl_equal nat n) P))))))) H)))) (\lambda (n0: nat).(or_intror (eq T 
-(TSort n) (TLRef n0)) ((eq T (TSort n) (TLRef n0)) \to (\forall (P: Prop).P)) 
-(\lambda (H: (eq T (TSort n) (TLRef n0))).(\lambda (P: Prop).(let H0 \def 
-(eq_ind T (TSort n) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | 
-(THead _ _ _) \Rightarrow False])) I (TLRef n0) H) in (False_ind P H0)))))) 
-(\lambda (k: K).(\lambda (t: T).(\lambda (_: (or (eq T (TSort n) t) ((eq T 
-(TSort n) t) \to (\forall (P: Prop).P)))).(\lambda (t0: T).(\lambda (_: (or 
-(eq T (TSort n) t0) ((eq T (TSort n) t0) \to (\forall (P: 
-Prop).P)))).(or_intror (eq T (TSort n) (THead k t t0)) ((eq T (TSort n) 
-(THead k t t0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (TSort n) 
-(THead k t t0))).(\lambda (P: Prop).(let H2 \def (eq_ind T (TSort n) (\lambda 
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) 
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
-False])) I (THead k t t0) H1) in (False_ind P H2)))))))))) t2))) (\lambda (n: 
-nat).(\lambda (t2: T).(T_ind (\lambda (t: T).(or (eq T (TLRef n) t) ((eq T 
-(TLRef n) t) \to (\forall (P: Prop).P)))) (\lambda (n0: nat).(or_intror (eq T 
-(TLRef n) (TSort n0)) ((eq T (TLRef n) (TSort n0)) \to (\forall (P: Prop).P)) 
-(\lambda (H: (eq T (TLRef n) (TSort n0))).(\lambda (P: Prop).(let H0 \def 
-(eq_ind T (TLRef n) (\lambda (ee: T).(match ee in T return (\lambda (_: 
-T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | 
-(THead _ _ _) \Rightarrow False])) I (TSort n0) H) in (False_ind P H0)))))) 
-(\lambda (n0: nat).(let H_x \def (nat_dec n n0) in (let H \def H_x in (or_ind 
-(eq nat n n0) ((eq nat n n0) \to (\forall (P: Prop).P)) (or (eq T (TLRef n) 
-(TLRef n0)) ((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P))) (\lambda 
-(H0: (eq nat n n0)).(eq_ind nat n (\lambda (n1: nat).(or (eq T (TLRef n) 
-(TLRef n1)) ((eq T (TLRef n) (TLRef n1)) \to (\forall (P: Prop).P)))) 
-(or_introl (eq T (TLRef n) (TLRef n)) ((eq T (TLRef n) (TLRef n)) \to 
-(\forall (P: Prop).P)) (refl_equal T (TLRef n))) n0 H0)) (\lambda (H0: (((eq 
-nat n n0) \to (\forall (P: Prop).P)))).(or_intror (eq T (TLRef n) (TLRef n0)) 
-((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T 
-(TLRef n) (TLRef n0))).(\lambda (P: Prop).(let H2 \def (f_equal T nat 
-(\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _) 
-\Rightarrow n | (TLRef n1) \Rightarrow n1 | (THead _ _ _) \Rightarrow n])) 
-(TLRef n) (TLRef n0) H1) in (let H3 \def (eq_ind_r nat n0 (\lambda (n1: 
-nat).((eq nat n n1) \to (\forall (P0: Prop).P0))) H0 n H2) in (H3 (refl_equal 
-nat n) P))))))) H)))) (\lambda (k: K).(\lambda (t: T).(\lambda (_: (or (eq T 
-(TLRef n) t) ((eq T (TLRef n) t) \to (\forall (P: Prop).P)))).(\lambda (t0: 
-T).(\lambda (_: (or (eq T (TLRef n) t0) ((eq T (TLRef n) t0) \to (\forall (P: 
-Prop).P)))).(or_intror (eq T (TLRef n) (THead k t t0)) ((eq T (TLRef n) 
-(THead k t t0)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (TLRef n) 
-(THead k t t0))).(\lambda (P: Prop).(let H2 \def (eq_ind T (TLRef n) (\lambda 
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) 
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow 
-False])) I (THead k t t0) H1) in (False_ind P H2)))))))))) t2))) (\lambda (k: 
-K).(\lambda (t: T).(\lambda (H: ((\forall (t2: T).(or (eq T t t2) ((eq T t 
-t2) \to (\forall (P: Prop).P)))))).(\lambda (t0: T).(\lambda (H0: ((\forall 
-(t2: T).(or (eq T t0 t2) ((eq T t0 t2) \to (\forall (P: 
-Prop).P)))))).(\lambda (t2: T).(T_ind (\lambda (t3: T).(or (eq T (THead k t 
-t0) t3) ((eq T (THead k t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (n: 
-nat).(or_intror (eq T (THead k t t0) (TSort n)) ((eq T (THead k t t0) (TSort 
-n)) \to (\forall (P: Prop).P)) (\lambda (H1: (eq T (THead k t t0) (TSort 
-n))).(\lambda (P: Prop).(let H2 \def (eq_ind T (THead k t t0) (\lambda (ee: 
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow 
-False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I 
-(TSort n) H1) in (False_ind P H2)))))) (\lambda (n: nat).(or_intror (eq T 
-(THead k t t0) (TLRef n)) ((eq T (THead k t t0) (TLRef n)) \to (\forall (P: 
-Prop).P)) (\lambda (H1: (eq T (THead k t t0) (TLRef n))).(\lambda (P: 
-Prop).(let H2 \def (eq_ind T (THead k t t0) (\lambda (ee: T).(match ee in T 
-return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) 
-\Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TLRef n) H1) in 
-(False_ind P H2)))))) (\lambda (k0: K).(\lambda (t3: T).(\lambda (H1: (or (eq 
-T (THead k t t0) t3) ((eq T (THead k t t0) t3) \to (\forall (P: 
-Prop).P)))).(\lambda (t4: T).(\lambda (H2: (or (eq T (THead k t t0) t4) ((eq 
-T (THead k t t0) t4) \to (\forall (P: Prop).P)))).(let H_x \def (H t3) in 
-(let H3 \def H_x in (or_ind (eq T t t3) ((eq T t t3) \to (\forall (P: 
-Prop).P)) (or (eq T (THead k t t0) (THead k0 t3 t4)) ((eq T (THead k t t0) 
-(THead k0 t3 t4)) \to (\forall (P: Prop).P))) (\lambda (H4: (eq T t t3)).(let 
-H5 \def (eq_ind_r T t3 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T 
-(THead k t t0) t5) \to (\forall (P: Prop).P)))) H1 t H4) in (eq_ind T t 
-(\lambda (t5: T).(or (eq T (THead k t t0) (THead k0 t5 t4)) ((eq T (THead k t 
-t0) (THead k0 t5 t4)) \to (\forall (P: Prop).P)))) (let H_x0 \def (H0 t4) in 
-(let H6 \def H_x0 in (or_ind (eq T t0 t4) ((eq T t0 t4) \to (\forall (P: 
-Prop).P)) (or (eq T (THead k t t0) (THead k0 t t4)) ((eq T (THead k t t0) 
-(THead k0 t t4)) \to (\forall (P: Prop).P))) (\lambda (H7: (eq T t0 t4)).(let 
-H8 \def (eq_ind_r T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T 
-(THead k t t0) t5) \to (\forall (P: Prop).P)))) H2 t0 H7) in (eq_ind T t0 
-(\lambda (t5: T).(or (eq T (THead k t t0) (THead k0 t t5)) ((eq T (THead k t 
-t0) (THead k0 t t5)) \to (\forall (P: Prop).P)))) (let H_x1 \def 
-(terms_props__kind_dec k k0) in (let H9 \def H_x1 in (or_ind (eq K k k0) ((eq 
-K k k0) \to (\forall (P: Prop).P)) (or (eq T (THead k t t0) (THead k0 t t0)) 
-((eq T (THead k t t0) (THead k0 t t0)) \to (\forall (P: Prop).P))) (\lambda 
-(H10: (eq K k k0)).(eq_ind K k (\lambda (k1: K).(or (eq T (THead k t t0) 
-(THead k1 t t0)) ((eq T (THead k t t0) (THead k1 t t0)) \to (\forall (P: 
-Prop).P)))) (or_introl (eq T (THead k t t0) (THead k t t0)) ((eq T (THead k t 
-t0) (THead k t t0)) \to (\forall (P: Prop).P)) (refl_equal T (THead k t t0))) 
-k0 H10)) (\lambda (H10: (((eq K k k0) \to (\forall (P: Prop).P)))).(or_intror 
-(eq T (THead k t t0) (THead k0 t t0)) ((eq T (THead k t t0) (THead k0 t t0)) 
-\to (\forall (P: Prop).P)) (\lambda (H11: (eq T (THead k t t0) (THead k0 t 
-t0))).(\lambda (P: Prop).(let H12 \def (f_equal T K (\lambda (e: T).(match e 
-in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k | (TLRef _) 
-\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) (THead k t t0) (THead k0 t 
-t0) H11) in (let H13 \def (eq_ind_r K k0 (\lambda (k1: K).((eq K k k1) \to 
-(\forall (P0: Prop).P0))) H10 k H12) in (H13 (refl_equal K k) P))))))) H9))) 
