\forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) ((eq B b1 b2) \to (\forall
(P: Prop).P))))
\def
- \lambda (b1: B).(let TMP_3 \def (\lambda (b: B).(\forall (b2: B).(let TMP_1
-\def (eq B b b2) in (let TMP_2 \def ((eq B b b2) \to (\forall (P: Prop).P))
-in (or TMP_1 TMP_2))))) in (let TMP_21 \def (\lambda (b2: B).(let TMP_6 \def
-(\lambda (b: B).(let TMP_4 \def (eq B Abbr b) in (let TMP_5 \def ((eq B Abbr
-b) \to (\forall (P: Prop).P)) in (or TMP_4 TMP_5)))) in (let TMP_7 \def (eq B
-Abbr Abbr) in (let TMP_8 \def ((eq B Abbr Abbr) \to (\forall (P: Prop).P)) in
-(let TMP_9 \def (refl_equal B Abbr) in (let TMP_10 \def (or_introl TMP_7
-TMP_8 TMP_9) in (let TMP_11 \def (eq B Abbr Abst) in (let TMP_12 \def ((eq B
-Abbr Abst) \to (\forall (P: Prop).P)) in (let TMP_14 \def (\lambda (H: (eq B
-Abbr Abst)).(\lambda (P: Prop).(let TMP_13 \def (\lambda (ee: B).(match ee
-with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
-False])) in (let H0 \def (eq_ind B Abbr TMP_13 I Abst H) in (False_ind P
-H0))))) in (let TMP_15 \def (or_intror TMP_11 TMP_12 TMP_14) in (let TMP_16
-\def (eq B Abbr Void) in (let TMP_17 \def ((eq B Abbr Void) \to (\forall (P:
-Prop).P)) in (let TMP_19 \def (\lambda (H: (eq B Abbr Void)).(\lambda (P:
-Prop).(let TMP_18 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow True
-| Abst \Rightarrow False | Void \Rightarrow False])) in (let H0 \def (eq_ind
-B Abbr TMP_18 I Void H) in (False_ind P H0))))) in (let TMP_20 \def
-(or_intror TMP_16 TMP_17 TMP_19) in (B_ind TMP_6 TMP_10 TMP_15 TMP_20
-b2))))))))))))))) in (let TMP_39 \def (\lambda (b2: B).(let TMP_24 \def
-(\lambda (b: B).(let TMP_22 \def (eq B Abst b) in (let TMP_23 \def ((eq B
-Abst b) \to (\forall (P: Prop).P)) in (or TMP_22 TMP_23)))) in (let TMP_25
-\def (eq B Abst Abbr) in (let TMP_26 \def ((eq B Abst Abbr) \to (\forall (P:
-Prop).P)) in (let TMP_28 \def (\lambda (H: (eq B Abst Abbr)).(\lambda (P:
-Prop).(let TMP_27 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow
-False | Abst \Rightarrow True | Void \Rightarrow False])) in (let H0 \def
-(eq_ind B Abst TMP_27 I Abbr H) in (False_ind P H0))))) in (let TMP_29 \def
-(or_intror TMP_25 TMP_26 TMP_28) in (let TMP_30 \def (eq B Abst Abst) in (let
-TMP_31 \def ((eq B Abst Abst) \to (\forall (P: Prop).P)) in (let TMP_32 \def
-(refl_equal B Abst) in (let TMP_33 \def (or_introl TMP_30 TMP_31 TMP_32) in
-(let TMP_34 \def (eq B Abst Void) in (let TMP_35 \def ((eq B Abst Void) \to
-(\forall (P: Prop).P)) in (let TMP_37 \def (\lambda (H: (eq B Abst
-Void)).(\lambda (P: Prop).(let TMP_36 \def (\lambda (ee: B).(match ee with
-[Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]))
-in (let H0 \def (eq_ind B Abst TMP_36 I Void H) in (False_ind P H0))))) in
-(let TMP_38 \def (or_intror TMP_34 TMP_35 TMP_37) in (B_ind TMP_24 TMP_29
-TMP_33 TMP_38 b2))))))))))))))) in (let TMP_57 \def (\lambda (b2: B).(let
-TMP_42 \def (\lambda (b: B).(let TMP_40 \def (eq B Void b) in (let TMP_41
-\def ((eq B Void b) \to (\forall (P: Prop).P)) in (or TMP_40 TMP_41)))) in
-(let TMP_43 \def (eq B Void Abbr) in (let TMP_44 \def ((eq B Void Abbr) \to
-(\forall (P: Prop).P)) in (let TMP_46 \def (\lambda (H: (eq B Void
-Abbr)).(\lambda (P: Prop).(let TMP_45 \def (\lambda (ee: B).(match ee with
-[Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]))
-in (let H0 \def (eq_ind B Void TMP_45 I Abbr H) in (False_ind P H0))))) in
-(let TMP_47 \def (or_intror TMP_43 TMP_44 TMP_46) in (let TMP_48 \def (eq B
-Void Abst) in (let TMP_49 \def ((eq B Void Abst) \to (\forall (P: Prop).P))
-in (let TMP_51 \def (\lambda (H: (eq B Void Abst)).(\lambda (P: Prop).(let
-TMP_50 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow False | Abst
-\Rightarrow False | Void \Rightarrow True])) in (let H0 \def (eq_ind B Void
-TMP_50 I Abst H) in (False_ind P H0))))) in (let TMP_52 \def (or_intror
-TMP_48 TMP_49 TMP_51) in (let TMP_53 \def (eq B Void Void) in (let TMP_54
-\def ((eq B Void Void) \to (\forall (P: Prop).P)) in (let TMP_55 \def
-(refl_equal B Void) in (let TMP_56 \def (or_introl TMP_53 TMP_54 TMP_55) in
-(B_ind TMP_42 TMP_47 TMP_52 TMP_56 b2))))))))))))))) in (B_ind TMP_3 TMP_21
-TMP_39 TMP_57 b1))))).
+ \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 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 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 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 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 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 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).
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 (let TMP_1 \def (eq B b1 b2) in (let TMP_2 \def ((eq B
-b1 b2) \to (\forall (P: Prop).P)) in (let TMP_3 \def (eq B b1 b2) in (let
-TMP_4 \def ((eq B b1 b2) \to False) in (let TMP_5 \def (or TMP_3 TMP_4) in
-(let TMP_8 \def (\lambda (H0: (eq B b1 b2)).(let TMP_6 \def (eq B b1 b2) in
-(let TMP_7 \def ((eq B b1 b2) \to False) in (or_introl TMP_6 TMP_7 H0)))) in
-(let TMP_12 \def (\lambda (H0: (((eq B b1 b2) \to (\forall (P:
-Prop).P)))).(let TMP_9 \def (eq B b1 b2) in (let TMP_10 \def ((eq B b1 b2)
-\to False) in (let TMP_11 \def (\lambda (H1: (eq B b1 b2)).(H0 H1 False)) in
-(or_intror TMP_9 TMP_10 TMP_11))))) in (or_ind TMP_1 TMP_2 TMP_5 TMP_8 TMP_12
-H))))))))))).
+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)))).
