1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
17 include "basic_1/T/fwd.ma".
19 theorem terms_props__bind_dec:
20 \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) ((eq B b1 b2) \to (\forall
23 \lambda (b1: B).(let TMP_3 \def (\lambda (b: B).(\forall (b2: B).(let TMP_1
24 \def (eq B b b2) in (let TMP_2 \def ((eq B b b2) \to (\forall (P: Prop).P))
25 in (or TMP_1 TMP_2))))) in (let TMP_21 \def (\lambda (b2: B).(let TMP_6 \def
26 (\lambda (b: B).(let TMP_4 \def (eq B Abbr b) in (let TMP_5 \def ((eq B Abbr
27 b) \to (\forall (P: Prop).P)) in (or TMP_4 TMP_5)))) in (let TMP_7 \def (eq B
28 Abbr Abbr) in (let TMP_8 \def ((eq B Abbr Abbr) \to (\forall (P: Prop).P)) in
29 (let TMP_9 \def (refl_equal B Abbr) in (let TMP_10 \def (or_introl TMP_7
30 TMP_8 TMP_9) in (let TMP_11 \def (eq B Abbr Abst) in (let TMP_12 \def ((eq B
31 Abbr Abst) \to (\forall (P: Prop).P)) in (let TMP_14 \def (\lambda (H: (eq B
32 Abbr Abst)).(\lambda (P: Prop).(let TMP_13 \def (\lambda (ee: B).(match ee
33 with [Abbr \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow
34 False])) in (let H0 \def (eq_ind B Abbr TMP_13 I Abst H) in (False_ind P
35 H0))))) in (let TMP_15 \def (or_intror TMP_11 TMP_12 TMP_14) in (let TMP_16
36 \def (eq B Abbr Void) in (let TMP_17 \def ((eq B Abbr Void) \to (\forall (P:
37 Prop).P)) in (let TMP_19 \def (\lambda (H: (eq B Abbr Void)).(\lambda (P:
38 Prop).(let TMP_18 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow True
39 | Abst \Rightarrow False | Void \Rightarrow False])) in (let H0 \def (eq_ind
40 B Abbr TMP_18 I Void H) in (False_ind P H0))))) in (let TMP_20 \def
41 (or_intror TMP_16 TMP_17 TMP_19) in (B_ind TMP_6 TMP_10 TMP_15 TMP_20
42 b2))))))))))))))) in (let TMP_39 \def (\lambda (b2: B).(let TMP_24 \def
43 (\lambda (b: B).(let TMP_22 \def (eq B Abst b) in (let TMP_23 \def ((eq B
44 Abst b) \to (\forall (P: Prop).P)) in (or TMP_22 TMP_23)))) in (let TMP_25
45 \def (eq B Abst Abbr) in (let TMP_26 \def ((eq B Abst Abbr) \to (\forall (P:
46 Prop).P)) in (let TMP_28 \def (\lambda (H: (eq B Abst Abbr)).(\lambda (P:
47 Prop).(let TMP_27 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow
48 False | Abst \Rightarrow True | Void \Rightarrow False])) in (let H0 \def
49 (eq_ind B Abst TMP_27 I Abbr H) in (False_ind P H0))))) in (let TMP_29 \def
50 (or_intror TMP_25 TMP_26 TMP_28) in (let TMP_30 \def (eq B Abst Abst) in (let
51 TMP_31 \def ((eq B Abst Abst) \to (\forall (P: Prop).P)) in (let TMP_32 \def
52 (refl_equal B Abst) in (let TMP_33 \def (or_introl TMP_30 TMP_31 TMP_32) in
53 (let TMP_34 \def (eq B Abst Void) in (let TMP_35 \def ((eq B Abst Void) \to
54 (\forall (P: Prop).P)) in (let TMP_37 \def (\lambda (H: (eq B Abst
55 Void)).(\lambda (P: Prop).(let TMP_36 \def (\lambda (ee: B).(match ee with
56 [Abbr \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]))
57 in (let H0 \def (eq_ind B Abst TMP_36 I Void H) in (False_ind P H0))))) in
58 (let TMP_38 \def (or_intror TMP_34 TMP_35 TMP_37) in (B_ind TMP_24 TMP_29
59 TMP_33 TMP_38 b2))))))))))))))) in (let TMP_57 \def (\lambda (b2: B).(let
60 TMP_42 \def (\lambda (b: B).(let TMP_40 \def (eq B Void b) in (let TMP_41
61 \def ((eq B Void b) \to (\forall (P: Prop).P)) in (or TMP_40 TMP_41)))) in
62 (let TMP_43 \def (eq B Void Abbr) in (let TMP_44 \def ((eq B Void Abbr) \to
63 (\forall (P: Prop).P)) in (let TMP_46 \def (\lambda (H: (eq B Void
64 Abbr)).(\lambda (P: Prop).(let TMP_45 \def (\lambda (ee: B).(match ee with
65 [Abbr \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]))
66 in (let H0 \def (eq_ind B Void TMP_45 I Abbr H) in (False_ind P H0))))) in
67 (let TMP_47 \def (or_intror TMP_43 TMP_44 TMP_46) in (let TMP_48 \def (eq B
68 Void Abst) in (let TMP_49 \def ((eq B Void Abst) \to (\forall (P: Prop).P))
69 in (let TMP_51 \def (\lambda (H: (eq B Void Abst)).(\lambda (P: Prop).(let
70 TMP_50 \def (\lambda (ee: B).(match ee with [Abbr \Rightarrow False | Abst
71 \Rightarrow False | Void \Rightarrow True])) in (let H0 \def (eq_ind B Void
72 TMP_50 I Abst H) in (False_ind P H0))))) in (let TMP_52 \def (or_intror
73 TMP_48 TMP_49 TMP_51) in (let TMP_53 \def (eq B Void Void) in (let TMP_54
74 \def ((eq B Void Void) \to (\forall (P: Prop).P)) in (let TMP_55 \def
75 (refl_equal B Void) in (let TMP_56 \def (or_introl TMP_53 TMP_54 TMP_55) in
76 (B_ind TMP_42 TMP_47 TMP_52 TMP_56 b2))))))))))))))) in (B_ind TMP_3 TMP_21
77 TMP_39 TMP_57 b1))))).
80 \forall (b1: B).(\forall (b2: B).(or (eq B b1 b2) (not (eq B b1 b2))))
82 \lambda (b1: B).(\lambda (b2: B).(let H_x \def (terms_props__bind_dec b1 b2)
83 in (let H \def H_x in (let TMP_1 \def (eq B b1 b2) in (let TMP_2 \def ((eq B
84 b1 b2) \to (\forall (P: Prop).P)) in (let TMP_3 \def (eq B b1 b2) in (let
85 TMP_4 \def ((eq B b1 b2) \to False) in (let TMP_5 \def (or TMP_3 TMP_4) in
86 (let TMP_8 \def (\lambda (H0: (eq B b1 b2)).(let TMP_6 \def (eq B b1 b2) in
87 (let TMP_7 \def ((eq B b1 b2) \to False) in (or_introl TMP_6 TMP_7 H0)))) in
88 (let TMP_12 \def (\lambda (H0: (((eq B b1 b2) \to (\forall (P:
89 Prop).P)))).(let TMP_9 \def (eq B b1 b2) in (let TMP_10 \def ((eq B b1 b2)
90 \to False) in (let TMP_11 \def (\lambda (H1: (eq B b1 b2)).(H0 H1 False)) in
91 (or_intror TMP_9 TMP_10 TMP_11))))) in (or_ind TMP_1 TMP_2 TMP_5 TMP_8 TMP_12
94 theorem terms_props__flat_dec:
95 \forall (f1: F).(\forall (f2: F).(or (eq F f1 f2) ((eq F f1 f2) \to (\forall
98 \lambda (f1: F).(let TMP_3 \def (\lambda (f: F).(\forall (f2: F).(let TMP_1
99 \def (eq F f f2) in (let TMP_2 \def ((eq F f f2) \to (\forall (P: Prop).P))
100 in (or TMP_1 TMP_2))))) in (let TMP_16 \def (\lambda (f2: F).(let TMP_6 \def
101 (\lambda (f: F).(let TMP_4 \def (eq F Appl f) in (let TMP_5 \def ((eq F Appl
102 f) \to (\forall (P: Prop).P)) in (or TMP_4 TMP_5)))) in (let TMP_7 \def (eq F
103 Appl Appl) in (let TMP_8 \def ((eq F Appl Appl) \to (\forall (P: Prop).P)) in
104 (let TMP_9 \def (refl_equal F Appl) in (let TMP_10 \def (or_introl TMP_7
105 TMP_8 TMP_9) in (let TMP_11 \def (eq F Appl Cast) in (let TMP_12 \def ((eq F
106 Appl Cast) \to (\forall (P: Prop).P)) in (let TMP_14 \def (\lambda (H: (eq F
107 Appl Cast)).(\lambda (P: Prop).(let TMP_13 \def (\lambda (ee: F).(match ee
108 with [Appl \Rightarrow True | Cast \Rightarrow False])) in (let H0 \def
109 (eq_ind F Appl TMP_13 I Cast H) in (False_ind P H0))))) in (let TMP_15 \def
110 (or_intror TMP_11 TMP_12 TMP_14) in (F_ind TMP_6 TMP_10 TMP_15 f2)))))))))))
111 in (let TMP_29 \def (\lambda (f2: F).(let TMP_19 \def (\lambda (f: F).(let
112 TMP_17 \def (eq F Cast f) in (let TMP_18 \def ((eq F Cast f) \to (\forall (P:
113 Prop).P)) in (or TMP_17 TMP_18)))) in (let TMP_20 \def (eq F Cast Appl) in
114 (let TMP_21 \def ((eq F Cast Appl) \to (\forall (P: Prop).P)) in (let TMP_23
115 \def (\lambda (H: (eq F Cast Appl)).(\lambda (P: Prop).(let TMP_22 \def
116 (\lambda (ee: F).(match ee with [Appl \Rightarrow False | Cast \Rightarrow
117 True])) in (let H0 \def (eq_ind F Cast TMP_22 I Appl H) in (False_ind P
118 H0))))) in (let TMP_24 \def (or_intror TMP_20 TMP_21 TMP_23) in (let TMP_25
119 \def (eq F Cast Cast) in (let TMP_26 \def ((eq F Cast Cast) \to (\forall (P:
120 Prop).P)) in (let TMP_27 \def (refl_equal F Cast) in (let TMP_28 \def
121 (or_introl TMP_25 TMP_26 TMP_27) in (F_ind TMP_19 TMP_24 TMP_28 f2)))))))))))
122 in (F_ind TMP_3 TMP_16 TMP_29 f1)))).