-t4 H7))) (\lambda (H7: (((eq T t0 t4) \to (\forall (P: Prop).P)))).(or_intror 
-(eq T (THead k t t0) (THead k0 t t4)) ((eq T (THead k t t0) (THead k0 t t4)) 
-\to (\forall (P: Prop).P)) (\lambda (H8: (eq T (THead k t t0) (THead k0 t 
-t4))).(\lambda (P: Prop).(let H9 \def (f_equal T K (\lambda (e: T).(match e 
-in T return (\lambda (_: T).K) with [(TSort _) \Rightarrow k | (TLRef _) 
-\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) (THead k t t0) (THead k0 t 
-t4) H8) in ((let H10 \def (f_equal T T (\lambda (e: T).(match e in T return 
-(\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 
-| (THead _ _ t5) \Rightarrow t5])) (THead k t t0) (THead k0 t t4) H8) in 
-(\lambda (_: (eq K k k0)).(let H12 \def (eq_ind_r T t4 (\lambda (t5: T).((eq 
-T t0 t5) \to (\forall (P0: Prop).P0))) H7 t0 H10) in (let H13 \def (eq_ind_r 
-T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T (THead k t t0) t5) 
-\to (\forall (P0: Prop).P0)))) H2 t0 H10) in (H12 (refl_equal T t0) P))))) 
-H9)))))) H6))) t3 H4))) (\lambda (H4: (((eq T t t3) \to (\forall (P: 
-Prop).P)))).(or_intror (eq T (THead k t t0) (THead k0 t3 t4)) ((eq T (THead k 
-t t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) (\lambda (H5: (eq T (THead 
-k t t0) (THead k0 t3 t4))).(\lambda (P: Prop).(let H6 \def (f_equal T K 
-(\lambda (e: T).(match e in T return (\lambda (_: T).K) with [(TSort _) 
-\Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) 
-(THead k t t0) (THead k0 t3 t4) H5) in ((let H7 \def (f_equal T T (\lambda 
-(e: T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t 
-| (TLRef _) \Rightarrow t | (THead _ t5 _) \Rightarrow t5])) (THead k t t0) 
-(THead k0 t3 t4) H5) in ((let H8 \def (f_equal T T (\lambda (e: T).(match e 
-in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | (TLRef _) 
-\Rightarrow t0 | (THead _ _ t5) \Rightarrow t5])) (THead k t t0) (THead k0 t3 
-t4) H5) in (\lambda (H9: (eq T t t3)).(\lambda (_: (eq K k k0)).(let H11 \def 
-(eq_ind_r T t4 (\lambda (t5: T).(or (eq T (THead k t t0) t5) ((eq T (THead k 
-t t0) t5) \to (\forall (P0: Prop).P0)))) H2 t0 H8) in (let H12 \def (eq_ind_r 
-T t3 (\lambda (t5: T).((eq T t t5) \to (\forall (P0: Prop).P0))) H4 t H9) in 
-(let H13 \def (eq_ind_r T t3 (\lambda (t5: T).(or (eq T (THead k t t0) t5) 
-((eq T (THead k t t0) t5) \to (\forall (P0: Prop).P0)))) H1 t H9) in (H12 
-(refl_equal T t) P))))))) H7)) H6)))))) H3)))))))) t2))))))) t1).
-(* COMMENTS
-Initial nodes: 2821
-END *)
+ \lambda (t1: T).(let TMP_447 \def (\lambda (t: T).(\forall (t2: T).(let 
+TMP_446 \def (eq T t t2) in (let TMP_445 \def ((eq T t t2) \to (\forall (P: 
+Prop).P)) in (or TMP_446 TMP_445))))) in (let TMP_444 \def (\lambda (n: 
+nat).(\lambda (t2: T).(let TMP_443 \def (\lambda (t: T).(let TMP_441 \def 
+(TSort n) in (let TMP_442 \def (eq T TMP_441 t) in (let TMP_440 \def ((eq T 
+(TSort n) t) \to (\forall (P: Prop).P)) in (or TMP_442 TMP_440))))) in (let 
+TMP_439 \def (\lambda (n0: nat).(let H_x \def (nat_dec n n0) in (let H \def 
+H_x in (let TMP_438 \def (eq nat n n0) in (let TMP_437 \def ((eq nat n n0) 
+\to (\forall (P: Prop).P)) in (let TMP_434 \def (TSort n) in (let TMP_433 
+\def (TSort n0) in (let TMP_435 \def (eq T TMP_434 TMP_433) in (let TMP_432 
+\def ((eq T (TSort n) (TSort n0)) \to (\forall (P: Prop).P)) in (let TMP_436 
+\def (or TMP_435 TMP_432) in (let TMP_431 \def (\lambda (H0: (eq nat n 
+n0)).(let TMP_430 \def (\lambda (n1: nat).(let TMP_428 \def (TSort n) in (let 
+TMP_427 \def (TSort n1) in (let TMP_429 \def (eq T TMP_428 TMP_427) in (let 
+TMP_426 \def ((eq T (TSort n) (TSort n1)) \to (\forall (P: Prop).P)) in (or 
+TMP_429 TMP_426)))))) in (let TMP_423 \def (TSort n) in (let TMP_422 \def 
+(TSort n) in (let TMP_424 \def (eq T TMP_423 TMP_422) in (let TMP_421 \def 
+((eq T (TSort n) (TSort n)) \to (\forall (P: Prop).P)) in (let TMP_419 \def 
+(TSort n) in (let TMP_420 \def (refl_equal T TMP_419) in (let TMP_425 \def 
+(or_introl TMP_424 TMP_421 TMP_420) in (eq_ind nat n TMP_430 TMP_425 n0 
+H0)))))))))) in (let TMP_418 \def (\lambda (H0: (((eq nat n n0) \to (\forall 
+(P: Prop).P)))).(let TMP_416 \def (TSort n) in (let TMP_415 \def (TSort n0) 
+in (let TMP_417 \def (eq T TMP_416 TMP_415) in (let TMP_414 \def ((eq T 
+(TSort n) (TSort n0)) \to (\forall (P: Prop).P)) in (let TMP_413 \def 
+(\lambda (H1: (eq T (TSort n) (TSort n0))).(\lambda (P: Prop).(let TMP_410 
+\def (\lambda (e: T).(match e in T with [(TSort n1) \Rightarrow n1 | (TLRef 
+_) \Rightarrow n | (THead _ _ _) \Rightarrow n])) in (let TMP_409 \def (TSort 
+n) in (let TMP_408 \def (TSort n0) in (let H2 \def (f_equal T nat TMP_410 
+TMP_409 TMP_408 H1) in (let TMP_411 \def (\lambda (n1: nat).((eq nat n n1) 
+\to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r nat n0 TMP_411 H0 n 
+H2) in (let TMP_412 \def (refl_equal nat n) in (H3 TMP_412 P)))))))))) in 
+(or_intror TMP_417 TMP_414 TMP_413))))))) in (or_ind TMP_438 TMP_437 TMP_436 
+TMP_431 TMP_418 H))))))))))))) in (let TMP_407 \def (\lambda (n0: nat).(let 
+TMP_405 \def (TSort n) in (let TMP_404 \def (TLRef n0) in (let TMP_406 \def 
+(eq T TMP_405 TMP_404) in (let TMP_403 \def ((eq T (TSort n) (TLRef n0)) \to 
+(\forall (P: Prop).P)) in (let TMP_402 \def (\lambda (H: (eq T (TSort n) 
+(TLRef n0))).(\lambda (P: Prop).(let TMP_401 \def (TSort n) in (let TMP_400 
+\def (\lambda (ee: T).(match ee in T with [(TSort _) \Rightarrow True | 
+(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let 
+TMP_399 \def (TLRef n0) in (let H0 \def (eq_ind T TMP_401 TMP_400 I TMP_399 
+H) in (False_ind P H0))))))) in (or_intror TMP_406 TMP_403 TMP_402))))))) in 
+(let TMP_398 \def (\lambda (k: K).(\lambda (t: T).(\lambda (_: (or (eq T 
+(TSort n) t) ((eq T (TSort n) t) \to (\forall (P: Prop).P)))).(\lambda (t0: 
+T).(\lambda (_: (or (eq T (TSort n) t0) ((eq T (TSort n) t0) \to (\forall (P: 
+Prop).P)))).(let TMP_396 \def (TSort n) in (let TMP_395 \def (THead k t t0) 
+in (let TMP_397 \def (eq T TMP_396 TMP_395) in (let TMP_394 \def ((eq T 
+(TSort n) (THead k t t0)) \to (\forall (P: Prop).P)) in (let TMP_393 \def 
+(\lambda (H1: (eq T (TSort n) (THead k t t0))).(\lambda (P: Prop).(let 
+TMP_392 \def (TSort n) in (let TMP_391 \def (\lambda (ee: T).(match ee in T 
+with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ 
+_) \Rightarrow False])) in (let TMP_390 \def (THead k t t0) in (let H2 \def 
+(eq_ind T TMP_392 TMP_391 I TMP_390 H1) in (False_ind P H2))))))) in 
+(or_intror TMP_397 TMP_394 TMP_393))))))))))) in (T_ind TMP_443 TMP_439 
+TMP_407 TMP_398 t2))))))) in (let TMP_389 \def (\lambda (n: nat).(\lambda 
+(t2: T).(let TMP_388 \def (\lambda (t: T).(let TMP_386 \def (TLRef n) in (let 
+TMP_387 \def (eq T TMP_386 t) in (let TMP_385 \def ((eq T (TLRef n) t) \to 
+(\forall (P: Prop).P)) in (or TMP_387 TMP_385))))) in (let TMP_384 \def 
+(\lambda (n0: nat).(let TMP_382 \def (TLRef n) in (let TMP_381 \def (TSort 
+n0) in (let TMP_383 \def (eq T TMP_382 TMP_381) in (let TMP_380 \def ((eq T 
