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/arity/fwd.ma".
20 \forall (g: G).(\forall (n: nat).(\forall (k: nat).(ex_2 C T (\lambda (c:
21 C).(\lambda (t: T).(arity g c t (ASort k n)))))))
23 \lambda (g: G).(\lambda (n: nat).(\lambda (k: nat).(let TMP_3 \def (\lambda
24 (n0: nat).(let TMP_2 \def (\lambda (c: C).(\lambda (t: T).(let TMP_1 \def
25 (ASort n0 n) in (arity g c t TMP_1)))) in (ex_2 C T TMP_2))) in (let TMP_5
26 \def (\lambda (c: C).(\lambda (t: T).(let TMP_4 \def (ASort O n) in (arity g
27 c t TMP_4)))) in (let TMP_6 \def (CSort O) in (let TMP_7 \def (TSort n) in
28 (let TMP_8 \def (CSort O) in (let TMP_9 \def (arity_sort g TMP_8 n) in (let
29 TMP_10 \def (ex_2_intro C T TMP_5 TMP_6 TMP_7 TMP_9) in (let TMP_30 \def
30 (\lambda (n0: nat).(\lambda (H: (ex_2 C T (\lambda (c: C).(\lambda (t:
31 T).(arity g c t (ASort n0 n)))))).(let H0 \def H in (let TMP_12 \def (\lambda
32 (c: C).(\lambda (t: T).(let TMP_11 \def (ASort n0 n) in (arity g c t
33 TMP_11)))) in (let TMP_15 \def (\lambda (c: C).(\lambda (t: T).(let TMP_13
34 \def (S n0) in (let TMP_14 \def (ASort TMP_13 n) in (arity g c t TMP_14)))))
35 in (let TMP_16 \def (ex_2 C T TMP_15) in (let TMP_29 \def (\lambda (x0:
36 C).(\lambda (x1: T).(\lambda (H1: (arity g x0 x1 (ASort n0 n))).(let TMP_19
37 \def (\lambda (c: C).(\lambda (t: T).(let TMP_17 \def (S n0) in (let TMP_18
38 \def (ASort TMP_17 n) in (arity g c t TMP_18))))) in (let TMP_20 \def (Bind
39 Abst) in (let TMP_21 \def (CHead x0 TMP_20 x1) in (let TMP_22 \def (TLRef O)
40 in (let TMP_23 \def (Bind Abst) in (let TMP_24 \def (CHead x0 TMP_23 x1) in
41 (let TMP_25 \def (getl_refl Abst x0 x1) in (let TMP_26 \def (S n0) in (let
42 TMP_27 \def (ASort TMP_26 n) in (let TMP_28 \def (arity_abst g TMP_24 x0 x1 O
43 TMP_25 TMP_27 H1) in (ex_2_intro C T TMP_19 TMP_21 TMP_22
44 TMP_28)))))))))))))) in (ex_2_ind C T TMP_12 TMP_16 TMP_29 H0)))))))) in
45 (nat_ind TMP_3 TMP_10 TMP_30 k))))))))))).
48 \forall (g: G).(\forall (c2: C).(\forall (t: T).(\forall (a: A).((arity g c2
49 t a) \to (\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1
50 c2) \to (arity g c1 (lift h d t) a)))))))))
52 \lambda (g: G).(\lambda (c2: C).(\lambda (t: T).(\lambda (a: A).(\lambda (H:
53 (arity g c2 t a)).(let TMP_2 \def (\lambda (c: C).(\lambda (t0: T).(\lambda
54 (a0: A).(\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c)
55 \to (let TMP_1 \def (lift h d t0) in (arity g c1 TMP_1 a0))))))))) in (let
56 TMP_10 \def (\lambda (c: C).(\lambda (n: nat).(\lambda (c1: C).(\lambda (h:
57 nat).(\lambda (d: nat).(\lambda (_: (drop h d c1 c)).(let TMP_3 \def (TSort
58 n) in (let TMP_5 \def (\lambda (t0: T).(let TMP_4 \def (ASort O n) in (arity
59 g c1 t0 TMP_4))) in (let TMP_6 \def (arity_sort g c1 n) in (let TMP_7 \def
60 (TSort n) in (let TMP_8 \def (lift h d TMP_7) in (let TMP_9 \def (lift_sort n
61 h d) in (eq_ind_r T TMP_3 TMP_5 TMP_6 TMP_8 TMP_9))))))))))))) in (let TMP_86
62 \def (\lambda (c: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
63 nat).(\lambda (H0: (getl i c (CHead d (Bind Abbr) u))).(\lambda (a0:
64 A).(\lambda (H1: (arity g d u a0)).(\lambda (H2: ((\forall (c1: C).(\forall
65 (h: nat).(\forall (d0: nat).((drop h d0 c1 d) \to (arity g c1 (lift h d0 u)
66 a0))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d0: nat).(\lambda (H3:
67 (drop h d0 c1 c)).(let TMP_11 \def (TLRef i) in (let TMP_12 \def (lift h d0
68 TMP_11) in (let TMP_13 \def (arity g c1 TMP_12 a0) in (let TMP_73 \def
69 (\lambda (H4: (lt i d0)).(let TMP_14 \def (TLRef i) in (let TMP_15 \def