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).(let TMP_3 \def (\lambda (f: F).(\forall (f2: F).(let TMP_1
-\def (eq F f f2) in (let TMP_2 \def ((eq F f f2) \to (\forall (P: Prop).P))
-in (or TMP_1 TMP_2))))) in (let TMP_16 \def (\lambda (f2: F).(let TMP_6 \def
-(\lambda (f: F).(let TMP_4 \def (eq F Appl f) in (let TMP_5 \def ((eq F Appl
-f) \to (\forall (P: Prop).P)) in (or TMP_4 TMP_5)))) in (let TMP_7 \def (eq F
-Appl Appl) in (let TMP_8 \def ((eq F Appl Appl) \to (\forall (P: Prop).P)) in
-(let TMP_9 \def (refl_equal F Appl) in (let TMP_10 \def (or_introl TMP_7
-TMP_8 TMP_9) in (let TMP_11 \def (eq F Appl Cast) in (let TMP_12 \def ((eq F
-Appl Cast) \to (\forall (P: Prop).P)) in (let TMP_14 \def (\lambda (H: (eq F
-Appl Cast)).(\lambda (P: Prop).(let TMP_13 \def (\lambda (ee: F).(match ee
-with [Appl \Rightarrow True | Cast \Rightarrow False])) in (let H0 \def
-(eq_ind F Appl TMP_13 I Cast H) in (False_ind P H0))))) in (let TMP_15 \def
-(or_intror TMP_11 TMP_12 TMP_14) in (F_ind TMP_6 TMP_10 TMP_15 f2)))))))))))
-in (let TMP_29 \def (\lambda (f2: F).(let TMP_19 \def (\lambda (f: F).(let
-TMP_17 \def (eq F Cast f) in (let TMP_18 \def ((eq F Cast f) \to (\forall (P:
-Prop).P)) in (or TMP_17 TMP_18)))) in (let TMP_20 \def (eq F Cast Appl) in
-(let TMP_21 \def ((eq F Cast Appl) \to (\forall (P: Prop).P)) in (let TMP_23
-\def (\lambda (H: (eq F Cast Appl)).(\lambda (P: Prop).(let TMP_22 \def
-(\lambda (ee: F).(match ee with [Appl \Rightarrow False | Cast \Rightarrow
-True])) in (let H0 \def (eq_ind F Cast TMP_22 I Appl H) in (False_ind P
-H0))))) in (let TMP_24 \def (or_intror TMP_20 TMP_21 TMP_23) in (let TMP_25
-\def (eq F Cast Cast) in (let TMP_26 \def ((eq F Cast Cast) \to (\forall (P:
-Prop).P)) in (let TMP_27 \def (refl_equal F Cast) in (let TMP_28 \def
-(or_introl TMP_25 TMP_26 TMP_27) in (F_ind TMP_19 TMP_24 TMP_28 f2)))))))))))
-in (F_ind TMP_3 TMP_16 TMP_29 f1)))).
+ \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 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 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).
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).(let TMP_3 \def (\lambda (k: K).(\forall (k2: K).(let TMP_1
-\def (eq K k k2) in (let TMP_2 \def ((eq K k k2) \to (\forall (P: Prop).P))
-in (or TMP_1 TMP_2))))) in (let TMP_49 \def (\lambda (b: B).(\lambda (k2:
-K).(let TMP_7 \def (\lambda (k: K).(let TMP_4 \def (Bind b) in (let TMP_5
-\def (eq K TMP_4 k) in (let TMP_6 \def ((eq K (Bind b) k) \to (\forall (P:
-Prop).P)) in (or TMP_5 TMP_6))))) in (let TMP_39 \def (\lambda (b0: B).(let
-H_x \def (terms_props__bind_dec b b0) in (let H \def H_x in (let TMP_8 \def
-(eq B b b0) in (let TMP_9 \def ((eq B b b0) \to (\forall (P: Prop).P)) in
-(let TMP_10 \def (Bind b) in (let TMP_11 \def (Bind b0) in (let TMP_12 \def
-(eq K TMP_10 TMP_11) in (let TMP_13 \def ((eq K (Bind b) (Bind b0)) \to
-(\forall (P: Prop).P)) in (let TMP_14 \def (or TMP_12 TMP_13) in (let TMP_27
-\def (\lambda (H0: (eq B b b0)).(let TMP_19 \def (\lambda (b1: B).(let TMP_15
-\def (Bind b) in (let TMP_16 \def (Bind b1) in (let TMP_17 \def (eq K TMP_15
-TMP_16) in (let TMP_18 \def ((eq K (Bind b) (Bind b1)) \to (\forall (P:
-Prop).P)) in (or TMP_17 TMP_18)))))) in (let TMP_20 \def (Bind b) in (let
-TMP_21 \def (Bind b) in (let TMP_22 \def (eq K TMP_20 TMP_21) in (let TMP_23
-\def ((eq K (Bind b) (Bind b)) \to (\forall (P: Prop).P)) in (let TMP_24 \def
-(Bind b) in (let TMP_25 \def (refl_equal K TMP_24) in (let TMP_26 \def
-(or_introl TMP_22 TMP_23 TMP_25) in (eq_ind B b TMP_19 TMP_26 b0 H0))))))))))
-in (let TMP_38 \def (\lambda (H0: (((eq B b b0) \to (\forall (P:
-Prop).P)))).(let TMP_28 \def (Bind b) in (let TMP_29 \def (Bind b0) in (let
-TMP_30 \def (eq K TMP_28 TMP_29) in (let TMP_31 \def ((eq K (Bind b) (Bind
-b0)) \to (\forall (P: Prop).P)) in (let TMP_37 \def (\lambda (H1: (eq K (Bind
-b) (Bind b0))).(\lambda (P: Prop).(let TMP_32 \def (\lambda (e: K).(match e
-with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])) in (let TMP_33
-\def (Bind b) in (let TMP_34 \def (Bind b0) in (let H2 \def (f_equal K B
-TMP_32 TMP_33 TMP_34 H1) in (let TMP_35 \def (\lambda (b1: B).((eq B b b1)
-\to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r B b0 TMP_35 H0 b H2)
-in (let TMP_36 \def (refl_equal B b) in (H3 TMP_36 P)))))))))) in (or_intror
-TMP_30 TMP_31 TMP_37))))))) in (or_ind TMP_8 TMP_9 TMP_14 TMP_27 TMP_38
-H))))))))))))) in (let TMP_48 \def (\lambda (f: F).(let TMP_40 \def (Bind b)
-in (let TMP_41 \def (Flat f) in (let TMP_42 \def (eq K TMP_40 TMP_41) in (let
-TMP_43 \def ((eq K (Bind b) (Flat f)) \to (\forall (P: Prop).P)) in (let
-TMP_47 \def (\lambda (H: (eq K (Bind b) (Flat f))).(\lambda (P: Prop).(let
-TMP_44 \def (Bind b) in (let TMP_45 \def (\lambda (ee: K).(match ee with
-[(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])) in (let TMP_46
-\def (Flat f) in (let H0 \def (eq_ind K TMP_44 TMP_45 I TMP_46 H) in
-(False_ind P H0))))))) in (or_intror TMP_42 TMP_43 TMP_47))))))) in (K_ind
-TMP_7 TMP_39 TMP_48 k2)))))) in (let TMP_95 \def (\lambda (f: F).(\lambda