+(TLRef n) (TSort n0)) \to (\forall (P: Prop).P)) in (let TMP_379 \def 
+(\lambda (H: (eq T (TLRef n) (TSort n0))).(\lambda (P: Prop).(let TMP_378 
+\def (TLRef n) in (let TMP_377 \def (\lambda (ee: T).(match ee in T with 
+[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) 
+\Rightarrow False])) in (let TMP_376 \def (TSort n0) in (let H0 \def (eq_ind 
+T TMP_378 TMP_377 I TMP_376 H) in (False_ind P H0))))))) in (or_intror 
+TMP_383 TMP_380 TMP_379))))))) in (let TMP_375 \def (\lambda (n0: nat).(let 
+H_x \def (nat_dec n n0) in (let H \def H_x in (let TMP_374 \def (eq nat n n0) 
+in (let TMP_373 \def ((eq nat n n0) \to (\forall (P: Prop).P)) in (let 
+TMP_370 \def (TLRef n) in (let TMP_369 \def (TLRef n0) in (let TMP_371 \def 
+(eq T TMP_370 TMP_369) in (let TMP_368 \def ((eq T (TLRef n) (TLRef n0)) \to 
+(\forall (P: Prop).P)) in (let TMP_372 \def (or TMP_371 TMP_368) in (let 
+TMP_367 \def (\lambda (H0: (eq nat n n0)).(let TMP_366 \def (\lambda (n1: 
+nat).(let TMP_364 \def (TLRef n) in (let TMP_363 \def (TLRef n1) in (let 
+TMP_365 \def (eq T TMP_364 TMP_363) in (let TMP_362 \def ((eq T (TLRef n) 
+(TLRef n1)) \to (\forall (P: Prop).P)) in (or TMP_365 TMP_362)))))) in (let 
+TMP_359 \def (TLRef n) in (let TMP_358 \def (TLRef n) in (let TMP_360 \def 
+(eq T TMP_359 TMP_358) in (let TMP_357 \def ((eq T (TLRef n) (TLRef n)) \to 
+(\forall (P: Prop).P)) in (let TMP_355 \def (TLRef n) in (let TMP_356 \def 
+(refl_equal T TMP_355) in (let TMP_361 \def (or_introl TMP_360 TMP_357 
+TMP_356) in (eq_ind nat n TMP_366 TMP_361 n0 H0)))))))))) in (let TMP_354 
+\def (\lambda (H0: (((eq nat n n0) \to (\forall (P: Prop).P)))).(let TMP_352 
+\def (TLRef n) in (let TMP_351 \def (TLRef n0) in (let TMP_353 \def (eq T 
+TMP_352 TMP_351) in (let TMP_350 \def ((eq T (TLRef n) (TLRef n0)) \to 
+(\forall (P: Prop).P)) in (let TMP_349 \def (\lambda (H1: (eq T (TLRef n) 
+(TLRef n0))).(\lambda (P: Prop).(let TMP_346 \def (\lambda (e: T).(match e in 
+T with [(TSort _) \Rightarrow n | (TLRef n1) \Rightarrow n1 | (THead _ _ _) 
+\Rightarrow n])) in (let TMP_345 \def (TLRef n) in (let TMP_344 \def (TLRef 
+n0) in (let H2 \def (f_equal T nat TMP_346 TMP_345 TMP_344 H1) in (let 
+TMP_347 \def (\lambda (n1: nat).((eq nat n n1) \to (\forall (P0: Prop).P0))) 
+in (let H3 \def (eq_ind_r nat n0 TMP_347 H0 n H2) in (let TMP_348 \def 
+(refl_equal nat n) in (H3 TMP_348 P)))))))))) in (or_intror TMP_353 TMP_350 
+TMP_349))))))) in (or_ind TMP_374 TMP_373 TMP_372 TMP_367 TMP_354 
+H))))))))))))) in (let TMP_343 \def (\lambda (k: K).(\lambda (t: T).(\lambda 
+(_: (or (eq T (TLRef n) t) ((eq T (TLRef n) t) \to (\forall (P: 
+Prop).P)))).(\lambda (t0: T).(\lambda (_: (or (eq T (TLRef n) t0) ((eq T 
+(TLRef n) t0) \to (\forall (P: Prop).P)))).(let TMP_341 \def (TLRef n) in 
+(let TMP_340 \def (THead k t t0) in (let TMP_342 \def (eq T TMP_341 TMP_340) 
+in (let TMP_339 \def ((eq T (TLRef n) (THead k t t0)) \to (\forall (P: 
+Prop).P)) in (let TMP_338 \def (\lambda (H1: (eq T (TLRef n) (THead k t 
+t0))).(\lambda (P: Prop).(let TMP_337 \def (TLRef n) in (let TMP_336 \def 
+(\lambda (ee: T).(match ee in T with [(TSort _) \Rightarrow False | (TLRef _) 
+\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_335 \def 
+(THead k t t0) in (let H2 \def (eq_ind T TMP_337 TMP_336 I TMP_335 H1) in 
+(False_ind P H2))))))) in (or_intror TMP_342 TMP_339 TMP_338))))))))))) in 
+(T_ind TMP_388 TMP_384 TMP_375 TMP_343 t2))))))) in (let TMP_334 \def 
+(\lambda (k: K).(\lambda (t: T).(\lambda (H: ((\forall (t2: T).(or (eq T t 
+t2) ((eq T t t2) \to (\forall (P: Prop).P)))))).(\lambda (t0: T).(\lambda 
+(H0: ((\forall (t2: T).(or (eq T t0 t2) ((eq T t0 t2) \to (\forall (P: 
+Prop).P)))))).(\lambda (t2: T).(let TMP_333 \def (\lambda (t3: T).(let 
+TMP_331 \def (THead k t t0) in (let TMP_332 \def (eq T TMP_331 t3) in (let 
+TMP_330 \def ((eq T (THead k t t0) t3) \to (\forall (P: Prop).P)) in (or 
+TMP_332 TMP_330))))) in (let TMP_329 \def (\lambda (n: nat).(let TMP_327 \def 
+(THead k t t0) in (let TMP_326 \def (TSort n) in (let TMP_328 \def (eq T 
+TMP_327 TMP_326) in (let TMP_325 \def ((eq T (THead k t t0) (TSort n)) \to 
+(\forall (P: Prop).P)) in (let TMP_324 \def (\lambda (H1: (eq T (THead k t 
+t0) (TSort n))).(\lambda (P: Prop).(let TMP_323 \def (THead k t t0) in (let 
+TMP_322 \def (\lambda (ee: T).(match ee in T with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) in 
+(let TMP_321 \def (TSort n) in (let H2 \def (eq_ind T TMP_323 TMP_322 I 
+TMP_321 H1) in (False_ind P H2))))))) in (or_intror TMP_328 TMP_325 
+TMP_324))))))) in (let TMP_320 \def (\lambda (n: nat).(let TMP_318 \def 
+(THead k t t0) in (let TMP_317 \def (TLRef n) in (let TMP_319 \def (eq T 
+TMP_318 TMP_317) in (let TMP_316 \def ((eq T (THead k t t0) (TLRef n)) \to 
+(\forall (P: Prop).P)) in (let TMP_315 \def (\lambda (H1: (eq T (THead k t 
+t0) (TLRef n))).(\lambda (P: Prop).(let TMP_314 \def (THead k t t0) in (let 
+TMP_313 \def (\lambda (ee: T).(match ee in T with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) in 
+(let TMP_312 \def (TLRef n) in (let H2 \def (eq_ind T TMP_314 TMP_313 I 
+TMP_312 H1) in (False_ind P H2))))))) in (or_intror TMP_319 TMP_316 
+TMP_315))))))) in (let TMP_311 \def (\lambda (k0: K).(\lambda (t3: 
+T).(\lambda (H1: (or (eq T (THead k t t0) t3) ((eq T (THead k t t0) t3) \to 
+(\forall (P: Prop).P)))).(\lambda (t4: T).(\lambda (H2: (or (eq T (THead k t 
+t0) t4) ((eq T (THead k t t0) t4) \to (\forall (P: Prop).P)))).(let H_x \def 
+(H t3) in (let H3 \def H_x in (let TMP_310 \def (eq T t t3) in (let TMP_309 
+\def ((eq T t t3) \to (\forall (P: Prop).P)) in (let TMP_306 \def (THead k t 
+t0) in (let TMP_305 \def (THead k0 t3 t4) in (let TMP_307 \def (eq T TMP_306 
+TMP_305) in (let TMP_304 \def ((eq T (THead k t t0) (THead k0 t3 t4)) \to 
+(\forall (P: Prop).P)) in (let TMP_308 \def (or TMP_307 TMP_304) in (let 
+TMP_303 \def (\lambda (H4: (eq T t t3)).(let TMP_228 \def (\lambda (t5: 
+T).(let TMP_226 \def (THead k t t0) in (let TMP_227 \def (eq T TMP_226 t5) in 
+(let TMP_225 \def ((eq T (THead k t t0) t5) \to (\forall (P: Prop).P)) in (or 
+TMP_227 TMP_225))))) in (let H5 \def (eq_ind_r T t3 TMP_228 H1 t H4) in (let 
+TMP_302 \def (\lambda (t5: T).(let TMP_300 \def (THead k t t0) in (let 
+TMP_299 \def (THead k0 t5 t4) in (let TMP_301 \def (eq T TMP_300 TMP_299) in 
+(let TMP_298 \def ((eq T (THead k t t0) (THead k0 t5 t4)) \to (\forall (P: 
+Prop).P)) in (or TMP_301 TMP_298)))))) in (let H_x0 \def (H0 t4) in (let H6 
+\def H_x0 in (let TMP_296 \def (eq T t0 t4) in (let TMP_295 \def ((eq T t0 
+t4) \to (\forall (P: Prop).P)) in (let TMP_292 \def (THead k t t0) in (let 
+TMP_291 \def (THead k0 t t4) in (let TMP_293 \def (eq T TMP_292 TMP_291) in 
+(let TMP_290 \def ((eq T (THead k t t0) (THead k0 t t4)) \to (\forall (P: 
+Prop).P)) in (let TMP_294 \def (or TMP_293 TMP_290) in (let TMP_289 \def 
+(\lambda (H7: (eq T t0 t4)).(let TMP_251 \def (\lambda (t5: T).(let TMP_249 