124 theorem terms_props__kind_dec:
125 \forall (k1: K).(\forall (k2: K).(or (eq K k1 k2) ((eq K k1 k2) \to (\forall
128 \lambda (k1: K).(let TMP_3 \def (\lambda (k: K).(\forall (k2: K).(let TMP_1
129 \def (eq K k k2) in (let TMP_2 \def ((eq K k k2) \to (\forall (P: Prop).P))
130 in (or TMP_1 TMP_2))))) in (let TMP_49 \def (\lambda (b: B).(\lambda (k2:
131 K).(let TMP_7 \def (\lambda (k: K).(let TMP_4 \def (Bind b) in (let TMP_5
132 \def (eq K TMP_4 k) in (let TMP_6 \def ((eq K (Bind b) k) \to (\forall (P:
133 Prop).P)) in (or TMP_5 TMP_6))))) in (let TMP_39 \def (\lambda (b0: B).(let
134 H_x \def (terms_props__bind_dec b b0) in (let H \def H_x in (let TMP_8 \def
135 (eq B b b0) in (let TMP_9 \def ((eq B b b0) \to (\forall (P: Prop).P)) in
136 (let TMP_10 \def (Bind b) in (let TMP_11 \def (Bind b0) in (let TMP_12 \def
137 (eq K TMP_10 TMP_11) in (let TMP_13 \def ((eq K (Bind b) (Bind b0)) \to
138 (\forall (P: Prop).P)) in (let TMP_14 \def (or TMP_12 TMP_13) in (let TMP_27
139 \def (\lambda (H0: (eq B b b0)).(let TMP_19 \def (\lambda (b1: B).(let TMP_15
140 \def (Bind b) in (let TMP_16 \def (Bind b1) in (let TMP_17 \def (eq K TMP_15
141 TMP_16) in (let TMP_18 \def ((eq K (Bind b) (Bind b1)) \to (\forall (P:
142 Prop).P)) in (or TMP_17 TMP_18)))))) in (let TMP_20 \def (Bind b) in (let
143 TMP_21 \def (Bind b) in (let TMP_22 \def (eq K TMP_20 TMP_21) in (let TMP_23
144 \def ((eq K (Bind b) (Bind b)) \to (\forall (P: Prop).P)) in (let TMP_24 \def
145 (Bind b) in (let TMP_25 \def (refl_equal K TMP_24) in (let TMP_26 \def
146 (or_introl TMP_22 TMP_23 TMP_25) in (eq_ind B b TMP_19 TMP_26 b0 H0))))))))))
147 in (let TMP_38 \def (\lambda (H0: (((eq B b b0) \to (\forall (P:
148 Prop).P)))).(let TMP_28 \def (Bind b) in (let TMP_29 \def (Bind b0) in (let
149 TMP_30 \def (eq K TMP_28 TMP_29) in (let TMP_31 \def ((eq K (Bind b) (Bind
150 b0)) \to (\forall (P: Prop).P)) in (let TMP_37 \def (\lambda (H1: (eq K (Bind
151 b) (Bind b0))).(\lambda (P: Prop).(let TMP_32 \def (\lambda (e: K).(match e
152 with [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b])) in (let TMP_33
153 \def (Bind b) in (let TMP_34 \def (Bind b0) in (let H2 \def (f_equal K B
154 TMP_32 TMP_33 TMP_34 H1) in (let TMP_35 \def (\lambda (b1: B).((eq B b b1)
155 \to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r B b0 TMP_35 H0 b H2)
156 in (let TMP_36 \def (refl_equal B b) in (H3 TMP_36 P)))))))))) in (or_intror
157 TMP_30 TMP_31 TMP_37))))))) in (or_ind TMP_8 TMP_9 TMP_14 TMP_27 TMP_38
158 H))))))))))))) in (let TMP_48 \def (\lambda (f: F).(let TMP_40 \def (Bind b)
159 in (let TMP_41 \def (Flat f) in (let TMP_42 \def (eq K TMP_40 TMP_41) in (let
160 TMP_43 \def ((eq K (Bind b) (Flat f)) \to (\forall (P: Prop).P)) in (let
161 TMP_47 \def (\lambda (H: (eq K (Bind b) (Flat f))).(\lambda (P: Prop).(let
162 TMP_44 \def (Bind b) in (let TMP_45 \def (\lambda (ee: K).(match ee with
163 [(Bind _) \Rightarrow True | (Flat _) \Rightarrow False])) in (let TMP_46
164 \def (Flat f) in (let H0 \def (eq_ind K TMP_44 TMP_45 I TMP_46 H) in
165 (False_ind P H0))))))) in (or_intror TMP_42 TMP_43 TMP_47))))))) in (K_ind
166 TMP_7 TMP_39 TMP_48 k2)))))) in (let TMP_95 \def (\lambda (f: F).(\lambda
167 (k2: K).(let TMP_53 \def (\lambda (k: K).(let TMP_50 \def (Flat f) in (let
168 TMP_51 \def (eq K TMP_50 k) in (let TMP_52 \def ((eq K (Flat f) k) \to
169 (\forall (P: Prop).P)) in (or TMP_51 TMP_52))))) in (let TMP_62 \def (\lambda
170 (b: B).(let TMP_54 \def (Flat f) in (let TMP_55 \def (Bind b) in (let TMP_56
171 \def (eq K TMP_54 TMP_55) in (let TMP_57 \def ((eq K (Flat f) (Bind b)) \to
172 (\forall (P: Prop).P)) in (let TMP_61 \def (\lambda (H: (eq K (Flat f) (Bind
173 b))).(\lambda (P: Prop).(let TMP_58 \def (Flat f) in (let TMP_59 \def
174 (\lambda (ee: K).(match ee with [(Bind _) \Rightarrow False | (Flat _)
175 \Rightarrow True])) in (let TMP_60 \def (Bind b) in (let H0 \def (eq_ind K
176 TMP_58 TMP_59 I TMP_60 H) in (False_ind P H0))))))) in (or_intror TMP_56
177 TMP_57 TMP_61))))))) in (let TMP_94 \def (\lambda (f0: F).(let H_x \def
178 (terms_props__flat_dec f f0) in (let H \def H_x in (let TMP_63 \def (eq F f
179 f0) in (let TMP_64 \def ((eq F f f0) \to (\forall (P: Prop).P)) in (let
180 TMP_65 \def (Flat f) in (let TMP_66 \def (Flat f0) in (let TMP_67 \def (eq K
181 TMP_65 TMP_66) in (let TMP_68 \def ((eq K (Flat f) (Flat f0)) \to (\forall
182 (P: Prop).P)) in (let TMP_69 \def (or TMP_67 TMP_68) in (let TMP_82 \def
183 (\lambda (H0: (eq F f f0)).(let TMP_74 \def (\lambda (f1: F).(let TMP_70 \def
184 (Flat f) in (let TMP_71 \def (Flat f1) in (let TMP_72 \def (eq K TMP_70
185 TMP_71) in (let TMP_73 \def ((eq K (Flat f) (Flat f1)) \to (\forall (P:
186 Prop).P)) in (or TMP_72 TMP_73)))))) in (let TMP_75 \def (Flat f) in (let
187 TMP_76 \def (Flat f) in (let TMP_77 \def (eq K TMP_75 TMP_76) in (let TMP_78
188 \def ((eq K (Flat f) (Flat f)) \to (\forall (P: Prop).P)) in (let TMP_79 \def
189 (Flat f) in (let TMP_80 \def (refl_equal K TMP_79) in (let TMP_81 \def
190 (or_introl TMP_77 TMP_78 TMP_80) in (eq_ind F f TMP_74 TMP_81 f0 H0))))))))))
191 in (let TMP_93 \def (\lambda (H0: (((eq F f f0) \to (\forall (P:
192 Prop).P)))).(let TMP_83 \def (Flat f) in (let TMP_84 \def (Flat f0) in (let
193 TMP_85 \def (eq K TMP_83 TMP_84) in (let TMP_86 \def ((eq K (Flat f) (Flat
194 f0)) \to (\forall (P: Prop).P)) in (let TMP_92 \def (\lambda (H1: (eq K (Flat
195 f) (Flat f0))).(\lambda (P: Prop).(let TMP_87 \def (\lambda (e: K).(match e
196 with [(Bind _) \Rightarrow f | (Flat f1) \Rightarrow f1])) in (let TMP_88
197 \def (Flat f) in (let TMP_89 \def (Flat f0) in (let H2 \def (f_equal K F
198 TMP_87 TMP_88 TMP_89 H1) in (let TMP_90 \def (\lambda (f1: F).((eq F f f1)
199 \to (\forall (P0: Prop).P0))) in (let H3 \def (eq_ind_r F f0 TMP_90 H0 f H2)
