include "basic_1/T/fwd.ma".
-theorem terms_props__bind_dec:
+fact 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).(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))))).
+ \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:
+lemma 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_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))))))))))).
+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:
+fact 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_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)))).
+ \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:
+fact 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_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)))).
+ \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:
+lemma 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_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
+ \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])) 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
+\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).(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))))).
+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])) 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])) (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:
+lemma 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_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 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))))))
+ \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 (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))))).
+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 (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:
+lemma 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_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
+ \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))) 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:
+(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 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 _)
+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]))
-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])) 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))))).
+(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