-(k2: K).(let TMP_53 \def (\lambda (k: K).(let TMP_50 \def (Flat f) in (let
-TMP_51 \def (eq K TMP_50 k) in (let TMP_52 \def ((eq K (Flat f) k) \to
-(\forall (P: Prop).P)) in (or TMP_51 TMP_52))))) in (let TMP_62 \def (\lambda
-(b: B).(let TMP_54 \def (Flat f) in (let TMP_55 \def (Bind b) in (let TMP_56
-\def (eq K TMP_54 TMP_55) in (let TMP_57 \def ((eq K (Flat f) (Bind b)) \to
-(\forall (P: Prop).P)) in (let TMP_61 \def (\lambda (H: (eq K (Flat f) (Bind
-b))).(\lambda (P: Prop).(let TMP_58 \def (Flat f) in (let TMP_59 \def
-(\lambda (ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _)
-\Rightarrow True])) in (let TMP_60 \def (Bind b) in (let H0 \def (eq_ind K
-TMP_58 TMP_59 I TMP_60 H) in (False_ind P H0))))))) in (or_intror TMP_56
-TMP_57 TMP_61))))))) in (let TMP_94 \def (\lambda (f0: F).(let H_x \def
-(terms_props__flat_dec f f0) in (let H \def H_x in (let TMP_63 \def (eq F f
-f0) in (let TMP_64 \def ((eq F f f0) \to (\forall (P: Prop).P)) in (let
-TMP_65 \def (Flat f) in (let TMP_66 \def (Flat f0) in (let TMP_67 \def (eq K
-TMP_65 TMP_66) in (let TMP_68 \def ((eq K (Flat f) (Flat f0)) \to (\forall
-(P: Prop).P)) in (let TMP_69 \def (or TMP_67 TMP_68) in (let TMP_82 \def
-(\lambda (H0: (eq F f f0)).(let TMP_74 \def (\lambda (f1: F).(let TMP_70 \def
-(Flat f) in (let TMP_71 \def (Flat f1) in (let TMP_72 \def (eq K TMP_70
-TMP_71) in (let TMP_73 \def ((eq K (Flat f) (Flat f1)) \to (\forall (P:
-Prop).P)) in (or TMP_72 TMP_73)))))) in (let TMP_75 \def (Flat f) in (let
-TMP_76 \def (Flat f) in (let TMP_77 \def (eq K TMP_75 TMP_76) in (let TMP_78
-\def ((eq K (Flat f) (Flat f)) \to (\forall (P: Prop).P)) in (let TMP_79 \def
-(Flat f) in (let TMP_80 \def (refl_equal K TMP_79) in (let TMP_81 \def
-(or_introl TMP_77 TMP_78 TMP_80) in (eq_ind F f TMP_74 TMP_81 f0 H0))))))))))
-in (let TMP_93 \def (\lambda (H0: (((eq F f f0) \to (\forall (P:
-Prop).P)))).(let TMP_83 \def (Flat f) in (let TMP_84 \def (Flat f0) in (let
-TMP_85 \def (eq K TMP_83 TMP_84) in (let TMP_86 \def ((eq K (Flat f) (Flat
-f0)) \to (\forall (P: Prop).P)) in (let TMP_92 \def (\lambda (H1: (eq K (Flat
-f) (Flat f0))).(\lambda (P: Prop).(let TMP_87 \def (\lambda (e: K).(match e
-with [(Bind _) \Rightarrow f | (Flat f1) \Rightarrow f1])) in (let TMP_88
-\def (Flat f) in (let TMP_89 \def (Flat f0) in (let H2 \def (f_equal K F
-TMP_87 TMP_88 TMP_89 H1) in (let TMP_90 \def (\lambda (f1: F).((eq F f f1)
-\to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r F f0 TMP_90 H0 f H2)
-in (let TMP_91 \def (refl_equal F f) in (H3 TMP_91 P)))))))))) in (or_intror
-TMP_85 TMP_86 TMP_92))))))) in (or_ind TMP_63 TMP_64 TMP_69 TMP_82 TMP_93
-H))))))))))))) in (K_ind TMP_53 TMP_62 TMP_94 k2)))))) in (K_ind TMP_3 TMP_49
-TMP_95 k1)))).
+ \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 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 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 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 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).
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).(let TMP_3 \def (\lambda (t: T).(\forall (t2: T).(let TMP_1
-\def (eq T t t2) in (let TMP_2 \def ((eq T t t2) \to (\forall (P: Prop).P))
-in (or TMP_1 TMP_2))))) in (let TMP_58 \def (\lambda (n: nat).(\lambda (t2:
-T).(let TMP_7 \def (\lambda (t: T).(let TMP_4 \def (TSort n) in (let TMP_5
-\def (eq T TMP_4 t) in (let TMP_6 \def ((eq T (TSort n) t) \to (\forall (P:
-Prop).P)) in (or TMP_5 TMP_6))))) in (let TMP_39 \def (\lambda (n0: nat).(let
-H_x \def (nat_dec n n0) in (let H \def H_x in (let TMP_8 \def (eq nat n n0)
-in (let TMP_9 \def ((eq nat n n0) \to (\forall (P: Prop).P)) in (let TMP_10
-\def (TSort n) in (let TMP_11 \def (TSort n0) in (let TMP_12 \def (eq T
-TMP_10 TMP_11) in (let TMP_13 \def ((eq T (TSort n) (TSort n0)) \to (\forall
-(P: Prop).P)) in (let TMP_14 \def (or TMP_12 TMP_13) in (let TMP_27 \def
-(\lambda (H0: (eq nat n n0)).(let TMP_19 \def (\lambda (n1: nat).(let TMP_15
-\def (TSort n) in (let TMP_16 \def (TSort n1) in (let TMP_17 \def (eq T
-TMP_15 TMP_16) in (let TMP_18 \def ((eq T (TSort n) (TSort n1)) \to (\forall
-(P: Prop).P)) in (or TMP_17 TMP_18)))))) in (let TMP_20 \def (TSort n) in
-(let TMP_21 \def (TSort n) in (let TMP_22 \def (eq T TMP_20 TMP_21) in (let
-TMP_23 \def ((eq T (TSort n) (TSort n)) \to (\forall (P: Prop).P)) in (let
-TMP_24 \def (TSort n) in (let TMP_25 \def (refl_equal T TMP_24) in (let
-TMP_26 \def (or_introl TMP_22 TMP_23 TMP_25) in (eq_ind nat n TMP_19 TMP_26
-n0 H0)))))))))) in (let TMP_38 \def (\lambda (H0: (((eq nat n n0) \to
-(\forall (P: Prop).P)))).(let TMP_28 \def (TSort n) in (let TMP_29 \def
-(TSort n0) in (let TMP_30 \def (eq T TMP_28 TMP_29) in (let TMP_31 \def ((eq
-T (TSort n) (TSort n0)) \to (\forall (P: Prop).P)) in (let TMP_37 \def
-(\lambda (H1: (eq T (TSort n) (TSort n0))).(\lambda (P: Prop).(let TMP_32
-\def (\lambda (e: T).(match e with [(TSort n1) \Rightarrow n1 | (TLRef _)
-\Rightarrow n | (THead _ _ _) \Rightarrow n])) in (let TMP_33 \def (TSort n)
-in (let TMP_34 \def (TSort n0) in (let H2 \def (f_equal T nat TMP_32 TMP_33
-TMP_34 H1) in (let TMP_35 \def (\lambda (n1: nat).((eq nat n n1) \to (\forall