200 in (let TMP_91 \def (refl_equal F f) in (H3 TMP_91 P)))))))))) in (or_intror
201 TMP_85 TMP_86 TMP_92))))))) in (or_ind TMP_63 TMP_64 TMP_69 TMP_82 TMP_93
202 H))))))))))))) in (K_ind TMP_53 TMP_62 TMP_94 k2)))))) in (K_ind TMP_3 TMP_49
206 \forall (t1: T).(\forall (t2: T).(or (eq T t1 t2) ((eq T t1 t2) \to (\forall
209 \lambda (t1: T).(let TMP_3 \def (\lambda (t: T).(\forall (t2: T).(let TMP_1
210 \def (eq T t t2) in (let TMP_2 \def ((eq T t t2) \to (\forall (P: Prop).P))
211 in (or TMP_1 TMP_2))))) in (let TMP_58 \def (\lambda (n: nat).(\lambda (t2:
212 T).(let TMP_7 \def (\lambda (t: T).(let TMP_4 \def (TSort n) in (let TMP_5
213 \def (eq T TMP_4 t) in (let TMP_6 \def ((eq T (TSort n) t) \to (\forall (P:
214 Prop).P)) in (or TMP_5 TMP_6))))) in (let TMP_39 \def (\lambda (n0: nat).(let
215 H_x \def (nat_dec n n0) in (let H \def H_x in (let TMP_8 \def (eq nat n n0)
216 in (let TMP_9 \def ((eq nat n n0) \to (\forall (P: Prop).P)) in (let TMP_10
217 \def (TSort n) in (let TMP_11 \def (TSort n0) in (let TMP_12 \def (eq T
218 TMP_10 TMP_11) in (let TMP_13 \def ((eq T (TSort n) (TSort n0)) \to (\forall
219 (P: Prop).P)) in (let TMP_14 \def (or TMP_12 TMP_13) in (let TMP_27 \def
220 (\lambda (H0: (eq nat n n0)).(let TMP_19 \def (\lambda (n1: nat).(let TMP_15
221 \def (TSort n) in (let TMP_16 \def (TSort n1) in (let TMP_17 \def (eq T
222 TMP_15 TMP_16) in (let TMP_18 \def ((eq T (TSort n) (TSort n1)) \to (\forall
223 (P: Prop).P)) in (or TMP_17 TMP_18)))))) in (let TMP_20 \def (TSort n) in
224 (let TMP_21 \def (TSort n) in (let TMP_22 \def (eq T TMP_20 TMP_21) in (let
225 TMP_23 \def ((eq T (TSort n) (TSort n)) \to (\forall (P: Prop).P)) in (let
226 TMP_24 \def (TSort n) in (let TMP_25 \def (refl_equal T TMP_24) in (let
227 TMP_26 \def (or_introl TMP_22 TMP_23 TMP_25) in (eq_ind nat n TMP_19 TMP_26
228 n0 H0)))))))))) in (let TMP_38 \def (\lambda (H0: (((eq nat n n0) \to
229 (\forall (P: Prop).P)))).(let TMP_28 \def (TSort n) in (let TMP_29 \def
230 (TSort n0) in (let TMP_30 \def (eq T TMP_28 TMP_29) in (let TMP_31 \def ((eq
231 T (TSort n) (TSort n0)) \to (\forall (P: Prop).P)) in (let TMP_37 \def
232 (\lambda (H1: (eq T (TSort n) (TSort n0))).(\lambda (P: Prop).(let TMP_32
233 \def (\lambda (e: T).(match e with [(TSort n1) \Rightarrow n1 | (TLRef _)
234 \Rightarrow n | (THead _ _ _) \Rightarrow n])) in (let TMP_33 \def (TSort n)
235 in (let TMP_34 \def (TSort n0) in (let H2 \def (f_equal T nat TMP_32 TMP_33
236 TMP_34 H1) in (let TMP_35 \def (\lambda (n1: nat).((eq nat n n1) \to (\forall
237 (P0: Prop).P0))) in (let H3 \def (eq_ind_r nat n0 TMP_35 H0 n H2) in (let
238 TMP_36 \def (refl_equal nat n) in (H3 TMP_36 P)))))))))) in (or_intror TMP_30
239 TMP_31 TMP_37))))))) in (or_ind TMP_8 TMP_9 TMP_14 TMP_27 TMP_38
240 H))))))))))))) in (let TMP_48 \def (\lambda (n0: nat).(let TMP_40 \def (TSort
241 n) in (let TMP_41 \def (TLRef n0) in (let TMP_42 \def (eq T TMP_40 TMP_41) in
242 (let TMP_43 \def ((eq T (TSort n) (TLRef n0)) \to (\forall (P: Prop).P)) in
243 (let TMP_47 \def (\lambda (H: (eq T (TSort n) (TLRef n0))).(\lambda (P:
244 Prop).(let TMP_44 \def (TSort n) in (let TMP_45 \def (\lambda (ee: T).(match
245 ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _
246 _ _) \Rightarrow False])) in (let TMP_46 \def (TLRef n0) in (let H0 \def
247 (eq_ind T TMP_44 TMP_45 I TMP_46 H) in (False_ind P H0))))))) in (or_intror
248 TMP_42 TMP_43 TMP_47))))))) in (let TMP_57 \def (\lambda (k: K).(\lambda (t:
249 T).(\lambda (_: (or (eq T (TSort n) t) ((eq T (TSort n) t) \to (\forall (P:
250 Prop).P)))).(\lambda (t0: T).(\lambda (_: (or (eq T (TSort n) t0) ((eq T
251 (TSort n) t0) \to (\forall (P: Prop).P)))).(let TMP_49 \def (TSort n) in (let
252 TMP_50 \def (THead k t t0) in (let TMP_51 \def (eq T TMP_49 TMP_50) in (let
253 TMP_52 \def ((eq T (TSort n) (THead k t t0)) \to (\forall (P: Prop).P)) in
254 (let TMP_56 \def (\lambda (H1: (eq T (TSort n) (THead k t t0))).(\lambda (P:
255 Prop).(let TMP_53 \def (TSort n) in (let TMP_54 \def (\lambda (ee: T).(match
256 ee with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _
257 _ _) \Rightarrow False])) in (let TMP_55 \def (THead k t t0) in (let H2 \def
258 (eq_ind T TMP_53 TMP_54 I TMP_55 H1) in (False_ind P H2))))))) in (or_intror
259 TMP_51 TMP_52 TMP_56))))))))))) in (T_ind TMP_7 TMP_39 TMP_48 TMP_57
260 t2))))))) in (let TMP_113 \def (\lambda (n: nat).(\lambda (t2: T).(let TMP_62
261 \def (\lambda (t: T).(let TMP_59 \def (TLRef n) in (let TMP_60 \def (eq T
262 TMP_59 t) in (let TMP_61 \def ((eq T (TLRef n) t) \to (\forall (P: Prop).P))
263 in (or TMP_60 TMP_61))))) in (let TMP_71 \def (\lambda (n0: nat).(let TMP_63
264 \def (TLRef n) in (let TMP_64 \def (TSort n0) in (let TMP_65 \def (eq T
265 TMP_63 TMP_64) in (let TMP_66 \def ((eq T (TLRef n) (TSort n0)) \to (\forall
266 (P: Prop).P)) in (let TMP_70 \def (\lambda (H: (eq T (TLRef n) (TSort
267 n0))).(\lambda (P: Prop).(let TMP_67 \def (TLRef n) in (let TMP_68 \def
268 (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
269 \Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_69 \def
270 (TSort n0) in (let H0 \def (eq_ind T TMP_67 TMP_68 I TMP_69 H) in (False_ind
271 P H0))))))) in (or_intror TMP_65 TMP_66 TMP_70))))))) in (let TMP_103 \def
272 (\lambda (n0: nat).(let H_x \def (nat_dec n n0) in (let H \def H_x in (let
273 TMP_72 \def (eq nat n n0) in (let TMP_73 \def ((eq nat n n0) \to (\forall (P:
274 Prop).P)) in (let TMP_74 \def (TLRef n) in (let TMP_75 \def (TLRef n0) in
275 (let TMP_76 \def (eq T TMP_74 TMP_75) in (let TMP_77 \def ((eq T (TLRef n)
276 (TLRef n0)) \to (\forall (P: Prop).P)) in (let TMP_78 \def (or TMP_76 TMP_77)
277 in (let TMP_91 \def (\lambda (H0: (eq nat n n0)).(let TMP_83 \def (\lambda
278 (n1: nat).(let TMP_79 \def (TLRef n) in (let TMP_80 \def (TLRef n1) in (let