+\def (THead k t t0) in (let TMP_250 \def (eq T TMP_249 t5) in (let TMP_248 
+\def ((eq T (THead k t t0) t5) \to (\forall (P: Prop).P)) in (or TMP_250 
+TMP_248))))) in (let H8 \def (eq_ind_r T t4 TMP_251 H2 t0 H7) in (let TMP_288 
+\def (\lambda (t5: T).(let TMP_286 \def (THead k t t0) in (let TMP_285 \def 
+(THead k0 t t5) in (let TMP_287 \def (eq T TMP_286 TMP_285) in (let TMP_284 
+\def ((eq T (THead k t t0) (THead k0 t t5)) \to (\forall (P: Prop).P)) in (or 
+TMP_287 TMP_284)))))) in (let H_x1 \def (terms_props__kind_dec k k0) in (let 
+H9 \def H_x1 in (let TMP_282 \def (eq K k k0) in (let TMP_281 \def ((eq K k 
+k0) \to (\forall (P: Prop).P)) in (let TMP_278 \def (THead k t t0) in (let 
+TMP_277 \def (THead k0 t t0) in (let TMP_279 \def (eq T TMP_278 TMP_277) in 
+(let TMP_276 \def ((eq T (THead k t t0) (THead k0 t t0)) \to (\forall (P: 
+Prop).P)) in (let TMP_280 \def (or TMP_279 TMP_276) in (let TMP_275 \def 
+(\lambda (H10: (eq K k k0)).(let TMP_274 \def (\lambda (k1: K).(let TMP_272 
+\def (THead k t t0) in (let TMP_271 \def (THead k1 t t0) in (let TMP_273 \def 
+(eq T TMP_272 TMP_271) in (let TMP_270 \def ((eq T (THead k t t0) (THead k1 t 
+t0)) \to (\forall (P: Prop).P)) in (or TMP_273 TMP_270)))))) in (let TMP_267 
+\def (THead k t t0) in (let TMP_266 \def (THead k t t0) in (let TMP_268 \def 
+(eq T TMP_267 TMP_266) in (let TMP_265 \def ((eq T (THead k t t0) (THead k t 
+t0)) \to (\forall (P: Prop).P)) in (let TMP_263 \def (THead k t t0) in (let 
+TMP_264 \def (refl_equal T TMP_263) in (let TMP_269 \def (or_introl TMP_268 
+TMP_265 TMP_264) in (eq_ind K k TMP_274 TMP_269 k0 H10)))))))))) in (let 
+TMP_262 \def (\lambda (H10: (((eq K k k0) \to (\forall (P: Prop).P)))).(let 
+TMP_260 \def (THead k t t0) in (let TMP_259 \def (THead k0 t t0) in (let 
+TMP_261 \def (eq T TMP_260 TMP_259) in (let TMP_258 \def ((eq T (THead k t 
+t0) (THead k0 t t0)) \to (\forall (P: Prop).P)) in (let TMP_257 \def (\lambda 
+(H11: (eq T (THead k t t0) (THead k0 t t0))).(\lambda (P: Prop).(let TMP_254 
+\def (\lambda (e: T).(match e in T with [(TSort _) \Rightarrow k | (TLRef _) 
+\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in (let TMP_253 \def (THead 
+k t t0) in (let TMP_252 \def (THead k0 t t0) in (let H12 \def (f_equal T K 
+TMP_254 TMP_253 TMP_252 H11) in (let TMP_255 \def (\lambda (k1: K).((eq K k 
+k1) \to (\forall (P0: Prop).P0))) in (let H13 \def (eq_ind_r K k0 TMP_255 H10 
+k H12) in (let TMP_256 \def (refl_equal K k) in (H13 TMP_256 P)))))))))) in 
+(or_intror TMP_261 TMP_258 TMP_257))))))) in (let TMP_283 \def (or_ind 
+TMP_282 TMP_281 TMP_280 TMP_275 TMP_262 H9) in (eq_ind T t0 TMP_288 TMP_283 
+t4 H7))))))))))))))))) in (let TMP_247 \def (\lambda (H7: (((eq T t0 t4) \to 
+(\forall (P: Prop).P)))).(let TMP_245 \def (THead k t t0) in (let TMP_244 
+\def (THead k0 t t4) in (let TMP_246 \def (eq T TMP_245 TMP_244) in (let 
+TMP_243 \def ((eq T (THead k t t0) (THead k0 t t4)) \to (\forall (P: 
+Prop).P)) in (let TMP_242 \def (\lambda (H8: (eq T (THead k t t0) (THead k0 t 
+t4))).(\lambda (P: Prop).(let TMP_231 \def (\lambda (e: T).(match e in T with 
+[(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _) 
+\Rightarrow k1])) in (let TMP_230 \def (THead k t t0) in (let TMP_229 \def 
+(THead k0 t t4) in (let H9 \def (f_equal T K TMP_231 TMP_230 TMP_229 H8) in 
+(let TMP_234 \def (\lambda (e: T).(match e in T with [(TSort _) \Rightarrow 
+t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t5) \Rightarrow t5])) in (let 
+TMP_233 \def (THead k t t0) in (let TMP_232 \def (THead k0 t t4) in (let H10 
+\def (f_equal T T TMP_234 TMP_233 TMP_232 H8) in (let TMP_241 \def (\lambda 
+(_: (eq K k k0)).(let TMP_235 \def (\lambda (t5: T).((eq T t0 t5) \to 
+(\forall (P0: Prop).P0))) in (let H12 \def (eq_ind_r T t4 TMP_235 H7 t0 H10) 
+in (let TMP_239 \def (\lambda (t5: T).(let TMP_237 \def (THead k t t0) in 
+(let TMP_238 \def (eq T TMP_237 t5) in (let TMP_236 \def ((eq T (THead k t 
+t0) t5) \to (\forall (P0: Prop).P0)) in (or TMP_238 TMP_236))))) in (let H13 
+\def (eq_ind_r T t4 TMP_239 H2 t0 H10) in (let TMP_240 \def (refl_equal T t0) 
+in (H12 TMP_240 P))))))) in (TMP_241 H9)))))))))))) in (or_intror TMP_246 
+TMP_243 TMP_242))))))) in (let TMP_297 \def (or_ind TMP_296 TMP_295 TMP_294 
+TMP_289 TMP_247 H6) in (eq_ind T t TMP_302 TMP_297 t3 H4))))))))))))))))) in 
+(let TMP_224 \def (\lambda (H4: (((eq T t t3) \to (\forall (P: 
+Prop).P)))).(let TMP_222 \def (THead k t t0) in (let TMP_221 \def (THead k0 
+t3 t4) in (let TMP_223 \def (eq T TMP_222 TMP_221) in (let TMP_220 \def ((eq 
+T (THead k t t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) in (let TMP_219 
+\def (\lambda (H5: (eq T (THead k t t0) (THead k0 t3 t4))).(\lambda (P: 
+Prop).(let TMP_200 \def (\lambda (e: T).(match e in T with [(TSort _) 
+\Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in 
+(let TMP_199 \def (THead k t t0) in (let TMP_198 \def (THead k0 t3 t4) in 
+(let H6 \def (f_equal T K TMP_200 TMP_199 TMP_198 H5) in (let TMP_203 \def 
+(\lambda (e: T).(match e in T with [(TSort _) \Rightarrow t | (TLRef _) 
+\Rightarrow t | (THead _ t5 _) \Rightarrow t5])) in (let TMP_202 \def (THead 
+k t t0) in (let TMP_201 \def (THead k0 t3 t4) in (let H7 \def (f_equal T T 
+TMP_203 TMP_202 TMP_201 H5) in (let TMP_206 \def (\lambda (e: T).(match e in 
+T with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t5) 
+\Rightarrow t5])) in (let TMP_205 \def (THead k t t0) in (let TMP_204 \def 
+(THead k0 t3 t4) in (let H8 \def (f_equal T T TMP_206 TMP_205 TMP_204 H5) in 
+(let TMP_217 \def (\lambda (H9: (eq T t t3)).(\lambda (_: (eq K k k0)).(let 
+TMP_210 \def (\lambda (t5: T).(let TMP_208 \def (THead k t t0) in (let 
+TMP_209 \def (eq T TMP_208 t5) in (let TMP_207 \def ((eq T (THead k t t0) t5) 
+\to (\forall (P0: Prop).P0)) in (or TMP_209 TMP_207))))) in (let H11 \def 
+(eq_ind_r T t4 TMP_210 H2 t0 H8) in (let TMP_211 \def (\lambda (t5: T).((eq T 
+t t5) \to (\forall (P0: Prop).P0))) in (let H12 \def (eq_ind_r T t3 TMP_211 
+H4 t H9) in (let TMP_215 \def (\lambda (t5: T).(let TMP_213 \def (THead k t 
+t0) in (let TMP_214 \def (eq T TMP_213 t5) in (let TMP_212 \def ((eq T (THead 
+k t t0) t5) \to (\forall (P0: Prop).P0)) in (or TMP_214 TMP_212))))) in (let 
+H13 \def (eq_ind_r T t3 TMP_215 H1 t H9) in (let TMP_216 \def (refl_equal T 
+t) in (H12 TMP_216 P)))))))))) in (let TMP_218 \def (TMP_217 H7) in (TMP_218 
+H6))))))))))))))))) in (or_intror TMP_223 TMP_220 TMP_219))))))) in (or_ind 
+TMP_310 TMP_309 TMP_308 TMP_303 TMP_224 H3))))))))))))))))) in (T_ind TMP_333 
+TMP_329 TMP_320 TMP_311 t2))))))))))) in (T_ind TMP_447 TMP_444 TMP_389 
+TMP_334 t1))))).
 
 theorem binder_dec:
  \forall (t: T).(or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: 
 T).(eq T t (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall 
 (u: T).((eq T t (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))
 \def
- \lambda (t: T).(T_ind (\lambda (t0: T).(or (ex_3 B T T (\lambda (b: 