-(P0: Prop).P0))) in (let H3 \def (eq_ind_r nat n0 TMP_35 H0 n H2) in (let
-TMP_36 \def (refl_equal nat n) in (H3 TMP_36 P)))))))))) in (or_intror TMP_30
-TMP_31 TMP_37))))))) in (or_ind TMP_8 TMP_9 TMP_14 TMP_27 TMP_38
-H))))))))))))) in (let TMP_48 \def (\lambda (n0: nat).(let TMP_40 \def (TSort
-n) in (let TMP_41 \def (TLRef n0) in (let TMP_42 \def (eq T TMP_40 TMP_41) in
-(let TMP_43 \def ((eq T (TSort n) (TLRef n0)) \to (\forall (P: Prop).P)) in
-(let TMP_47 \def (\lambda (H: (eq T (TSort n) (TLRef n0))).(\lambda (P:
-Prop).(let TMP_44 \def (TSort n) in (let TMP_45 \def (\lambda (ee: T).(match
-ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _
-_ _) \Rightarrow False])) in (let TMP_46 \def (TLRef n0) in (let H0 \def
-(eq_ind T TMP_44 TMP_45 I TMP_46 H) in (False_ind P H0))))))) in (or_intror
-TMP_42 TMP_43 TMP_47))))))) in (let TMP_57 \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_49 \def (TSort n) in (let
-TMP_50 \def (THead k t t0) in (let TMP_51 \def (eq T TMP_49 TMP_50) in (let
-TMP_52 \def ((eq T (TSort n) (THead k t t0)) \to (\forall (P: Prop).P)) in
-(let TMP_56 \def (\lambda (H1: (eq T (TSort n) (THead k t t0))).(\lambda (P:
-Prop).(let TMP_53 \def (TSort n) in (let TMP_54 \def (\lambda (ee: T).(match
-ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _
-_ _) \Rightarrow False])) in (let TMP_55 \def (THead k t t0) in (let H2 \def
-(eq_ind T TMP_53 TMP_54 I TMP_55 H1) in (False_ind P H2))))))) in (or_intror
-TMP_51 TMP_52 TMP_56))))))))))) in (T_ind TMP_7 TMP_39 TMP_48 TMP_57
-t2))))))) in (let TMP_113 \def (\lambda (n: nat).(\lambda (t2: T).(let TMP_62
-\def (\lambda (t: T).(let TMP_59 \def (TLRef n) in (let TMP_60 \def (eq T
-TMP_59 t) in (let TMP_61 \def ((eq T (TLRef n) t) \to (\forall (P: Prop).P))
-in (or TMP_60 TMP_61))))) in (let TMP_71 \def (\lambda (n0: nat).(let TMP_63
-\def (TLRef n) in (let TMP_64 \def (TSort n0) in (let TMP_65 \def (eq T
-TMP_63 TMP_64) in (let TMP_66 \def ((eq T (TLRef n) (TSort n0)) \to (\forall
-(P: Prop).P)) in (let TMP_70 \def (\lambda (H: (eq T (TLRef n) (TSort
-n0))).(\lambda (P: Prop).(let TMP_67 \def (TLRef n) in (let TMP_68 \def
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_69 \def
-(TSort n0) in (let H0 \def (eq_ind T TMP_67 TMP_68 I TMP_69 H) in (False_ind
-P H0))))))) in (or_intror TMP_65 TMP_66 TMP_70))))))) in (let TMP_103 \def
-(\lambda (n0: nat).(let H_x \def (nat_dec n n0) in (let H \def H_x in (let
-TMP_72 \def (eq nat n n0) in (let TMP_73 \def ((eq nat n n0) \to (\forall (P:
-Prop).P)) in (let TMP_74 \def (TLRef n) in (let TMP_75 \def (TLRef n0) in
-(let TMP_76 \def (eq T TMP_74 TMP_75) in (let TMP_77 \def ((eq T (TLRef n)
-(TLRef n0)) \to (\forall (P: Prop).P)) in (let TMP_78 \def (or TMP_76 TMP_77)
-in (let TMP_91 \def (\lambda (H0: (eq nat n n0)).(let TMP_83 \def (\lambda
-(n1: nat).(let TMP_79 \def (TLRef n) in (let TMP_80 \def (TLRef n1) in (let
-TMP_81 \def (eq T TMP_79 TMP_80) in (let TMP_82 \def ((eq T (TLRef n) (TLRef
-n1)) \to (\forall (P: Prop).P)) in (or TMP_81 TMP_82)))))) in (let TMP_84
-\def (TLRef n) in (let TMP_85 \def (TLRef n) in (let TMP_86 \def (eq T TMP_84
-TMP_85) in (let TMP_87 \def ((eq T (TLRef n) (TLRef n)) \to (\forall (P:
-Prop).P)) in (let TMP_88 \def (TLRef n) in (let TMP_89 \def (refl_equal T
-TMP_88) in (let TMP_90 \def (or_introl TMP_86 TMP_87 TMP_89) in (eq_ind nat n
-TMP_83 TMP_90 n0 H0)))))))))) in (let TMP_102 \def (\lambda (H0: (((eq nat n
-n0) \to (\forall (P: Prop).P)))).(let TMP_92 \def (TLRef n) in (let TMP_93
-\def (TLRef n0) in (let TMP_94 \def (eq T TMP_92 TMP_93) in (let TMP_95 \def
-((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P)) in (let TMP_101 \def
-(\lambda (H1: (eq T (TLRef n) (TLRef n0))).(\lambda (P: Prop).(let TMP_96
-\def (\lambda (e: T).(match e with [(TSort _) \Rightarrow n | (TLRef n1)
-\Rightarrow n1 | (THead _ _ _) \Rightarrow n])) in (let TMP_97 \def (TLRef n)
-in (let TMP_98 \def (TLRef n0) in (let H2 \def (f_equal T nat TMP_96 TMP_97
-TMP_98 H1) in (let TMP_99 \def (\lambda (n1: nat).((eq nat n n1) \to (\forall
-(P0: Prop).P0))) in (let H3 \def (eq_ind_r nat n0 TMP_99 H0 n H2) in (let
-TMP_100 \def (refl_equal nat n) in (H3 TMP_100 P)))))))))) in (or_intror
-TMP_94 TMP_95 TMP_101))))))) in (or_ind TMP_72 TMP_73 TMP_78 TMP_91 TMP_102
-H))))))))))))) in (let TMP_112 \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_104 \def (TLRef n) in
-(let TMP_105 \def (THead k t t0) in (let TMP_106 \def (eq T TMP_104 TMP_105)
-in (let TMP_107 \def ((eq T (TLRef n) (THead k t t0)) \to (\forall (P:
-Prop).P)) in (let TMP_111 \def (\lambda (H1: (eq T (TLRef n) (THead k t
-t0))).(\lambda (P: Prop).(let TMP_108 \def (TLRef n) in (let TMP_109 \def
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_110 \def
-(THead k t t0) in (let H2 \def (eq_ind T TMP_108 TMP_109 I TMP_110 H1) in
-(False_ind P H2))))))) in (or_intror TMP_106 TMP_107 TMP_111))))))))))) in
-(T_ind TMP_62 TMP_71 TMP_103 TMP_112 t2))))))) in (let TMP_250 \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_117 \def (\lambda (t3: T).(let
-TMP_114 \def (THead k t t0) in (let TMP_115 \def (eq T TMP_114 t3) in (let