279 TMP_81 \def (eq T TMP_79 TMP_80) in (let TMP_82 \def ((eq T (TLRef n) (TLRef
280 n1)) \to (\forall (P: Prop).P)) in (or TMP_81 TMP_82)))))) in (let TMP_84
281 \def (TLRef n) in (let TMP_85 \def (TLRef n) in (let TMP_86 \def (eq T TMP_84
282 TMP_85) in (let TMP_87 \def ((eq T (TLRef n) (TLRef n)) \to (\forall (P:
283 Prop).P)) in (let TMP_88 \def (TLRef n) in (let TMP_89 \def (refl_equal T
284 TMP_88) in (let TMP_90 \def (or_introl TMP_86 TMP_87 TMP_89) in (eq_ind nat n
285 TMP_83 TMP_90 n0 H0)))))))))) in (let TMP_102 \def (\lambda (H0: (((eq nat n
286 n0) \to (\forall (P: Prop).P)))).(let TMP_92 \def (TLRef n) in (let TMP_93
287 \def (TLRef n0) in (let TMP_94 \def (eq T TMP_92 TMP_93) in (let TMP_95 \def
288 ((eq T (TLRef n) (TLRef n0)) \to (\forall (P: Prop).P)) in (let TMP_101 \def
289 (\lambda (H1: (eq T (TLRef n) (TLRef n0))).(\lambda (P: Prop).(let TMP_96
290 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow n | (TLRef n1)
291 \Rightarrow n1 | (THead _ _ _) \Rightarrow n])) in (let TMP_97 \def (TLRef n)
292 in (let TMP_98 \def (TLRef n0) in (let H2 \def (f_equal T nat TMP_96 TMP_97
293 TMP_98 H1) in (let TMP_99 \def (\lambda (n1: nat).((eq nat n n1) \to (\forall
294 (P0: Prop).P0))) in (let H3 \def (eq_ind_r nat n0 TMP_99 H0 n H2) in (let
295 TMP_100 \def (refl_equal nat n) in (H3 TMP_100 P)))))))))) in (or_intror
296 TMP_94 TMP_95 TMP_101))))))) in (or_ind TMP_72 TMP_73 TMP_78 TMP_91 TMP_102
297 H))))))))))))) in (let TMP_112 \def (\lambda (k: K).(\lambda (t: T).(\lambda
298 (_: (or (eq T (TLRef n) t) ((eq T (TLRef n) t) \to (\forall (P:
299 Prop).P)))).(\lambda (t0: T).(\lambda (_: (or (eq T (TLRef n) t0) ((eq T
300 (TLRef n) t0) \to (\forall (P: Prop).P)))).(let TMP_104 \def (TLRef n) in
301 (let TMP_105 \def (THead k t t0) in (let TMP_106 \def (eq T TMP_104 TMP_105)
302 in (let TMP_107 \def ((eq T (TLRef n) (THead k t t0)) \to (\forall (P:
303 Prop).P)) in (let TMP_111 \def (\lambda (H1: (eq T (TLRef n) (THead k t
304 t0))).(\lambda (P: Prop).(let TMP_108 \def (TLRef n) in (let TMP_109 \def
305 (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
306 \Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_110 \def
307 (THead k t t0) in (let H2 \def (eq_ind T TMP_108 TMP_109 I TMP_110 H1) in
308 (False_ind P H2))))))) in (or_intror TMP_106 TMP_107 TMP_111))))))))))) in
309 (T_ind TMP_62 TMP_71 TMP_103 TMP_112 t2))))))) in (let TMP_250 \def (\lambda
310 (k: K).(\lambda (t: T).(\lambda (H: ((\forall (t2: T).(or (eq T t t2) ((eq T
311 t t2) \to (\forall (P: Prop).P)))))).(\lambda (t0: T).(\lambda (H0: ((\forall
312 (t2: T).(or (eq T t0 t2) ((eq T t0 t2) \to (\forall (P:
313 Prop).P)))))).(\lambda (t2: T).(let TMP_117 \def (\lambda (t3: T).(let
314 TMP_114 \def (THead k t t0) in (let TMP_115 \def (eq T TMP_114 t3) in (let
315 TMP_116 \def ((eq T (THead k t t0) t3) \to (\forall (P: Prop).P)) in (or
316 TMP_115 TMP_116))))) in (let TMP_126 \def (\lambda (n: nat).(let TMP_118 \def
317 (THead k t t0) in (let TMP_119 \def (TSort n) in (let TMP_120 \def (eq T
318 TMP_118 TMP_119) in (let TMP_121 \def ((eq T (THead k t t0) (TSort n)) \to
319 (\forall (P: Prop).P)) in (let TMP_125 \def (\lambda (H1: (eq T (THead k t
320 t0) (TSort n))).(\lambda (P: Prop).(let TMP_122 \def (THead k t t0) in (let
321 TMP_123 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False |
322 (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) in (let
323 TMP_124 \def (TSort n) in (let H2 \def (eq_ind T TMP_122 TMP_123 I TMP_124
324 H1) in (False_ind P H2))))))) in (or_intror TMP_120 TMP_121 TMP_125))))))) in
325 (let TMP_135 \def (\lambda (n: nat).(let TMP_127 \def (THead k t t0) in (let
326 TMP_128 \def (TLRef n) in (let TMP_129 \def (eq T TMP_127 TMP_128) in (let
327 TMP_130 \def ((eq T (THead k t t0) (TLRef n)) \to (\forall (P: Prop).P)) in
328 (let TMP_134 \def (\lambda (H1: (eq T (THead k t t0) (TLRef n))).(\lambda (P:
329 Prop).(let TMP_131 \def (THead k t t0) in (let TMP_132 \def (\lambda (ee:
330 T).(match ee with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False
331 | (THead _ _ _) \Rightarrow True])) in (let TMP_133 \def (TLRef n) in (let H2
332 \def (eq_ind T TMP_131 TMP_132 I TMP_133 H1) in (False_ind P H2))))))) in
333 (or_intror TMP_129 TMP_130 TMP_134))))))) in (let TMP_249 \def (\lambda (k0:
334 K).(\lambda (t3: T).(\lambda (H1: (or (eq T (THead k t t0) t3) ((eq T (THead
335 k t t0) t3) \to (\forall (P: Prop).P)))).(\lambda (t4: T).(\lambda (H2: (or
336 (eq T (THead k t t0) t4) ((eq T (THead k t t0) t4) \to (\forall (P:
337 Prop).P)))).(let H_x \def (H t3) in (let H3 \def H_x in (let TMP_136 \def (eq
338 T t t3) in (let TMP_137 \def ((eq T t t3) \to (\forall (P: Prop).P)) in (let
339 TMP_138 \def (THead k t t0) in (let TMP_139 \def (THead k0 t3 t4) in (let
340 TMP_140 \def (eq T TMP_138 TMP_139) in (let TMP_141 \def ((eq T (THead k t
341 t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) in (let TMP_142 \def (or
342 TMP_140 TMP_141) in (let TMP_221 \def (\lambda (H4: (eq T t t3)).(let TMP_146
343 \def (\lambda (t5: T).(let TMP_143 \def (THead k t t0) in (let TMP_144 \def
344 (eq T TMP_143 t5) in (let TMP_145 \def ((eq T (THead k t t0) t5) \to (\forall
345 (P: Prop).P)) in (or TMP_144 TMP_145))))) in (let H5 \def (eq_ind_r T t3
346 TMP_146 H1 t H4) in (let TMP_151 \def (\lambda (t5: T).(let TMP_147 \def
347 (THead k t t0) in (let TMP_148 \def (THead k0 t5 t4) in (let TMP_149 \def (eq
348 T TMP_147 TMP_148) in (let TMP_150 \def ((eq T (THead k t t0) (THead k0 t5
349 t4)) \to (\forall (P: Prop).P)) in (or TMP_149 TMP_150)))))) in (let H_x0
350 \def (H0 t4) in (let H6 \def H_x0 in (let TMP_152 \def (eq T t0 t4) in (let
351 TMP_153 \def ((eq T t0 t4) \to (\forall (P: Prop).P)) in (let TMP_154 \def