-B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w u)))))) 
-(\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b) w 
-u)) \to (\forall (P: Prop).P))))))) (\lambda (n: nat).(or_intror (ex_3 B T T 
-(\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T (TSort n) (THead (Bind 
-b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (TSort n) 
-(THead (Bind b) w u)) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda 
-(w: T).(\lambda (u: T).(\lambda (H: (eq T (TSort n) (THead (Bind b) w 
-u))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TSort n) (\lambda (ee: 
-T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow 
-True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I 
-(THead (Bind b) w u) H) in (False_ind P H0))))))))) (\lambda (n: 
-nat).(or_intror (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: 
-T).(eq T (TLRef n) (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: 
-T).(\forall (u: T).((eq T (TLRef n) (THead (Bind b) w u)) \to (\forall (P: 
-Prop).P))))) (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(\lambda (H: (eq 
-T (TLRef n) (THead (Bind b) w u))).(\lambda (P: Prop).(let H0 \def (eq_ind T 
-(TLRef n) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with 
-[(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) 
-\Rightarrow False])) I (THead (Bind b) w u) H) in (False_ind P H0))))))))) 
-(\lambda (k: K).(K_ind (\lambda (k0: K).(\forall (t0: T).((or (ex_3 B T T 
-(\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w 
-u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead 
-(Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (\forall (t1: T).((or (ex_3 
-B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind 
-b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead 
-(Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (or (ex_3 B T T (\lambda 
-(b: B).(\lambda (w: T).(\lambda (u: T).(eq T (THead k0 t0 t1) (THead (Bind b) 
-w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (THead k0 t0 
-t1) (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))))))) (\lambda (b: 
-B).(\lambda (t0: T).(\lambda (_: (or (ex_3 B T T (\lambda (b0: B).(\lambda 
-(w: T).(\lambda (u: T).(eq T t0 (THead (Bind b0) w u)))))) (\forall (b0: 
-B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b0) w u)) \to 
-(\forall (P: Prop).P))))))).(\lambda (t1: T).(\lambda (_: (or (ex_3 B T T 
-(\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind b0) w 
-u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead 
-(Bind b0) w u)) \to (\forall (P: Prop).P))))))).(or_introl (ex_3 B T T 
-(\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T (THead (Bind b) t0 t1) 
-(THead (Bind b0) w u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u: 
-T).((eq T (THead (Bind b) t0 t1) (THead (Bind b0) w u)) \to (\forall (P: 
-Prop).P))))) (ex_3_intro B T T (\lambda (b0: B).(\lambda (w: T).(\lambda (u: 
-T).(eq T (THead (Bind b) t0 t1) (THead (Bind b0) w u))))) b t0 t1 (refl_equal 
-T (THead (Bind b) t0 t1))))))))) (\lambda (f: F).(\lambda (t0: T).(\lambda 
-(_: (or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0 
+ \lambda (t: T).(let TMP_516 \def (\lambda (t0: T).(let TMP_514 \def (\lambda 
+(b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_512 \def (Bind b) in (let 
+TMP_513 \def (THead TMP_512 w u) in (eq T t0 TMP_513)))))) in (let TMP_515 
+\def (ex_3 B T T TMP_514) in (let TMP_511 \def (\forall (b: B).(\forall (w: 
+T).(\forall (u: T).((eq T t0 (THead (Bind b) w u)) \to (\forall (P: 
+Prop).P))))) in (or TMP_515 TMP_511))))) in (let TMP_510 \def (\lambda (n: 
+nat).(let TMP_508 \def (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(let 
+TMP_507 \def (TSort n) in (let TMP_505 \def (Bind b) in (let TMP_506 \def 
+(THead TMP_505 w u) in (eq T TMP_507 TMP_506))))))) in (let TMP_509 \def 
+(ex_3 B T T TMP_508) in (let TMP_504 \def (\forall (b: B).(\forall (w: 
+T).(\forall (u: T).((eq T (TSort n) (THead (Bind b) w u)) \to (\forall (P: 
+Prop).P))))) in (let TMP_503 \def (\lambda (b: B).(\lambda (w: T).(\lambda 
+(u: T).(\lambda (H: (eq T (TSort n) (THead (Bind b) w u))).(\lambda (P: 
+Prop).(let TMP_502 \def (TSort n) in (let TMP_501 \def (\lambda (ee: 
+T).(match ee in T with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow 
+False | (THead _ _ _) \Rightarrow False])) in (let TMP_499 \def (Bind b) in 
+(let TMP_500 \def (THead TMP_499 w u) in (let H0 \def (eq_ind T TMP_502 
+TMP_501 I TMP_500 H) in (False_ind P H0))))))))))) in (or_intror TMP_509 
+TMP_504 TMP_503)))))) in (let TMP_498 \def (\lambda (n: nat).(let TMP_496 
+\def (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_495 \def (TLRef 
+n) in (let TMP_493 \def (Bind b) in (let TMP_494 \def (THead TMP_493 w u) in 
+(eq T TMP_495 TMP_494))))))) in (let TMP_497 \def (ex_3 B T T TMP_496) in 
+(let TMP_492 \def (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T 
+(TLRef n) (THead (Bind b) w u)) \to (\forall (P: Prop).P))))) in (let TMP_491 
+\def (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(\lambda (H: (eq T 
+(TLRef n) (THead (Bind b) w u))).(\lambda (P: Prop).(let TMP_490 \def (TLRef 
+n) in (let TMP_489 \def (\lambda (ee: T).(match ee in T with [(TSort _) 
+\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow 
+False])) in (let TMP_487 \def (Bind b) in (let TMP_488 \def (THead TMP_487 w 
+u) in (let H0 \def (eq_ind T TMP_490 TMP_489 I TMP_488 H) in (False_ind P 
+H0))))))))))) in (or_intror TMP_497 TMP_492 TMP_491)))))) in (let TMP_486 
+\def (\lambda (k: K).(let TMP_485 \def (\lambda (k0: K).(\forall (t0: T).((or 
+(ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead 
+(Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 
+(THead (Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (\forall (t1: 
+T).((or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 
 (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: 
-T).((eq T t0 (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))).(\lambda 
-(t1: T).(\lambda (_: (or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda 
-(u: T).(eq T t1 (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: 
-T).(\forall (u: T).((eq T t1 (THead (Bind b) w u)) \to (\forall (P: 
-Prop).P))))))).(or_intror (ex_3 B T T (\lambda (b: B).(\lambda (w: 
-T).(\lambda (u: T).(eq T (THead (Flat f) t0 t1) (THead (Bind b) w u)))))) 
-(\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (THead (Flat f) t0 t1) 
-(THead (Bind b) w u)) \to (\forall (P: Prop).P))))) (\lambda (b: B).(\lambda 
-(w: T).(\lambda (u: T).(\lambda (H1: (eq T (THead (Flat f) t0 t1) (THead 
-(Bind b) w u))).(\lambda (P: Prop).(let H2 \def (eq_ind T (THead (Flat f) t0 
-t1) (\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort 
-_) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k0 _ _) 
-\Rightarrow (match k0 in K return (\lambda (_: K).Prop) with [(Bind _) 
-\Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind b) w u) H1) 
-in (False_ind P H2))))))))))))) k)) t).