-TMP_116 \def ((eq T (THead k t t0) t3) \to (\forall (P: Prop).P)) in (or
-TMP_115 TMP_116))))) in (let TMP_126 \def (\lambda (n: nat).(let TMP_118 \def
-(THead k t t0) in (let TMP_119 \def (TSort n) in (let TMP_120 \def (eq T
-TMP_118 TMP_119) in (let TMP_121 \def ((eq T (THead k t t0) (TSort n)) \to
-(\forall (P: Prop).P)) in (let TMP_125 \def (\lambda (H1: (eq T (THead k t
-t0) (TSort n))).(\lambda (P: Prop).(let TMP_122 \def (THead k t t0) in (let
-TMP_123 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
-(TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let
-TMP_124 \def (TSort n) in (let H2 \def (eq_ind T TMP_122 TMP_123 I TMP_124
-H1) in (False_ind P H2))))))) in (or_intror TMP_120 TMP_121 TMP_125))))))) in
-(let TMP_135 \def (\lambda (n: nat).(let TMP_127 \def (THead k t t0) in (let
-TMP_128 \def (TLRef n) in (let TMP_129 \def (eq T TMP_127 TMP_128) in (let
-TMP_130 \def ((eq T (THead k t t0) (TLRef n)) \to (\forall (P: Prop).P)) in
-(let TMP_134 \def (\lambda (H1: (eq T (THead k t t0) (TLRef n))).(\lambda (P:
-Prop).(let TMP_131 \def (THead k t t0) in (let TMP_132 \def (\lambda (ee:
+ \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 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 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 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 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 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 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 with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
-| (THead _ _ _) \Rightarrow True])) in (let TMP_133 \def (TLRef n) in (let H2
-\def (eq_ind T TMP_131 TMP_132 I TMP_133 H1) in (False_ind P H2))))))) in
-(or_intror TMP_129 TMP_130 TMP_134))))))) in (let TMP_249 \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_136 \def (eq
-T t t3) in (let TMP_137 \def ((eq T t t3) \to (\forall (P: Prop).P)) in (let
-TMP_138 \def (THead k t t0) in (let TMP_139 \def (THead k0 t3 t4) in (let
-TMP_140 \def (eq T TMP_138 TMP_139) in (let TMP_141 \def ((eq T (THead k t
-t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) in (let TMP_142 \def (or
-TMP_140 TMP_141) in (let TMP_221 \def (\lambda (H4: (eq T t t3)).(let TMP_146
-\def (\lambda (t5: T).(let TMP_143 \def (THead k t t0) in (let TMP_144 \def
-(eq T TMP_143 t5) in (let TMP_145 \def ((eq T (THead k t t0) t5) \to (\forall
-(P: Prop).P)) in (or TMP_144 TMP_145))))) in (let H5 \def (eq_ind_r T t3
-TMP_146 H1 t H4) in (let TMP_151 \def (\lambda (t5: T).(let TMP_147 \def
-(THead k t t0) in (let TMP_148 \def (THead k0 t5 t4) in (let TMP_149 \def (eq
-T TMP_147 TMP_148) in (let TMP_150 \def ((eq T (THead k t t0) (THead k0 t5
-t4)) \to (\forall (P: Prop).P)) in (or TMP_149 TMP_150)))))) in (let H_x0
-\def (H0 t4) in (let H6 \def H_x0 in (let TMP_152 \def (eq T t0 t4) in (let
-TMP_153 \def ((eq T t0 t4) \to (\forall (P: Prop).P)) in (let TMP_154 \def
-(THead k t t0) in (let TMP_155 \def (THead k0 t t4) in (let TMP_156 \def (eq
-T TMP_154 TMP_155) in (let TMP_157 \def ((eq T (THead k t t0) (THead k0 t
-t4)) \to (\forall (P: Prop).P)) in (let TMP_158 \def (or TMP_156 TMP_157) in
-(let TMP_200 \def (\lambda (H7: (eq T t0 t4)).(let TMP_162 \def (\lambda (t5:
-T).(let TMP_159 \def (THead k t t0) in (let TMP_160 \def (eq T TMP_159 t5) in
-(let TMP_161 \def ((eq T (THead k t t0) t5) \to (\forall (P: Prop).P)) in (or
-TMP_160 TMP_161))))) in (let H8 \def (eq_ind_r T t4 TMP_162 H2 t0 H7) in (let
-TMP_167 \def (\lambda (t5: T).(let TMP_163 \def (THead k t t0) in (let
-TMP_164 \def (THead k0 t t5) in (let TMP_165 \def (eq T TMP_163 TMP_164) in
-(let TMP_166 \def ((eq T (THead k t t0) (THead k0 t t5)) \to (\forall (P:
-Prop).P)) in (or TMP_165 TMP_166)))))) in (let H_x1 \def
-(terms_props__kind_dec k k0) in (let H9 \def H_x1 in (let TMP_168 \def (eq K
-k k0) in (let TMP_169 \def ((eq K k k0) \to (\forall (P: Prop).P)) in (let
-TMP_170 \def (THead k t t0) in (let TMP_171 \def (THead k0 t t0) in (let
-TMP_172 \def (eq T TMP_170 TMP_171) in (let TMP_173 \def ((eq T (THead k t
-t0) (THead k0 t t0)) \to (\forall (P: Prop).P)) in (let TMP_174 \def (or
-TMP_172 TMP_173) in (let TMP_187 \def (\lambda (H10: (eq K k k0)).(let
-TMP_179 \def (\lambda (k1: K).(let TMP_175 \def (THead k t t0) in (let
-TMP_176 \def (THead k1 t t0) in (let TMP_177 \def (eq T TMP_175 TMP_176) in
-(let TMP_178 \def ((eq T (THead k t t0) (THead k1 t t0)) \to (\forall (P:
-Prop).P)) in (or TMP_177 TMP_178)))))) in (let TMP_180 \def (THead k t t0) in
-(let TMP_181 \def (THead k t t0) in (let TMP_182 \def (eq T TMP_180 TMP_181)
-in (let TMP_183 \def ((eq T (THead k t t0) (THead k t t0)) \to (\forall (P:
-Prop).P)) in (let TMP_184 \def (THead k t t0) in (let TMP_185 \def
-(refl_equal T TMP_184) in (let TMP_186 \def (or_introl TMP_182 TMP_183
-TMP_185) in (eq_ind K k TMP_179 TMP_186 k0 H10)))))))))) in (let TMP_198 \def
-(\lambda (H10: (((eq K k k0) \to (\forall (P: Prop).P)))).(let TMP_188 \def
-(THead k t t0) in (let TMP_189 \def (THead k0 t t0) in (let TMP_190 \def (eq
-T TMP_188 TMP_189) in (let TMP_191 \def ((eq T (THead k t t0) (THead k0 t