352 (THead k t t0) in (let TMP_155 \def (THead k0 t t4) in (let TMP_156 \def (eq
353 T TMP_154 TMP_155) in (let TMP_157 \def ((eq T (THead k t t0) (THead k0 t
354 t4)) \to (\forall (P: Prop).P)) in (let TMP_158 \def (or TMP_156 TMP_157) in
355 (let TMP_200 \def (\lambda (H7: (eq T t0 t4)).(let TMP_162 \def (\lambda (t5:
356 T).(let TMP_159 \def (THead k t t0) in (let TMP_160 \def (eq T TMP_159 t5) in
357 (let TMP_161 \def ((eq T (THead k t t0) t5) \to (\forall (P: Prop).P)) in (or
358 TMP_160 TMP_161))))) in (let H8 \def (eq_ind_r T t4 TMP_162 H2 t0 H7) in (let
359 TMP_167 \def (\lambda (t5: T).(let TMP_163 \def (THead k t t0) in (let
360 TMP_164 \def (THead k0 t t5) in (let TMP_165 \def (eq T TMP_163 TMP_164) in
361 (let TMP_166 \def ((eq T (THead k t t0) (THead k0 t t5)) \to (\forall (P:
362 Prop).P)) in (or TMP_165 TMP_166)))))) in (let H_x1 \def
363 (terms_props__kind_dec k k0) in (let H9 \def H_x1 in (let TMP_168 \def (eq K
364 k k0) in (let TMP_169 \def ((eq K k k0) \to (\forall (P: Prop).P)) in (let
365 TMP_170 \def (THead k t t0) in (let TMP_171 \def (THead k0 t t0) in (let
366 TMP_172 \def (eq T TMP_170 TMP_171) in (let TMP_173 \def ((eq T (THead k t
367 t0) (THead k0 t t0)) \to (\forall (P: Prop).P)) in (let TMP_174 \def (or
368 TMP_172 TMP_173) in (let TMP_187 \def (\lambda (H10: (eq K k k0)).(let
369 TMP_179 \def (\lambda (k1: K).(let TMP_175 \def (THead k t t0) in (let
370 TMP_176 \def (THead k1 t t0) in (let TMP_177 \def (eq T TMP_175 TMP_176) in
371 (let TMP_178 \def ((eq T (THead k t t0) (THead k1 t t0)) \to (\forall (P:
372 Prop).P)) in (or TMP_177 TMP_178)))))) in (let TMP_180 \def (THead k t t0) in
373 (let TMP_181 \def (THead k t t0) in (let TMP_182 \def (eq T TMP_180 TMP_181)
374 in (let TMP_183 \def ((eq T (THead k t t0) (THead k t t0)) \to (\forall (P:
375 Prop).P)) in (let TMP_184 \def (THead k t t0) in (let TMP_185 \def
376 (refl_equal T TMP_184) in (let TMP_186 \def (or_introl TMP_182 TMP_183
377 TMP_185) in (eq_ind K k TMP_179 TMP_186 k0 H10)))))))))) in (let TMP_198 \def
378 (\lambda (H10: (((eq K k k0) \to (\forall (P: Prop).P)))).(let TMP_188 \def
379 (THead k t t0) in (let TMP_189 \def (THead k0 t t0) in (let TMP_190 \def (eq
380 T TMP_188 TMP_189) in (let TMP_191 \def ((eq T (THead k t t0) (THead k0 t
381 t0)) \to (\forall (P: Prop).P)) in (let TMP_197 \def (\lambda (H11: (eq T
382 (THead k t t0) (THead k0 t t0))).(\lambda (P: Prop).(let TMP_192 \def
383 (\lambda (e: T).(match e with [(TSort _) \Rightarrow k | (TLRef _)
384 \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in (let TMP_193 \def (THead
385 k t t0) in (let TMP_194 \def (THead k0 t t0) in (let H12 \def (f_equal T K
386 TMP_192 TMP_193 TMP_194 H11) in (let TMP_195 \def (\lambda (k1: K).((eq K k
387 k1) \to (\forall (P0: Prop).P0))) in (let H13 \def (eq_ind_r K k0 TMP_195 H10
388 k H12) in (let TMP_196 \def (refl_equal K k) in (H13 TMP_196 P)))))))))) in
389 (or_intror TMP_190 TMP_191 TMP_197))))))) in (let TMP_199 \def (or_ind
390 TMP_168 TMP_169 TMP_174 TMP_187 TMP_198 H9) in (eq_ind T t0 TMP_167 TMP_199
391 t4 H7))))))))))))))))) in (let TMP_219 \def (\lambda (H7: (((eq T t0 t4) \to
392 (\forall (P: Prop).P)))).(let TMP_201 \def (THead k t t0) in (let TMP_202
393 \def (THead k0 t t4) in (let TMP_203 \def (eq T TMP_201 TMP_202) in (let
394 TMP_204 \def ((eq T (THead k t t0) (THead k0 t t4)) \to (\forall (P:
395 Prop).P)) in (let TMP_218 \def (\lambda (H8: (eq T (THead k t t0) (THead k0 t
396 t4))).(\lambda (P: Prop).(let TMP_205 \def (\lambda (e: T).(match e with
397 [(TSort _) \Rightarrow k | (TLRef _) \Rightarrow k | (THead k1 _ _)
398 \Rightarrow k1])) in (let TMP_206 \def (THead k t t0) in (let TMP_207 \def
399 (THead k0 t t4) in (let H9 \def (f_equal T K TMP_205 TMP_206 TMP_207 H8) in
400 (let TMP_208 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 |
401 (TLRef _) \Rightarrow t0 | (THead _ _ t5) \Rightarrow t5])) in (let TMP_209
402 \def (THead k t t0) in (let TMP_210 \def (THead k0 t t4) in (let H10 \def
403 (f_equal T T TMP_208 TMP_209 TMP_210 H8) in (let TMP_217 \def (\lambda (_:
404 (eq K k k0)).(let TMP_211 \def (\lambda (t5: T).((eq T t0 t5) \to (\forall
405 (P0: Prop).P0))) in (let H12 \def (eq_ind_r T t4 TMP_211 H7 t0 H10) in (let
406 TMP_215 \def (\lambda (t5: T).(let TMP_212 \def (THead k t t0) in (let
407 TMP_213 \def (eq T TMP_212 t5) in (let TMP_214 \def ((eq T (THead k t t0) t5)
408 \to (\forall (P0: Prop).P0)) in (or TMP_213 TMP_214))))) in (let H13 \def
409 (eq_ind_r T t4 TMP_215 H2 t0 H10) in (let TMP_216 \def (refl_equal T t0) in
410 (H12 TMP_216 P))))))) in (TMP_217 H9)))))))))))) in (or_intror TMP_203
411 TMP_204 TMP_218))))))) in (let TMP_220 \def (or_ind TMP_152 TMP_153 TMP_158
412 TMP_200 TMP_219 H6) in (eq_ind T t TMP_151 TMP_220 t3 H4))))))))))))))))) in
413 (let TMP_248 \def (\lambda (H4: (((eq T t t3) \to (\forall (P:
414 Prop).P)))).(let TMP_222 \def (THead k t t0) in (let TMP_223 \def (THead k0
415 t3 t4) in (let TMP_224 \def (eq T TMP_222 TMP_223) in (let TMP_225 \def ((eq
416 T (THead k t t0) (THead k0 t3 t4)) \to (\forall (P: Prop).P)) in (let TMP_247
417 \def (\lambda (H5: (eq T (THead k t t0) (THead k0 t3 t4))).(\lambda (P:
418 Prop).(let TMP_226 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow
419 k | (TLRef _) \Rightarrow k | (THead k1 _ _) \Rightarrow k1])) in (let
420 TMP_227 \def (THead k t t0) in (let TMP_228 \def (THead k0 t3 t4) in (let H6
421 \def (f_equal T K TMP_226 TMP_227 TMP_228 H5) in (let TMP_229 \def (\lambda
422 (e: T).(match e with [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t |
423 (THead _ t5 _) \Rightarrow t5])) in (let TMP_230 \def (THead k t t0) in (let
424 TMP_231 \def (THead k0 t3 t4) in (let H7 \def (f_equal T T TMP_229 TMP_230
425 TMP_231 H5) in (let TMP_232 \def (\lambda (e: T).(match e with [(TSort _)