-(* COMMENTS
-Initial nodes: 1063
-END *)
+T).((eq T t1 (THead (Bind b) w u)) \to (\forall (P: Prop).P)))))) \to (let 
+TMP_483 \def (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_482 
+\def (THead k0 t0 t1) in (let TMP_480 \def (Bind b) in (let TMP_481 \def 
+(THead TMP_480 w u) in (eq T TMP_482 TMP_481))))))) in (let TMP_484 \def 
+(ex_3 B T T TMP_483) in (let TMP_479 \def (\forall (b: B).(\forall (w: 
+T).(\forall (u: T).((eq T (THead k0 t0 t1) (THead (Bind b) w u)) \to (\forall 
+(P: Prop).P))))) in (or TMP_484 TMP_479))))))))) in (let TMP_478 \def 
+(\lambda (b: B).(\lambda (t0: T).(\lambda (_: (or (ex_3 B T T (\lambda (b0: 
+B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b0) w u)))))) 
+(\forall (b0: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b0) w 
+u)) \to (\forall (P: Prop).P))))))).(\lambda (t1: T).(\lambda (_: (or (ex_3 B 
+T T (\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind 
+b0) w u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u: T).((eq T t1 
+(THead (Bind b0) w u)) \to (\forall (P: Prop).P))))))).(let TMP_476 \def 
+(\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(let TMP_474 \def (Bind b) 
+in (let TMP_475 \def (THead TMP_474 t0 t1) in (let TMP_472 \def (Bind b0) in 
+(let TMP_473 \def (THead TMP_472 w u) in (eq T TMP_475 TMP_473)))))))) in 
+(let TMP_477 \def (ex_3 B T T TMP_476) in (let TMP_471 \def (\forall (b0: 
+B).(\forall (w: T).(\forall (u: T).((eq T (THead (Bind b) t0 t1) (THead (Bind 
+b0) w u)) \to (\forall (P: Prop).P))))) in (let TMP_469 \def (\lambda (b0: 
+B).(\lambda (w: T).(\lambda (u: T).(let TMP_467 \def (Bind b) in (let TMP_468 
+\def (THead TMP_467 t0 t1) in (let TMP_465 \def (Bind b0) in (let TMP_466 
+\def (THead TMP_465 w u) in (eq T TMP_468 TMP_466)))))))) in (let TMP_462 
+\def (Bind b) in (let TMP_463 \def (THead TMP_462 t0 t1) in (let TMP_464 \def 
+(refl_equal T TMP_463) in (let TMP_470 \def (ex_3_intro B T T TMP_469 b t0 t1 
+TMP_464) in (or_introl TMP_477 TMP_471 TMP_470)))))))))))))) in (let TMP_461 
+\def (\lambda (f: F).(\lambda (t0: T).(\lambda (_: (or (ex_3 B T T (\lambda 
+(b: B).(\lambda (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w u)))))) 
+(\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b) w 
+u)) \to (\forall (P: Prop).P))))))).(\lambda (t1: T).(\lambda (_: (or (ex_3 B 
+T T (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind b) 
+w u)))))) (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead 
+(Bind b) w u)) \to (\forall (P: Prop).P))))))).(let TMP_459 \def (\lambda (b: 
+B).(\lambda (w: T).(\lambda (u: T).(let TMP_457 \def (Flat f) in (let TMP_458 
+\def (THead TMP_457 t0 t1) in (let TMP_455 \def (Bind b) in (let TMP_456 \def 
+(THead TMP_455 w u) in (eq T TMP_458 TMP_456)))))))) in (let TMP_460 \def 
+(ex_3 B T T TMP_459) in (let TMP_454 \def (\forall (b: B).(\forall (w: 
+T).(\forall (u: T).((eq T (THead (Flat f) t0 t1) (THead (Bind b) w u)) \to 
+(\forall (P: Prop).P))))) in (let TMP_453 \def (\lambda (b: B).(\lambda (w: 
+T).(\lambda (u: T).(\lambda (H1: (eq T (THead (Flat f) t0 t1) (THead (Bind b) 
+w u))).(\lambda (P: Prop).(let TMP_451 \def (Flat f) in (let TMP_452 \def 
+(THead TMP_451 t0 t1) in (let TMP_450 \def (\lambda (ee: T).(match ee in T 
+with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k0 _ 
+_) \Rightarrow (match k0 in K with [(Bind _) \Rightarrow False | (Flat _) 
+\Rightarrow True])])) in (let TMP_448 \def (Bind b) in (let TMP_449 \def 
+(THead TMP_448 w u) in (let H2 \def (eq_ind T TMP_452 TMP_450 I TMP_449 H1) 
+in (False_ind P H2)))))))))))) in (or_intror TMP_460 TMP_454 
+TMP_453)))))))))) in (K_ind TMP_485 TMP_478 TMP_461 k))))) in (T_ind TMP_516 
+TMP_510 TMP_498 TMP_486 t))))).