-t0)) \to (\forall (P: Prop).P)) in (let TMP_197 \def (\lambda (H11: (eq T
-(THead k t t0) (THead k0 t t0))).(\lambda (P: Prop).(let TMP_192 \def
+| (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 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
+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 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 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 with [(TSort _) \Rightarrow k | (TLRef _)
-\Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in (let TMP_193 \def (THead
-k t t0) in (let TMP_194 \def (THead k0 t t0) in (let H12 \def (f_equal T K
-TMP_192 TMP_193 TMP_194 H11) in (let TMP_195 \def (\lambda (k1: K).((eq K k
-k1) \to (\forall (P0: Prop).P0))) in (let H13 \def (eq_ind_r K k0 TMP_195 H10
-k H12) in (let TMP_196 \def (refl_equal K k) in (H13 TMP_196 P)))))))))) in
-(or_intror TMP_190 TMP_191 TMP_197))))))) in (let TMP_199 \def (or_ind
-TMP_168 TMP_169 TMP_174 TMP_187 TMP_198 H9) in (eq_ind T t0 TMP_167 TMP_199
-t4 H7))))))))))))))))) in (let TMP_219 \def (\lambda (H7: (((eq T t0 t4) \to
-(\forall (P: Prop).P)))).(let TMP_201 \def (THead k t t0) in (let TMP_202
-\def (THead k0 t t4) in (let TMP_203 \def (eq T TMP_201 TMP_202) in (let
-TMP_204 \def ((eq T (THead k t t0) (THead k0 t t4)) \to (\forall (P:
-Prop).P)) in (let TMP_218 \def (\lambda (H8: (eq T (THead k t t0) (THead k0 t
-t4))).(\lambda (P: Prop).(let TMP_205 \def (\lambda (e: T).(match e with
-[(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _)
-\Rightarrow k1])) in (let TMP_206 \def (THead k t t0) in (let TMP_207 \def
-(THead k0 t t4) in (let H9 \def (f_equal T K TMP_205 TMP_206 TMP_207 H8) in
-(let TMP_208 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 |
-(TLRef _) \Rightarrow t0 | (THead _ _ t5) \Rightarrow t5])) in (let TMP_209
-\def (THead k t t0) in (let TMP_210 \def (THead k0 t t4) in (let H10 \def
-(f_equal T T TMP_208 TMP_209 TMP_210 H8) in (let TMP_217 \def (\lambda (_:
-(eq K k k0)).(let TMP_211 \def (\lambda (t5: T).((eq T t0 t5) \to (\forall
-(P0: Prop).P0))) in (let H12 \def (eq_ind_r T t4 TMP_211 H7 t0 H10) in (let
-TMP_215 \def (\lambda (t5: T).(let TMP_212 \def (THead k t t0) in (let
-TMP_213 \def (eq T TMP_212 t5) in (let TMP_214 \def ((eq T (THead k t t0) t5)
-\to (\forall (P0: Prop).P0)) in (or TMP_213 TMP_214))))) in (let H13 \def
-(eq_ind_r T t4 TMP_215 H2 t0 H10) in (let TMP_216 \def (refl_equal T t0) in
-(H12 TMP_216 P))))))) in (TMP_217 H9)))))))))))) in (or_intror TMP_203
-TMP_204 TMP_218))))))) in (let TMP_220 \def (or_ind TMP_152 TMP_153 TMP_158
-TMP_200 TMP_219 H6) in (eq_ind T t TMP_151 TMP_220 t3 H4))))))))))))))))) in
-(let TMP_248 \def (\lambda (H4: (((eq T t t3) \to (\forall (P:
-Prop).P)))).(let TMP_222 \def (THead k t t0) in (let TMP_223 \def (THead k0
-t3 t4) in (let TMP_224 \def (eq T TMP_222 TMP_223) in (let TMP_225 \def ((eq
-T (THead k t t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) in (let TMP_247
-\def (\lambda (H5: (eq T (THead k t t0) (THead k0 t3 t4))).(\lambda (P:
-Prop).(let TMP_226 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow
-k | (TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in (let
-TMP_227 \def (THead k t t0) in (let TMP_228 \def (THead k0 t3 t4) in (let H6
-\def (f_equal T K TMP_226 TMP_227 TMP_228 H5) in (let TMP_229 \def (\lambda
-(e: T).(match e with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t |
-(THead _ t5 _) \Rightarrow t5])) in (let TMP_230 \def (THead k t t0) in (let
-TMP_231 \def (THead k0 t3 t4) in (let H7 \def (f_equal T T TMP_229 TMP_230
-TMP_231 H5) in (let TMP_232 \def (\lambda (e: T).(match e with [(TSort _)
-\Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t5) \Rightarrow t5]))
-in (let TMP_233 \def (THead k t t0) in (let TMP_234 \def (THead k0 t3 t4) in
-(let H8 \def (f_equal T T TMP_232 TMP_233 TMP_234 H5) in (let TMP_245 \def
-(\lambda (H9: (eq T t t3)).(\lambda (_: (eq K k k0)).(let TMP_238 \def
-(\lambda (t5: T).(let TMP_235 \def (THead k t t0) in (let TMP_236 \def (eq T
-TMP_235 t5) in (let TMP_237 \def ((eq T (THead k t t0) t5) \to (\forall (P0:
-Prop).P0)) in (or TMP_236 TMP_237))))) in (let H11 \def (eq_ind_r T t4
-TMP_238 H2 t0 H8) in (let TMP_239 \def (\lambda (t5: T).((eq T t t5) \to
-(\forall (P0: Prop).P0))) in (let H12 \def (eq_ind_r T t3 TMP_239 H4 t H9) in
-(let TMP_243 \def (\lambda (t5: T).(let TMP_240 \def (THead k t t0) in (let
-TMP_241 \def (eq T TMP_240 t5) in (let TMP_242 \def ((eq T (THead k t t0) t5)
-\to (\forall (P0: Prop).P0)) in (or TMP_241 TMP_242))))) in (let H13 \def
-(eq_ind_r T t3 TMP_243 H1 t H9) in (let TMP_244 \def (refl_equal T t) in (H12
-TMP_244 P)))))))))) in (let TMP_246 \def (TMP_245 H7) in (TMP_246
-H6))))))))))))))))) in (or_intror TMP_224 TMP_225 TMP_247))))))) in (or_ind
-TMP_136 TMP_137 TMP_142 TMP_221 TMP_248 H3))))))))))))))))) in (T_ind TMP_117
-TMP_126 TMP_135 TMP_249 t2))))))))))) in (T_ind TMP_3 TMP_58 TMP_113 TMP_250
-t1))))).
+\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 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 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).