426 \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t5) \Rightarrow t5]))
427 in (let TMP_233 \def (THead k t t0) in (let TMP_234 \def (THead k0 t3 t4) in
428 (let H8 \def (f_equal T T TMP_232 TMP_233 TMP_234 H5) in (let TMP_245 \def
429 (\lambda (H9: (eq T t t3)).(\lambda (_: (eq K k k0)).(let TMP_238 \def
430 (\lambda (t5: T).(let TMP_235 \def (THead k t t0) in (let TMP_236 \def (eq T
431 TMP_235 t5) in (let TMP_237 \def ((eq T (THead k t t0) t5) \to (\forall (P0:
432 Prop).P0)) in (or TMP_236 TMP_237))))) in (let H11 \def (eq_ind_r T t4
433 TMP_238 H2 t0 H8) in (let TMP_239 \def (\lambda (t5: T).((eq T t t5) \to
434 (\forall (P0: Prop).P0))) in (let H12 \def (eq_ind_r T t3 TMP_239 H4 t H9) in
435 (let TMP_243 \def (\lambda (t5: T).(let TMP_240 \def (THead k t t0) in (let
436 TMP_241 \def (eq T TMP_240 t5) in (let TMP_242 \def ((eq T (THead k t t0) t5)
437 \to (\forall (P0: Prop).P0)) in (or TMP_241 TMP_242))))) in (let H13 \def
438 (eq_ind_r T t3 TMP_243 H1 t H9) in (let TMP_244 \def (refl_equal T t) in (H12
439 TMP_244 P)))))))))) in (let TMP_246 \def (TMP_245 H7) in (TMP_246
440 H6))))))))))))))))) in (or_intror TMP_224 TMP_225 TMP_247))))))) in (or_ind
441 TMP_136 TMP_137 TMP_142 TMP_221 TMP_248 H3))))))))))))))))) in (T_ind TMP_117
442 TMP_126 TMP_135 TMP_249 t2))))))))))) in (T_ind TMP_3 TMP_58 TMP_113 TMP_250
446 \forall (t: T).(or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u:
447 T).(eq T t (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w: T).(\forall
448 (u: T).((eq T t (THead (Bind b) w u)) \to (\forall (P: Prop).P))))))
450 \lambda (t: T).(let TMP_6 \def (\lambda (t0: T).(let TMP_3 \def (\lambda (b:
451 B).(\lambda (w: T).(\lambda (u: T).(let TMP_1 \def (Bind b) in (let TMP_2
452 \def (THead TMP_1 w u) in (eq T t0 TMP_2)))))) in (let TMP_4 \def (ex_3 B T T
453 TMP_3) in (let TMP_5 \def (\forall (b: B).(\forall (w: T).(\forall (u:
454 T).((eq T t0 (THead (Bind b) w u)) \to (\forall (P: Prop).P))))) in (or TMP_4
455 TMP_5))))) in (let TMP_18 \def (\lambda (n: nat).(let TMP_10 \def (\lambda
456 (b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_7 \def (TSort n) in (let
457 TMP_8 \def (Bind b) in (let TMP_9 \def (THead TMP_8 w u) in (eq T TMP_7
458 TMP_9))))))) in (let TMP_11 \def (ex_3 B T T TMP_10) in (let TMP_12 \def
459 (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (TSort n) (THead (Bind
460 b) w u)) \to (\forall (P: Prop).P))))) in (let TMP_17 \def (\lambda (b:
461 B).(\lambda (w: T).(\lambda (u: T).(\lambda (H: (eq T (TSort n) (THead (Bind
462 b) w u))).(\lambda (P: Prop).(let TMP_13 \def (TSort n) in (let TMP_14 \def
463 (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True | (TLRef _)
464 \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let TMP_15 \def
465 (Bind b) in (let TMP_16 \def (THead TMP_15 w u) in (let H0 \def (eq_ind T
466 TMP_13 TMP_14 I TMP_16 H) in (False_ind P H0))))))))))) in (or_intror TMP_11
467 TMP_12 TMP_17)))))) in (let TMP_30 \def (\lambda (n: nat).(let TMP_22 \def
468 (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(let TMP_19 \def (TLRef n) in
469 (let TMP_20 \def (Bind b) in (let TMP_21 \def (THead TMP_20 w u) in (eq T
470 TMP_19 TMP_21))))))) in (let TMP_23 \def (ex_3 B T T TMP_22) in (let TMP_24
471 \def (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (TLRef n) (THead
472 (Bind b) w u)) \to (\forall (P: Prop).P))))) in (let TMP_29 \def (\lambda (b:
473 B).(\lambda (w: T).(\lambda (u: T).(\lambda (H: (eq T (TLRef n) (THead (Bind
474 b) w u))).(\lambda (P: Prop).(let TMP_25 \def (TLRef n) in (let TMP_26 \def
475 (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False | (TLRef _)
476 \Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let TMP_27 \def
477 (Bind b) in (let TMP_28 \def (THead TMP_27 w u) in (let H0 \def (eq_ind T
478 TMP_25 TMP_26 I TMP_28 H) in (False_ind P H0))))))))))) in (or_intror TMP_23
479 TMP_24 TMP_29)))))) in (let TMP_69 \def (\lambda (k: K).(let TMP_37 \def
480 (\lambda (k0: K).(\forall (t0: T).((or (ex_3 B T T (\lambda (b: B).(\lambda
481 (w: T).(\lambda (u: T).(eq T t0 (THead (Bind b) w u)))))) (\forall (b:
482 B).(\forall (w: T).(\forall (u: T).((eq T t0 (THead (Bind b) w u)) \to
483 (\forall (P: Prop).P)))))) \to (\forall (t1: T).((or (ex_3 B T T (\lambda (b:
484 B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind b) w u))))))
485 (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead (Bind b) w
486 u)) \to (\forall (P: Prop).P)))))) \to (let TMP_34 \def (\lambda (b:
487 B).(\lambda (w: T).(\lambda (u: T).(let TMP_31 \def (THead k0 t0 t1) in (let
488 TMP_32 \def (Bind b) in (let TMP_33 \def (THead TMP_32 w u) in (eq T TMP_31
489 TMP_33))))))) in (let TMP_35 \def (ex_3 B T T TMP_34) in (let TMP_36 \def
490 (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T (THead k0 t0 t1)
491 (THead (Bind b) w u)) \to (\forall (P: Prop).P))))) in (or TMP_35
492 TMP_36))))))))) in (let TMP_54 \def (\lambda (b: B).(\lambda (t0: T).(\lambda
493 (_: (or (ex_3 B T T (\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(eq T t0
494 (THead (Bind b0) w u)))))) (\forall (b0: B).(\forall (w: T).(\forall (u:
495 T).((eq T t0 (THead (Bind b0) w u)) \to (\forall (P: Prop).P))))))).(\lambda
496 (t1: T).(\lambda (_: (or (ex_3 B T T (\lambda (b0: B).(\lambda (w:
497 T).(\lambda (u: T).(eq T t1 (THead (Bind b0) w u)))))) (\forall (b0:
498 B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead (Bind b0) w u)) \to
499 (\forall (P: Prop).P))))))).(let TMP_42 \def (\lambda (b0: B).(\lambda (w:
500 T).(\lambda (u: T).(let TMP_38 \def (Bind b) in (let TMP_39 \def (THead
501 TMP_38 t0 t1) in (let TMP_40 \def (Bind b0) in (let TMP_41 \def (THead TMP_40
502 w u) in (eq T TMP_39 TMP_41)))))))) in (let TMP_43 \def (ex_3 B T T TMP_42)