 
 theorem abst_dec:
  \forall (u: T).(\forall (v: T).(or (ex T (\lambda (t: T).(eq T u (THead 
 (Bind Abst) v t)))) (\forall (t: T).((eq T u (THead (Bind Abst) v t)) \to 
 (\forall (P: Prop).P)))))
 \def
- \lambda (u: T).(T_ind (\lambda (t: T).(\forall (v: T).(or (ex T (\lambda 
-(t0: T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T t (THead 
-(Bind Abst) v t0)) \to (\forall (P: Prop).P)))))) (\lambda (n: nat).(\lambda 
-(v: T).(or_intror (ex T (\lambda (t: T).(eq T (TSort n) (THead (Bind Abst) v 
-t)))) (\forall (t: T).((eq T (TSort n) (THead (Bind Abst) v t)) \to (\forall 
-(P: Prop).P))) (\lambda (t: T).(\lambda (H: (eq T (TSort n) (THead (Bind 
-Abst) v t))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TSort n) (\lambda 
-(ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) 
-\Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow 
-False])) I (THead (Bind Abst) v t) H) in (False_ind P H0)))))))) (\lambda (n: 
-nat).(\lambda (v: T).(or_intror (ex T (\lambda (t: T).(eq T (TLRef n) (THead 
-(Bind Abst) v t)))) (\forall (t: T).((eq T (TLRef n) (THead (Bind Abst) v t)) 
-\to (\forall (P: Prop).P))) (\lambda (t: T).(\lambda (H: (eq T (TLRef n) 
-(THead (Bind Abst) v t))).(\lambda (P: Prop).(let H0 \def (eq_ind T (TLRef n) 
-(\lambda (ee: T).(match ee in T return (\lambda (_: T).Prop) with [(TSort _) 
-\Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow 
-False])) I (THead (Bind Abst) v t) H) in (False_ind P H0)))))))) (\lambda (k: 
-K).(\lambda (t: T).(\lambda (_: ((\forall (v: T).(or (ex T (\lambda (t0: 
-T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T t (THead (Bind 
-Abst) v t0)) \to (\forall (P: Prop).P))))))).(\lambda (t0: T).(\lambda (_: 
-((\forall (v: T).(or (ex T (\lambda (t1: T).(eq T t0 (THead (Bind Abst) v 
-t1)))) (\forall (t1: T).((eq T t0 (THead (Bind Abst) v t1)) \to (\forall (P: 
-Prop).P))))))).(\lambda (v: T).(let H_x \def (terms_props__kind_dec k (Bind 
-Abst)) in (let H1 \def H_x in (or_ind (eq K k (Bind Abst)) ((eq K k (Bind 
-Abst)) \to (\forall (P: Prop).P)) (or (ex T (\lambda (t1: T).(eq T (THead k t 
-t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead k t t0) (THead 
-(Bind Abst) v t1)) \to (\forall (P: Prop).P)))) (\lambda (H2: (eq K k (Bind 
-Abst))).(eq_ind_r K (Bind Abst) (\lambda (k0: K).(or (ex T (\lambda (t1: 
-T).(eq T (THead k0 t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T 
-(THead k0 t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))))) (let 
-H_x0 \def (term_dec t v) in (let H3 \def H_x0 in (or_ind (eq T t v) ((eq T t 
-v) \to (\forall (P: Prop).P)) (or (ex T (\lambda (t1: T).(eq T (THead (Bind 
-Abst) t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead (Bind 
-Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P)))) (\lambda 
-(H4: (eq T t v)).(eq_ind T t (\lambda (t1: T).(or (ex T (\lambda (t2: T).(eq 
-T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2)))) (\forall (t2: T).((eq 
-T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2)) \to (\forall (P: 
-Prop).P))))) (or_introl (ex T (\lambda (t1: T).(eq T (THead (Bind Abst) t t0) 
-(THead (Bind Abst) t t1)))) (\forall (t1: T).((eq T (THead (Bind Abst) t t0) 
-(THead (Bind Abst) t t1)) \to (\forall (P: Prop).P))) (ex_intro T (\lambda 
-(t1: T).(eq T (THead (Bind Abst) t t0) (THead (Bind Abst) t t1))) t0 
-(refl_equal T (THead (Bind Abst) t t0)))) v H4)) (\lambda (H4: (((eq T t v) 
-\to (\forall (P: Prop).P)))).(or_intror (ex T (\lambda (t1: T).(eq T (THead 
-(Bind Abst) t t0) (THead (Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead 
-(Bind Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) 
-(\lambda (t1: T).(\lambda (H5: (eq T (THead (Bind Abst) t t0) (THead (Bind 
-Abst) v t1))).(\lambda (P: Prop).(let H6 \def (f_equal T T (\lambda (e: 
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t | 
-(TLRef _) \Rightarrow t | (THead _ t2 _) \Rightarrow t2])) (THead (Bind Abst) 
-t t0) (THead (Bind Abst) v t1) H5) in ((let H7 \def (f_equal T T (\lambda (e: 
-T).(match e in T return (\lambda (_: T).T) with [(TSort _) \Rightarrow t0 | 
-(TLRef _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) (THead (Bind 
-Abst) t t0) (THead (Bind Abst) v t1) H5) in (\lambda (H8: (eq T t v)).(H4 H8 
-P))) H6))))))) H3))) k H2)) (\lambda (H2: (((eq K k (Bind Abst)) \to (\forall 
-(P: Prop).P)))).(or_intror (ex T (\lambda (t1: T).(eq T (THead k t t0) (THead 
-(Bind Abst) v t1)))) (\forall (t1: T).((eq T (THead k t t0) (THead (Bind 
-Abst) v t1)) \to (\forall (P: Prop).P))) (\lambda (t1: T).(\lambda (H3: (eq T 
-(THead k t t0) (THead (Bind Abst) v t1))).(\lambda (P: Prop).(let H4 \def 
-(f_equal T K (\lambda (e: T).(match e in T return (\lambda (_: T).K) with 
+ \lambda (u: T).(let TMP_646 \def (\lambda (t: T).(\forall (v: T).(let 
+TMP_644 \def (\lambda (t0: T).(let TMP_642 \def (Bind Abst) in (let TMP_643 
+\def (THead TMP_642 v t0) in (eq T t TMP_643)))) in (let TMP_645 \def (ex T 
+TMP_644) in (let TMP_641 \def (\forall (t0: T).((eq T t (THead (Bind Abst) v 
+t0)) \to (\forall (P: Prop).P))) in (or TMP_645 TMP_641)))))) in (let TMP_640 
+\def (\lambda (n: nat).(\lambda (v: T).(let TMP_638 \def (\lambda (t: T).(let 
+TMP_637 \def (TSort n) in (let TMP_635 \def (Bind Abst) in (let TMP_636 \def 
+(THead TMP_635 v t) in (eq T TMP_637 TMP_636))))) in (let TMP_639 \def (ex T 
+TMP_638) in (let TMP_634 \def (\forall (t: T).((eq T (TSort n) (THead (Bind 
+Abst) v t)) \to (\forall (P: Prop).P))) in (let TMP_633 \def (\lambda (t: 
+T).(\lambda (H: (eq T (TSort n) (THead (Bind Abst) v t))).(\lambda (P: 
+Prop).(let TMP_632 \def (TSort n) in (let TMP_631 \def (\lambda (ee: 
+T).(match ee in T with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow 
+False | (THead _ _ _) \Rightarrow False])) in (let TMP_629 \def (Bind Abst) 
+in (let TMP_630 \def (THead TMP_629 v t) in (let H0 \def (eq_ind T TMP_632 
+TMP_631 I TMP_630 H) in (False_ind P H0))))))))) in (or_intror TMP_639 
+TMP_634 TMP_633))))))) in (let TMP_628 \def (\lambda (n: nat).(\lambda (v: 
+T).(let TMP_626 \def (\lambda (t: T).(let TMP_625 \def (TLRef n) in (let 
+TMP_623 \def (Bind Abst) in (let TMP_624 \def (THead TMP_623 v t) in (eq T 
+TMP_625 TMP_624))))) in (let TMP_627 \def (ex T TMP_626) in (let TMP_622 \def 
+(\forall (t: T).((eq T (TLRef n) (THead (Bind Abst) v t)) \to (\forall (P: 
+Prop).P))) in (let TMP_621 \def (\lambda (t: T).(\lambda (H: (eq T (TLRef n) 
+(THead (Bind Abst) v t))).(\lambda (P: Prop).(let TMP_620 \def (TLRef n) in 
+(let TMP_619 \def (\lambda (ee: T).(match ee in T with [(TSort _) \Rightarrow 
+False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) in 
+(let TMP_617 \def (Bind Abst) in (let TMP_618 \def (THead TMP_617 v t) in 
+(let H0 \def (eq_ind T TMP_620 TMP_619 I TMP_618 H) in (False_ind P 
+H0))))))))) in (or_intror TMP_627 TMP_622 TMP_621))))))) in (let TMP_616 \def 
+(\lambda (k: K).(\lambda (t: T).(\lambda (_: ((\forall (v: T).(or (ex T 
+(\lambda (t0: T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T 
+t (THead (Bind Abst) v t0)) \to (\forall (P: Prop).P))))))).(\lambda (t0: 
+T).(\lambda (_: ((\forall (v: T).(or (ex T (\lambda (t1: T).(eq T t0 (THead 