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).(let TMP_6 \def (\lambda (t0: T).(let TMP_3 \def (\lambda (b:
-B).(\lambda (w: T).(\lambda (u: T).(let TMP_1 \def (Bind b) in (let TMP_2
-\def (THead TMP_1 w u) in (eq T t0 TMP_2)))))) in (let TMP_4 \def (ex_3 B T T
-TMP_3) in (let TMP_5 \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_4
-TMP_5))))) in (let TMP_18 \def (\lambda (n: nat).(let TMP_10 \def (\lambda
-(b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_7 \def (TSort n) in (let
-TMP_8 \def (Bind b) in (let TMP_9 \def (THead TMP_8 w u) in (eq T TMP_7
-TMP_9))))))) in (let TMP_11 \def (ex_3 B T T TMP_10) in (let TMP_12 \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_17 \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_13 \def (TSort n) in (let TMP_14 \def
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _)
-\Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_15 \def
-(Bind b) in (let TMP_16 \def (THead TMP_15 w u) in (let H0 \def (eq_ind T
-TMP_13 TMP_14 I TMP_16 H) in (False_ind P H0))))))))))) in (or_intror TMP_11
-TMP_12 TMP_17)))))) in (let TMP_30 \def (\lambda (n: nat).(let TMP_22 \def
-(\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_19 \def (TLRef n) in
-(let TMP_20 \def (Bind b) in (let TMP_21 \def (THead TMP_20 w u) in (eq T
-TMP_19 TMP_21))))))) in (let TMP_23 \def (ex_3 B T T TMP_22) in (let TMP_24
-\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_29 \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_25 \def (TLRef n) in (let TMP_26 \def
-(\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
-\Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_27 \def
-(Bind b) in (let TMP_28 \def (THead TMP_27 w u) in (let H0 \def (eq_ind T
-TMP_25 TMP_26 I TMP_28 H) in (False_ind P H0))))))))))) in (or_intror TMP_23
-TMP_24 TMP_29)))))) in (let TMP_69 \def (\lambda (k: K).(let TMP_37 \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 t1 (THead (Bind b) w
-u)) \to (\forall (P: Prop).P)))))) \to (let TMP_34 \def (\lambda (b:
-B).(\lambda (w: T).(\lambda (u: T).(let TMP_31 \def (THead k0 t0 t1) in (let
-TMP_32 \def (Bind b) in (let TMP_33 \def (THead TMP_32 w u) in (eq T TMP_31
-TMP_33))))))) in (let TMP_35 \def (ex_3 B T T TMP_34) in (let TMP_36 \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_35
-TMP_36))))))))) in (let TMP_54 \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
+ \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 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 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 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_42 \def (\lambda (b0: B).(\lambda (w:
-T).(\lambda (u: T).(let TMP_38 \def (Bind b) in (let TMP_39 \def (THead
-TMP_38 t0 t1) in (let TMP_40 \def (Bind b0) in (let TMP_41 \def (THead TMP_40
-w u) in (eq T TMP_39 TMP_41)))))))) in (let TMP_43 \def (ex_3 B T T TMP_42)
-in (let TMP_44 \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_49 \def (\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(let
-TMP_45 \def (Bind b) in (let TMP_46 \def (THead TMP_45 t0 t1) in (let TMP_47
-\def (Bind b0) in (let TMP_48 \def (THead TMP_47 w u) in (eq T TMP_46
-TMP_48)))))))) in (let TMP_50 \def (Bind b) in (let TMP_51 \def (THead TMP_50
-t0 t1) in (let TMP_52 \def (refl_equal T TMP_51) in (let TMP_53 \def
-(ex_3_intro B T T TMP_49 b t0 t1 TMP_52) in (or_introl TMP_43 TMP_44
-TMP_53)))))))))))))) in (let TMP_68 \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_59 \def (\lambda (b: B).(\lambda
-(w: T).(\lambda (u: T).(let TMP_55 \def (Flat f) in (let TMP_56 \def (THead
-TMP_55 t0 t1) in (let TMP_57 \def (Bind b) in (let TMP_58 \def (THead TMP_57
-w u) in (eq T TMP_56 TMP_58)))))))) in (let TMP_60 \def (ex_3 B T T TMP_59)
-in (let TMP_61 \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_67 \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_62 \def (Flat f) in (let TMP_63 \def (THead TMP_62 t0 t1) in
-(let TMP_64 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False
-| (TLRef _) \Rightarrow False | (THead k0 _ _) \Rightarrow (match k0 with
-[(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) in (let TMP_65
-\def (Bind b) in (let TMP_66 \def (THead TMP_65 w u) in (let H2 \def (eq_ind
-T TMP_63 TMP_64 I TMP_66 H1) in (False_ind P H2)))))))))))) in (or_intror
-TMP_60 TMP_61 TMP_67)))))))))) in (K_ind TMP_37 TMP_54 TMP_68 k))))) in
-(T_ind TMP_6 TMP_18 TMP_30 TMP_69 t))))).
+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
+(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 with [(TSort _) \Rightarrow False | (TLRef _)
+\Rightarrow False | (THead k0 _ _) \Rightarrow (match k0 with [(Bind _)
+\Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind b) w u) H1)
+in (False_ind P H2))))))))))))) k)) 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).(let TMP_6 \def (\lambda (t: T).(\forall (v: T).(let TMP_3
-\def (\lambda (t0: T).(let TMP_1 \def (Bind Abst) in (let TMP_2 \def (THead
-TMP_1 v t0) in (eq T t TMP_2)))) in (let TMP_4 \def (ex T TMP_3) in (let
-TMP_5 \def (\forall (t0: T).((eq T t (THead (Bind Abst) v t0)) \to (\forall
-(P: Prop).P))) in (or TMP_4 TMP_5)))))) in (let TMP_18 \def (\lambda (n:
-nat).(\lambda (v: T).(let TMP_10 \def (\lambda (t: T).(let TMP_7 \def (TSort
-n) in (let TMP_8 \def (Bind Abst) in (let TMP_9 \def (THead TMP_8 v t) in (eq
-T TMP_7 TMP_9))))) in (let TMP_11 \def (ex T TMP_10) in (let TMP_12 \def
-(\forall (t: T).((eq T (TSort n) (THead (Bind Abst) v t)) \to (\forall (P:
-Prop).P))) in (let TMP_17 \def (\lambda (t: T).(\lambda (H: (eq T (TSort n)
-(THead (Bind Abst) v t))).(\lambda (P: Prop).(let TMP_13 \def (TSort n) in
-(let TMP_14 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True
-| (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let
-TMP_15 \def (Bind Abst) in (let TMP_16 \def (THead TMP_15 v t) in (let H0
-\def (eq_ind T TMP_13 TMP_14 I TMP_16 H) in (False_ind P H0))))))))) in
-(or_intror TMP_11 TMP_12 TMP_17))))))) in (let TMP_30 \def (\lambda (n:
-nat).(\lambda (v: T).(let TMP_22 \def (\lambda (t: T).(let TMP_19 \def (TLRef
-n) in (let TMP_20 \def (Bind Abst) in (let TMP_21 \def (THead TMP_20 v t) in
-(eq T TMP_19 TMP_21))))) in (let TMP_23 \def (ex T TMP_22) in (let TMP_24
-\def (\forall (t: T).((eq T (TLRef n) (THead (Bind Abst) v t)) \to (\forall
-(P: Prop).P))) in (let TMP_29 \def (\lambda (t: T).(\lambda (H: (eq T (TLRef
-n) (THead (Bind Abst) v t))).(\lambda (P: Prop).(let TMP_25 \def (TLRef n) in
-(let TMP_26 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False
-| (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let
-TMP_27 \def (Bind Abst) in (let TMP_28 \def (THead TMP_27 v t) in (let H0
-\def (eq_ind T TMP_25 TMP_26 I TMP_28 H) in (False_ind P H0))))))))) in