503 in (let TMP_44 \def (\forall (b0: B).(\forall (w: T).(\forall (u: T).((eq T
504 (THead (Bind b) t0 t1) (THead (Bind b0) w u)) \to (\forall (P: Prop).P)))))
505 in (let TMP_49 \def (\lambda (b0: B).(\lambda (w: T).(\lambda (u: T).(let
506 TMP_45 \def (Bind b) in (let TMP_46 \def (THead TMP_45 t0 t1) in (let TMP_47
507 \def (Bind b0) in (let TMP_48 \def (THead TMP_47 w u) in (eq T TMP_46
508 TMP_48)))))))) in (let TMP_50 \def (Bind b) in (let TMP_51 \def (THead TMP_50
509 t0 t1) in (let TMP_52 \def (refl_equal T TMP_51) in (let TMP_53 \def
510 (ex_3_intro B T T TMP_49 b t0 t1 TMP_52) in (or_introl TMP_43 TMP_44
511 TMP_53)))))))))))))) in (let TMP_68 \def (\lambda (f: F).(\lambda (t0:
512 T).(\lambda (_: (or (ex_3 B T T (\lambda (b: B).(\lambda (w: T).(\lambda (u:
513 T).(eq T t0 (THead (Bind b) w u)))))) (\forall (b: B).(\forall (w:
514 T).(\forall (u: T).((eq T t0 (THead (Bind b) w u)) \to (\forall (P:
515 Prop).P))))))).(\lambda (t1: T).(\lambda (_: (or (ex_3 B T T (\lambda (b:
516 B).(\lambda (w: T).(\lambda (u: T).(eq T t1 (THead (Bind b) w u))))))
517 (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T t1 (THead (Bind b) w
518 u)) \to (\forall (P: Prop).P))))))).(let TMP_59 \def (\lambda (b: B).(\lambda
519 (w: T).(\lambda (u: T).(let TMP_55 \def (Flat f) in (let TMP_56 \def (THead
520 TMP_55 t0 t1) in (let TMP_57 \def (Bind b) in (let TMP_58 \def (THead TMP_57
521 w u) in (eq T TMP_56 TMP_58)))))))) in (let TMP_60 \def (ex_3 B T T TMP_59)
522 in (let TMP_61 \def (\forall (b: B).(\forall (w: T).(\forall (u: T).((eq T
523 (THead (Flat f) t0 t1) (THead (Bind b) w u)) \to (\forall (P: Prop).P))))) in
524 (let TMP_67 \def (\lambda (b: B).(\lambda (w: T).(\lambda (u: T).(\lambda
525 (H1: (eq T (THead (Flat f) t0 t1) (THead (Bind b) w u))).(\lambda (P:
526 Prop).(let TMP_62 \def (Flat f) in (let TMP_63 \def (THead TMP_62 t0 t1) in
527 (let TMP_64 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False
528 | (TLRef _) \Rightarrow False | (THead k0 _ _) \Rightarrow (match k0 with
529 [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) in (let TMP_65
530 \def (Bind b) in (let TMP_66 \def (THead TMP_65 w u) in (let H2 \def (eq_ind
531 T TMP_63 TMP_64 I TMP_66 H1) in (False_ind P H2)))))))))))) in (or_intror
532 TMP_60 TMP_61 TMP_67)))))))))) in (K_ind TMP_37 TMP_54 TMP_68 k))))) in
533 (T_ind TMP_6 TMP_18 TMP_30 TMP_69 t))))).
536 \forall (u: T).(\forall (v: T).(or (ex T (\lambda (t: T).(eq T u (THead
537 (Bind Abst) v t)))) (\forall (t: T).((eq T u (THead (Bind Abst) v t)) \to
538 (\forall (P: Prop).P)))))
540 \lambda (u: T).(let TMP_6 \def (\lambda (t: T).(\forall (v: T).(let TMP_3
541 \def (\lambda (t0: T).(let TMP_1 \def (Bind Abst) in (let TMP_2 \def (THead
542 TMP_1 v t0) in (eq T t TMP_2)))) in (let TMP_4 \def (ex T TMP_3) in (let
543 TMP_5 \def (\forall (t0: T).((eq T t (THead (Bind Abst) v t0)) \to (\forall
544 (P: Prop).P))) in (or TMP_4 TMP_5)))))) in (let TMP_18 \def (\lambda (n:
545 nat).(\lambda (v: T).(let TMP_10 \def (\lambda (t: T).(let TMP_7 \def (TSort
546 n) in (let TMP_8 \def (Bind Abst) in (let TMP_9 \def (THead TMP_8 v t) in (eq
547 T TMP_7 TMP_9))))) in (let TMP_11 \def (ex T TMP_10) in (let TMP_12 \def
548 (\forall (t: T).((eq T (TSort n) (THead (Bind Abst) v t)) \to (\forall (P:
549 Prop).P))) in (let TMP_17 \def (\lambda (t: T).(\lambda (H: (eq T (TSort n)
550 (THead (Bind Abst) v t))).(\lambda (P: Prop).(let TMP_13 \def (TSort n) in
551 (let TMP_14 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow True
552 | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) in (let
553 TMP_15 \def (Bind Abst) in (let TMP_16 \def (THead TMP_15 v t) in (let H0
554 \def (eq_ind T TMP_13 TMP_14 I TMP_16 H) in (False_ind P H0))))))))) in
555 (or_intror TMP_11 TMP_12 TMP_17))))))) in (let TMP_30 \def (\lambda (n:
556 nat).(\lambda (v: T).(let TMP_22 \def (\lambda (t: T).(let TMP_19 \def (TLRef
557 n) in (let TMP_20 \def (Bind Abst) in (let TMP_21 \def (THead TMP_20 v t) in
558 (eq T TMP_19 TMP_21))))) in (let TMP_23 \def (ex T TMP_22) in (let TMP_24
559 \def (\forall (t: T).((eq T (TLRef n) (THead (Bind Abst) v t)) \to (\forall
560 (P: Prop).P))) in (let TMP_29 \def (\lambda (t: T).(\lambda (H: (eq T (TLRef
561 n) (THead (Bind Abst) v t))).(\lambda (P: Prop).(let TMP_25 \def (TLRef n) in
562 (let TMP_26 \def (\lambda (ee: T).(match ee with [(TSort _) \Rightarrow False
563 | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) in (let
564 TMP_27 \def (Bind Abst) in (let TMP_28 \def (THead TMP_27 v t) in (let H0
565 \def (eq_ind T TMP_25 TMP_26 I TMP_28 H) in (False_ind P H0))))))))) in
566 (or_intror TMP_23 TMP_24 TMP_29))))))) in (let TMP_130 \def (\lambda (k:
567 K).(\lambda (t: T).(\lambda (_: ((\forall (v: T).(or (ex T (\lambda (t0:
568 T).(eq T t (THead (Bind Abst) v t0)))) (\forall (t0: T).((eq T t (THead (Bind
569 Abst) v t0)) \to (\forall (P: Prop).P))))))).(\lambda (t0: T).(\lambda (_:
570 ((\forall (v: T).(or (ex T (\lambda (t1: T).(eq T t0 (THead (Bind Abst) v
571 t1)))) (\forall (t1: T).((eq T t0 (THead (Bind Abst) v t1)) \to (\forall (P:
572 Prop).P))))))).(\lambda (v: T).(let TMP_31 \def (Bind Abst) in (let H_x \def
573 (terms_props__kind_dec k TMP_31) in (let H1 \def H_x in (let TMP_32 \def
574 (Bind Abst) in (let TMP_33 \def (eq K k TMP_32) in (let TMP_34 \def ((eq K k
575 (Bind Abst)) \to (\forall (P: Prop).P)) in (let TMP_38 \def (\lambda (t1:
576 T).(let TMP_35 \def (THead k t t0) in (let TMP_36 \def (Bind Abst) in (let
577 TMP_37 \def (THead TMP_36 v t1) in (eq T TMP_35 TMP_37))))) in (let TMP_39
578 \def (ex T TMP_38) in (let TMP_40 \def (\forall (t1: T).((eq T (THead k t t0)
579 (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let TMP_41 \def (or
580 TMP_39 TMP_40) in (let TMP_107 \def (\lambda (H2: (eq K k (Bind Abst))).(let