+(Bind Abst) v t1)))) (\forall (t1: T).((eq T t0 (THead (Bind Abst) v t1)) \to 
+(\forall (P: Prop).P))))))).(\lambda (v: T).(let TMP_517 \def (Bind Abst) in 
+(let H_x \def (terms_props__kind_dec k TMP_517) in (let H1 \def H_x in (let 
+TMP_614 \def (Bind Abst) in (let TMP_615 \def (eq K k TMP_614) in (let 
+TMP_613 \def ((eq K k (Bind Abst)) \to (\forall (P: Prop).P)) in (let TMP_610 
+\def (\lambda (t1: T).(let TMP_609 \def (THead k t t0) in (let TMP_607 \def 
+(Bind Abst) in (let TMP_608 \def (THead TMP_607 v t1) in (eq T TMP_609 
+TMP_608))))) in (let TMP_611 \def (ex T TMP_610) in (let TMP_606 \def 
+(\forall (t1: T).((eq T (THead k t t0) (THead (Bind Abst) v t1)) \to (\forall 
+(P: Prop).P))) in (let TMP_612 \def (or TMP_611 TMP_606) in (let TMP_605 \def 
+(\lambda (H2: (eq K k (Bind Abst))).(let TMP_604 \def (Bind Abst) in (let 
+TMP_603 \def (\lambda (k0: K).(let TMP_601 \def (\lambda (t1: T).(let TMP_600 
+\def (THead k0 t t0) in (let TMP_598 \def (Bind Abst) in (let TMP_599 \def 
+(THead TMP_598 v t1) in (eq T TMP_600 TMP_599))))) in (let TMP_602 \def (ex T 
+TMP_601) in (let TMP_597 \def (\forall (t1: T).((eq T (THead k0 t t0) (THead 
+(Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (or TMP_602 TMP_597))))) in 
+(let H_x0 \def (term_dec t v) in (let H3 \def H_x0 in (let TMP_595 \def (eq T 
+t v) in (let TMP_594 \def ((eq T t v) \to (\forall (P: Prop).P)) in (let 
+TMP_591 \def (\lambda (t1: T).(let TMP_589 \def (Bind Abst) in (let TMP_590 
+\def (THead TMP_589 t t0) in (let TMP_587 \def (Bind Abst) in (let TMP_588 
+\def (THead TMP_587 v t1) in (eq T TMP_590 TMP_588)))))) in (let TMP_592 \def 
+(ex T TMP_591) in (let TMP_586 \def (\forall (t1: T).((eq T (THead (Bind 
+Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let 
+TMP_593 \def (or TMP_592 TMP_586) in (let TMP_585 \def (\lambda (H4: (eq T t 
+v)).(let TMP_584 \def (\lambda (t1: T).(let TMP_582 \def (\lambda (t2: 
+T).(let TMP_580 \def (Bind Abst) in (let TMP_581 \def (THead TMP_580 t t0) in 
+(let TMP_578 \def (Bind Abst) in (let TMP_579 \def (THead TMP_578 t1 t2) in 
+(eq T TMP_581 TMP_579)))))) in (let TMP_583 \def (ex T TMP_582) in (let 
+TMP_577 \def (\forall (t2: T).((eq T (THead (Bind Abst) t t0) (THead (Bind 
+Abst) t1 t2)) \to (\forall (P: Prop).P))) in (or TMP_583 TMP_577))))) in (let 
+TMP_574 \def (\lambda (t1: T).(let TMP_572 \def (Bind Abst) in (let TMP_573 
+\def (THead TMP_572 t t0) in (let TMP_570 \def (Bind Abst) in (let TMP_571 
+\def (THead TMP_570 t t1) in (eq T TMP_573 TMP_571)))))) in (let TMP_575 \def 
+(ex T TMP_574) in (let TMP_569 \def (\forall (t1: T).((eq T (THead (Bind 
+Abst) t t0) (THead (Bind Abst) t t1)) \to (\forall (P: Prop).P))) in (let 
+TMP_567 \def (\lambda (t1: T).(let TMP_565 \def (Bind Abst) in (let TMP_566 
+\def (THead TMP_565 t t0) in (let TMP_563 \def (Bind Abst) in (let TMP_564 
+\def (THead TMP_563 t t1) in (eq T TMP_566 TMP_564)))))) in (let TMP_560 \def 
+(Bind Abst) in (let TMP_561 \def (THead TMP_560 t t0) in (let TMP_562 \def 
+(refl_equal T TMP_561) in (let TMP_568 \def (ex_intro T TMP_567 t0 TMP_562) 
+in (let TMP_576 \def (or_introl TMP_575 TMP_569 TMP_568) in (eq_ind T t 
+TMP_584 TMP_576 v H4)))))))))))) in (let TMP_559 \def (\lambda (H4: (((eq T t 
+v) \to (\forall (P: Prop).P)))).(let TMP_557 \def (\lambda (t1: T).(let 
+TMP_555 \def (Bind Abst) in (let TMP_556 \def (THead TMP_555 t t0) in (let 
+TMP_553 \def (Bind Abst) in (let TMP_554 \def (THead TMP_553 v t1) in (eq T 
+TMP_556 TMP_554)))))) in (let TMP_558 \def (ex T TMP_557) in (let TMP_552 
+\def (\forall (t1: T).((eq T (THead (Bind Abst) t t0) (THead (Bind Abst) v 
+t1)) \to (\forall (P: Prop).P))) in (let TMP_551 \def (\lambda (t1: 
+T).(\lambda (H5: (eq T (THead (Bind Abst) t t0) (THead (Bind Abst) v 
+t1))).(\lambda (P: Prop).(let TMP_544 \def (\lambda (e: T).(match e in T with 
+[(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t2 _) 
+\Rightarrow t2])) in (let TMP_542 \def (Bind Abst) in (let TMP_543 \def 
+(THead TMP_542 t t0) in (let TMP_540 \def (Bind Abst) in (let TMP_541 \def 
+(THead TMP_540 v t1) in (let H6 \def (f_equal T T TMP_544 TMP_543 TMP_541 H5) 
+in (let TMP_549 \def (\lambda (e: T).(match e in T with [(TSort _) 
+\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) 
+in (let TMP_547 \def (Bind Abst) in (let TMP_548 \def (THead TMP_547 t t0) in 
+(let TMP_545 \def (Bind Abst) in (let TMP_546 \def (THead TMP_545 v t1) in 
+(let H7 \def (f_equal T T TMP_549 TMP_548 TMP_546 H5) in (let TMP_550 \def 
+(\lambda (H8: (eq T t v)).(H4 H8 P)) in (TMP_550 H6))))))))))))))))) in 
+(or_intror TMP_558 TMP_552 TMP_551)))))) in (let TMP_596 \def (or_ind TMP_595 
+TMP_594 TMP_593 TMP_585 TMP_559 H3) in (eq_ind_r K TMP_604 TMP_603 TMP_596 k 
+H2))))))))))))))) in (let TMP_539 \def (\lambda (H2: (((eq K k (Bind Abst)) 
+\to (\forall (P: Prop).P)))).(let TMP_537 \def (\lambda (t1: T).(let TMP_536 
+\def (THead k t t0) in (let TMP_534 \def (Bind Abst) in (let TMP_535 \def 
+(THead TMP_534 v t1) in (eq T TMP_536 TMP_535))))) in (let TMP_538 \def (ex T 
+TMP_537) in (let TMP_533 \def (\forall (t1: T).((eq T (THead k t t0) (THead 
+(Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let TMP_532 \def (\lambda 
+(t1: T).(\lambda (H3: (eq T (THead k t t0) (THead (Bind Abst) v 
+t1))).(\lambda (P: Prop).(let TMP_521 \def (\lambda (e: T).(match e in T with 
 [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k0 _ _) 
-\Rightarrow k0])) (THead k t t0) (THead (Bind Abst) v t1) H3) in ((let H5 
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) 
-with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t2 _) 
-\Rightarrow t2])) (THead k t t0) (THead (Bind Abst) v t1) H3) in ((let H6 
-\def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) 
-with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t2) 
-\Rightarrow t2])) (THead k t t0) (THead (Bind Abst) v t1) H3) in (\lambda (_: 
-(eq T t v)).(\lambda (H8: (eq K k (Bind Abst))).(H2 H8 P)))) H5)) H4))))))) 
-H1))))))))) u).
-(* COMMENTS
-Initial nodes: 1305
-END *)
+\Rightarrow k0])) in (let TMP_520 \def (THead k t t0) in (let TMP_518 \def 
+(Bind Abst) in (let TMP_519 \def (THead TMP_518 v t1) in (let H4 \def 
+(f_equal T K TMP_521 TMP_520 TMP_519 H3) in (let TMP_525 \def (\lambda (e: 
+T).(match e in T with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | 
+(THead _ t2 _) \Rightarrow t2])) in (let TMP_524 \def (THead k t t0) in (let 
+TMP_522 \def (Bind Abst) in (let TMP_523 \def (THead TMP_522 v t1) in (let H5 
+\def (f_equal T T TMP_525 TMP_524 TMP_523 H3) in (let TMP_529 \def (\lambda 
+(e: T).(match e in T with [(TSort _) \Rightarrow t0 | (TLRef _) \Rightarrow 
+t0 | (THead _ _ t2) \Rightarrow t2])) in (let TMP_528 \def (THead k t t0) in 
+(let TMP_526 \def (Bind Abst) in (let TMP_527 \def (THead TMP_526 v t1) in 
+(let H6 \def (f_equal T T TMP_529 TMP_528 TMP_527 H3) in (let TMP_530 \def 
+(\lambda (_: (eq T t v)).(\lambda (H8: (eq K k (Bind Abst))).(H2 H8 P))) in 
+(let TMP_531 \def (TMP_530 H5) in (TMP_531 H4))))))))))))))))))))) in 
+(or_intror TMP_538 TMP_533 TMP_532)))))) in (or_ind TMP_615 TMP_613 TMP_612 
+TMP_605 TMP_539 H1))))))))))))))))))) in (T_ind TMP_646 TMP_640 TMP_628 
+TMP_616 u))))).