-(or_intror TMP_23 TMP_24 TMP_29))))))) in (let TMP_130 \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_31 \def (Bind Abst) in (let H_x \def
-(terms_props__kind_dec k TMP_31) in (let H1 \def H_x in (let TMP_32 \def
-(Bind Abst) in (let TMP_33 \def (eq K k TMP_32) in (let TMP_34 \def ((eq K k
-(Bind Abst)) \to (\forall (P: Prop).P)) in (let TMP_38 \def (\lambda (t1:
-T).(let TMP_35 \def (THead k t t0) in (let TMP_36 \def (Bind Abst) in (let
-TMP_37 \def (THead TMP_36 v t1) in (eq T TMP_35 TMP_37))))) in (let TMP_39
-\def (ex T TMP_38) in (let TMP_40 \def (\forall (t1: T).((eq T (THead k t t0)
-(THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let TMP_41 \def (or
-TMP_39 TMP_40) in (let TMP_107 \def (\lambda (H2: (eq K k (Bind Abst))).(let
-TMP_42 \def (Bind Abst) in (let TMP_49 \def (\lambda (k0: K).(let TMP_46 \def
-(\lambda (t1: T).(let TMP_43 \def (THead k0 t t0) in (let TMP_44 \def (Bind
-Abst) in (let TMP_45 \def (THead TMP_44 v t1) in (eq T TMP_43 TMP_45))))) in
-(let TMP_47 \def (ex T TMP_46) in (let TMP_48 \def (\forall (t1: T).((eq T
-(THead k0 t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (or
-TMP_47 TMP_48))))) in (let H_x0 \def (term_dec t v) in (let H3 \def H_x0 in
-(let TMP_50 \def (eq T t v) in (let TMP_51 \def ((eq T t v) \to (\forall (P:
-Prop).P)) in (let TMP_56 \def (\lambda (t1: T).(let TMP_52 \def (Bind Abst)
-in (let TMP_53 \def (THead TMP_52 t t0) in (let TMP_54 \def (Bind Abst) in
-(let TMP_55 \def (THead TMP_54 v t1) in (eq T TMP_53 TMP_55)))))) in (let
-TMP_57 \def (ex T TMP_56) in (let TMP_58 \def (\forall (t1: T).((eq T (THead
-(Bind Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in
-(let TMP_59 \def (or TMP_57 TMP_58) in (let TMP_85 \def (\lambda (H4: (eq T t
-v)).(let TMP_67 \def (\lambda (t1: T).(let TMP_64 \def (\lambda (t2: T).(let
-TMP_60 \def (Bind Abst) in (let TMP_61 \def (THead TMP_60 t t0) in (let
-TMP_62 \def (Bind Abst) in (let TMP_63 \def (THead TMP_62 t1 t2) in (eq T
-TMP_61 TMP_63)))))) in (let TMP_65 \def (ex T TMP_64) in (let TMP_66 \def
-(\forall (t2: T).((eq T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2))
-\to (\forall (P: Prop).P))) in (or TMP_65 TMP_66))))) in (let TMP_72 \def
-(\lambda (t1: T).(let TMP_68 \def (Bind Abst) in (let TMP_69 \def (THead
-TMP_68 t t0) in (let TMP_70 \def (Bind Abst) in (let TMP_71 \def (THead
-TMP_70 t t1) in (eq T TMP_69 TMP_71)))))) in (let TMP_73 \def (ex T TMP_72)
-in (let TMP_74 \def (\forall (t1: T).((eq T (THead (Bind Abst) t t0) (THead
-(Bind Abst) t t1)) \to (\forall (P: Prop).P))) in (let TMP_79 \def (\lambda
-(t1: T).(let TMP_75 \def (Bind Abst) in (let TMP_76 \def (THead TMP_75 t t0)
-in (let TMP_77 \def (Bind Abst) in (let TMP_78 \def (THead TMP_77 t t1) in
-(eq T TMP_76 TMP_78)))))) in (let TMP_80 \def (Bind Abst) in (let TMP_81 \def
-(THead TMP_80 t t0) in (let TMP_82 \def (refl_equal T TMP_81) in (let TMP_83
-\def (ex_intro T TMP_79 t0 TMP_82) in (let TMP_84 \def (or_introl TMP_73
-TMP_74 TMP_83) in (eq_ind T t TMP_67 TMP_84 v H4)))))))))))) in (let TMP_105
-\def (\lambda (H4: (((eq T t v) \to (\forall (P: Prop).P)))).(let TMP_90 \def
-(\lambda (t1: T).(let TMP_86 \def (Bind Abst) in (let TMP_87 \def (THead
-TMP_86 t t0) in (let TMP_88 \def (Bind Abst) in (let TMP_89 \def (THead
-TMP_88 v t1) in (eq T TMP_87 TMP_89)))))) in (let TMP_91 \def (ex T TMP_90)
-in (let TMP_92 \def (\forall (t1: T).((eq T (THead (Bind Abst) t t0) (THead
-(Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let TMP_104 \def (\lambda
-(t1: T).(\lambda (H5: (eq T (THead (Bind Abst) t t0) (THead (Bind Abst) v
-t1))).(\lambda (P: Prop).(let TMP_93 \def (\lambda (e: T).(match e with
-[(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t2 _)
-\Rightarrow t2])) in (let TMP_94 \def (Bind Abst) in (let TMP_95 \def (THead
-TMP_94 t t0) in (let TMP_96 \def (Bind Abst) in (let TMP_97 \def (THead
-TMP_96 v t1) in (let H6 \def (f_equal T T TMP_93 TMP_95 TMP_97 H5) in (let
-TMP_98 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef
-_) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) in (let TMP_99 \def
-(Bind Abst) in (let TMP_100 \def (THead TMP_99 t t0) in (let TMP_101 \def
-(Bind Abst) in (let TMP_102 \def (THead TMP_101 v t1) in (let H7 \def
-(f_equal T T TMP_98 TMP_100 TMP_102 H5) in (let TMP_103 \def (\lambda (H8:
-(eq T t v)).(H4 H8 P)) in (TMP_103 H6))))))))))))))))) in (or_intror TMP_91
-TMP_92 TMP_104)))))) in (let TMP_106 \def (or_ind TMP_50 TMP_51 TMP_59 TMP_85
-TMP_105 H3) in (eq_ind_r K TMP_42 TMP_49 TMP_106 k H2))))))))))))))) in (let
-TMP_129 \def (\lambda (H2: (((eq K k (Bind Abst)) \to (\forall (P:
-Prop).P)))).(let TMP_111 \def (\lambda (t1: T).(let TMP_108 \def (THead k t
-t0) in (let TMP_109 \def (Bind Abst) in (let TMP_110 \def (THead TMP_109 v
-t1) in (eq T TMP_108 TMP_110))))) in (let TMP_112 \def (ex T TMP_111) in (let
-TMP_113 \def (\forall (t1: T).((eq T (THead k t t0) (THead (Bind Abst) v t1))
-\to (\forall (P: Prop).P))) in (let TMP_128 \def (\lambda (t1: T).(\lambda
-(H3: (eq T (THead k t t0) (THead (Bind Abst) v t1))).(\lambda (P: Prop).(let
-TMP_114 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow k | (TLRef
-_) \Rightarrow k | (THead k0 _ _) \Rightarrow k0])) in (let TMP_115 \def
-(THead k t t0) in (let TMP_116 \def (Bind Abst) in (let TMP_117 \def (THead
-TMP_116 v t1) in (let H4 \def (f_equal T K TMP_114 TMP_115 TMP_117 H3) in
-(let TMP_118 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t |
-(TLRef _) \Rightarrow t | (THead _ t2 _) \Rightarrow t2])) in (let TMP_119
-\def (THead k t t0) in (let TMP_120 \def (Bind Abst) in (let TMP_121 \def
-(THead TMP_120 v t1) in (let H5 \def (f_equal T T TMP_118 TMP_119 TMP_121 H3)
-in (let TMP_122 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0
-| (TLRef _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) in (let TMP_123
-\def (THead k t t0) in (let TMP_124 \def (Bind Abst) in (let TMP_125 \def
-(THead TMP_124 v t1) in (let H6 \def (f_equal T T TMP_122 TMP_123 TMP_125 H3)
-in (let TMP_126 \def (\lambda (_: (eq T t v)).(\lambda (H8: (eq K k (Bind
-Abst))).(H2 H8 P))) in (let TMP_127 \def (TMP_126 H5) in (TMP_127
-H4))))))))))))))))))))) in (or_intror TMP_112 TMP_113 TMP_128)))))) in
-(or_ind TMP_33 TMP_34 TMP_41 TMP_107 TMP_129 H1))))))))))))))))))) in (T_ind
-TMP_6 TMP_18 TMP_30 TMP_130 u))))).
+ \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 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 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
+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 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 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 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 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).
projects / helm.git / blobdiff