581 TMP_42 \def (Bind Abst) in (let TMP_49 \def (\lambda (k0: K).(let TMP_46 \def
582 (\lambda (t1: T).(let TMP_43 \def (THead k0 t t0) in (let TMP_44 \def (Bind
583 Abst) in (let TMP_45 \def (THead TMP_44 v t1) in (eq T TMP_43 TMP_45))))) in
584 (let TMP_47 \def (ex T TMP_46) in (let TMP_48 \def (\forall (t1: T).((eq T
585 (THead k0 t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (or
586 TMP_47 TMP_48))))) in (let H_x0 \def (term_dec t v) in (let H3 \def H_x0 in
587 (let TMP_50 \def (eq T t v) in (let TMP_51 \def ((eq T t v) \to (\forall (P:
588 Prop).P)) in (let TMP_56 \def (\lambda (t1: T).(let TMP_52 \def (Bind Abst)
589 in (let TMP_53 \def (THead TMP_52 t t0) in (let TMP_54 \def (Bind Abst) in
590 (let TMP_55 \def (THead TMP_54 v t1) in (eq T TMP_53 TMP_55)))))) in (let
591 TMP_57 \def (ex T TMP_56) in (let TMP_58 \def (\forall (t1: T).((eq T (THead
592 (Bind Abst) t t0) (THead (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in
593 (let TMP_59 \def (or TMP_57 TMP_58) in (let TMP_85 \def (\lambda (H4: (eq T t
594 v)).(let TMP_67 \def (\lambda (t1: T).(let TMP_64 \def (\lambda (t2: T).(let
595 TMP_60 \def (Bind Abst) in (let TMP_61 \def (THead TMP_60 t t0) in (let
596 TMP_62 \def (Bind Abst) in (let TMP_63 \def (THead TMP_62 t1 t2) in (eq T
597 TMP_61 TMP_63)))))) in (let TMP_65 \def (ex T TMP_64) in (let TMP_66 \def
598 (\forall (t2: T).((eq T (THead (Bind Abst) t t0) (THead (Bind Abst) t1 t2))
599 \to (\forall (P: Prop).P))) in (or TMP_65 TMP_66))))) in (let TMP_72 \def
600 (\lambda (t1: T).(let TMP_68 \def (Bind Abst) in (let TMP_69 \def (THead
601 TMP_68 t t0) in (let TMP_70 \def (Bind Abst) in (let TMP_71 \def (THead
602 TMP_70 t t1) in (eq T TMP_69 TMP_71)))))) in (let TMP_73 \def (ex T TMP_72)
603 in (let TMP_74 \def (\forall (t1: T).((eq T (THead (Bind Abst) t t0) (THead
604 (Bind Abst) t t1)) \to (\forall (P: Prop).P))) in (let TMP_79 \def (\lambda
605 (t1: T).(let TMP_75 \def (Bind Abst) in (let TMP_76 \def (THead TMP_75 t t0)
606 in (let TMP_77 \def (Bind Abst) in (let TMP_78 \def (THead TMP_77 t t1) in
607 (eq T TMP_76 TMP_78)))))) in (let TMP_80 \def (Bind Abst) in (let TMP_81 \def
608 (THead TMP_80 t t0) in (let TMP_82 \def (refl_equal T TMP_81) in (let TMP_83
609 \def (ex_intro T TMP_79 t0 TMP_82) in (let TMP_84 \def (or_introl TMP_73
610 TMP_74 TMP_83) in (eq_ind T t TMP_67 TMP_84 v H4)))))))))))) in (let TMP_105
611 \def (\lambda (H4: (((eq T t v) \to (\forall (P: Prop).P)))).(let TMP_90 \def
612 (\lambda (t1: T).(let TMP_86 \def (Bind Abst) in (let TMP_87 \def (THead
613 TMP_86 t t0) in (let TMP_88 \def (Bind Abst) in (let TMP_89 \def (THead
614 TMP_88 v t1) in (eq T TMP_87 TMP_89)))))) in (let TMP_91 \def (ex T TMP_90)
615 in (let TMP_92 \def (\forall (t1: T).((eq T (THead (Bind Abst) t t0) (THead
616 (Bind Abst) v t1)) \to (\forall (P: Prop).P))) in (let TMP_104 \def (\lambda
617 (t1: T).(\lambda (H5: (eq T (THead (Bind Abst) t t0) (THead (Bind Abst) v
618 t1))).(\lambda (P: Prop).(let TMP_93 \def (\lambda (e: T).(match e with
619 [(TSort _) \Rightarrow t | (TLRef _) \Rightarrow t | (THead _ t2 _)
620 \Rightarrow t2])) in (let TMP_94 \def (Bind Abst) in (let TMP_95 \def (THead
621 TMP_94 t t0) in (let TMP_96 \def (Bind Abst) in (let TMP_97 \def (THead
622 TMP_96 v t1) in (let H6 \def (f_equal T T TMP_93 TMP_95 TMP_97 H5) in (let
623 TMP_98 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0 | (TLRef
624 _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) in (let TMP_99 \def
625 (Bind Abst) in (let TMP_100 \def (THead TMP_99 t t0) in (let TMP_101 \def
626 (Bind Abst) in (let TMP_102 \def (THead TMP_101 v t1) in (let H7 \def
627 (f_equal T T TMP_98 TMP_100 TMP_102 H5) in (let TMP_103 \def (\lambda (H8:
628 (eq T t v)).(H4 H8 P)) in (TMP_103 H6))))))))))))))))) in (or_intror TMP_91
629 TMP_92 TMP_104)))))) in (let TMP_106 \def (or_ind TMP_50 TMP_51 TMP_59 TMP_85
630 TMP_105 H3) in (eq_ind_r K TMP_42 TMP_49 TMP_106 k H2))))))))))))))) in (let
631 TMP_129 \def (\lambda (H2: (((eq K k (Bind Abst)) \to (\forall (P:
632 Prop).P)))).(let TMP_111 \def (\lambda (t1: T).(let TMP_108 \def (THead k t
633 t0) in (let TMP_109 \def (Bind Abst) in (let TMP_110 \def (THead TMP_109 v
634 t1) in (eq T TMP_108 TMP_110))))) in (let TMP_112 \def (ex T TMP_111) in (let
635 TMP_113 \def (\forall (t1: T).((eq T (THead k t t0) (THead (Bind Abst) v t1))
636 \to (\forall (P: Prop).P))) in (let TMP_128 \def (\lambda (t1: T).(\lambda
637 (H3: (eq T (THead k t t0) (THead (Bind Abst) v t1))).(\lambda (P: Prop).(let
638 TMP_114 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow k | (TLRef
639 _) \Rightarrow k | (THead k0 _ _) \Rightarrow k0])) in (let TMP_115 \def
640 (THead k t t0) in (let TMP_116 \def (Bind Abst) in (let TMP_117 \def (THead
641 TMP_116 v t1) in (let H4 \def (f_equal T K TMP_114 TMP_115 TMP_117 H3) in
642 (let TMP_118 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t |
643 (TLRef _) \Rightarrow t | (THead _ t2 _) \Rightarrow t2])) in (let TMP_119
644 \def (THead k t t0) in (let TMP_120 \def (Bind Abst) in (let TMP_121 \def
645 (THead TMP_120 v t1) in (let H5 \def (f_equal T T TMP_118 TMP_119 TMP_121 H3)
646 in (let TMP_122 \def (\lambda (e: T).(match e with [(TSort _) \Rightarrow t0
647 | (TLRef _) \Rightarrow t0 | (THead _ _ t2) \Rightarrow t2])) in (let TMP_123
648 \def (THead k t t0) in (let TMP_124 \def (Bind Abst) in (let TMP_125 \def
649 (THead TMP_124 v t1) in (let H6 \def (f_equal T T TMP_122 TMP_123 TMP_125 H3)
650 in (let TMP_126 \def (\lambda (_: (eq T t v)).(\lambda (H8: (eq K k (Bind
651 Abst))).(H2 H8 P))) in (let TMP_127 \def (TMP_126 H5) in (TMP_127
652 H4))))))))))))))))))))) in (or_intror TMP_112 TMP_113 TMP_128)))))) in
653 (or_ind TMP_33 TMP_34 TMP_41 TMP_107 TMP_129 H1))))))))))))))))))) in (T_ind
654 TMP_6 TMP_18 TMP_30 TMP_130 u))))).