70 (\lambda (t0: T).(arity g c1 t0 a0)) in (let TMP_16 \def (S i) in (let TMP_17
71 \def (S d0) in (let TMP_18 \def (S i) in (let TMP_19 \def (S TMP_18) in (let
72 TMP_20 \def (S d0) in (let TMP_21 \def (S i) in (let TMP_22 \def (le_n_S
73 TMP_21 d0 H4) in (let TMP_23 \def (le_S TMP_19 TMP_20 TMP_22) in (let TMP_24
74 \def (le_S_n TMP_16 TMP_17 TMP_23) in (let TMP_25 \def (le_S_n i d0 TMP_24)
75 in (let TMP_26 \def (Bind Abbr) in (let TMP_27 \def (CHead d TMP_26 u) in
76 (let H5 \def (drop_getl_trans_le i d0 TMP_25 c1 c h H3 TMP_27 H0) in (let
77 TMP_28 \def (\lambda (e0: C).(\lambda (_: C).(drop i O c1 e0))) in (let
78 TMP_30 \def (\lambda (e0: C).(\lambda (e1: C).(let TMP_29 \def (minus d0 i)
79 in (drop h TMP_29 e0 e1)))) in (let TMP_33 \def (\lambda (_: C).(\lambda (e1:
80 C).(let TMP_31 \def (Bind Abbr) in (let TMP_32 \def (CHead d TMP_31 u) in
81 (clear e1 TMP_32))))) in (let TMP_34 \def (TLRef i) in (let TMP_35 \def
82 (arity g c1 TMP_34 a0) in (let TMP_68 \def (\lambda (x0: C).(\lambda (x1:
83 C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0
84 x1)).(\lambda (H8: (clear x1 (CHead d (Bind Abbr) u))).(let TMP_36 \def
85 (minus d0 i) in (let TMP_37 \def (\lambda (n: nat).(drop h n x0 x1)) in (let
86 TMP_38 \def (S i) in (let TMP_39 \def (minus d0 TMP_38) in (let TMP_40 \def
87 (S TMP_39) in (let TMP_41 \def (minus_x_Sy d0 i H4) in (let H9 \def (eq_ind
88 nat TMP_36 TMP_37 H7 TMP_40 TMP_41) in (let TMP_42 \def (S i) in (let TMP_43
89 \def (minus d0 TMP_42) in (let H10 \def (drop_clear_S x1 x0 h TMP_43 H9 Abbr
90 d u H8) in (let TMP_49 \def (\lambda (c3: C).(let TMP_44 \def (Bind Abbr) in
91 (let TMP_45 \def (S i) in (let TMP_46 \def (minus d0 TMP_45) in (let TMP_47
92 \def (lift h TMP_46 u) in (let TMP_48 \def (CHead c3 TMP_44 TMP_47) in (clear
93 x0 TMP_48))))))) in (let TMP_52 \def (\lambda (c3: C).(let TMP_50 \def (S i)
94 in (let TMP_51 \def (minus d0 TMP_50) in (drop h TMP_51 c3 d)))) in (let
95 TMP_53 \def (TLRef i) in (let TMP_54 \def (arity g c1 TMP_53 a0) in (let
96 TMP_67 \def (\lambda (x: C).(\lambda (H11: (clear x0 (CHead x (Bind Abbr)
97 (lift h (minus d0 (S i)) u)))).(\lambda (H12: (drop h (minus d0 (S i)) x
98 d)).(let TMP_55 \def (S i) in (let TMP_56 \def (minus d0 TMP_55) in (let
99 TMP_57 \def (lift h TMP_56 u) in (let TMP_58 \def (Bind Abbr) in (let TMP_59
100 \def (S i) in (let TMP_60 \def (minus d0 TMP_59) in (let TMP_61 \def (lift h
101 TMP_60 u) in (let TMP_62 \def (CHead x TMP_58 TMP_61) in (let TMP_63 \def
102 (getl_intro i c1 TMP_62 x0 H6 H11) in (let TMP_64 \def (S i) in (let TMP_65
103 \def (minus d0 TMP_64) in (let TMP_66 \def (H2 x h TMP_65 H12) in (arity_abbr
104 g c1 x TMP_57 i TMP_63 a0 TMP_66)))))))))))))))) in (ex2_ind C TMP_49 TMP_52
105 TMP_54 TMP_67 H10))))))))))))))))))))) in (let TMP_69 \def (ex3_2_ind C C
106 TMP_28 TMP_30 TMP_33 TMP_35 TMP_68 H5) in (let TMP_70 \def (TLRef i) in (let
107 TMP_71 \def (lift h d0 TMP_70) in (let TMP_72 \def (lift_lref_lt i h d0 H4)
108 in (eq_ind_r T TMP_14 TMP_15 TMP_69 TMP_71 TMP_72)))))))))))))))))))))))))))
109 in (let TMP_85 \def (\lambda (H4: (le d0 i)).(let TMP_74 \def (plus i h) in
110 (let TMP_75 \def (TLRef TMP_74) in (let TMP_76 \def (\lambda (t0: T).(arity g
111 c1 t0 a0)) in (let TMP_77 \def (plus i h) in (let TMP_78 \def (Bind Abbr) in
112 (let TMP_79 \def (CHead d TMP_78 u) in (let TMP_80 \def (drop_getl_trans_ge i
113 c1 c d0 h H3 TMP_79 H0 H4) in (let TMP_81 \def (arity_abbr g c1 d u TMP_77
114 TMP_80 a0 H1) in (let TMP_82 \def (TLRef i) in (let TMP_83 \def (lift h d0
115 TMP_82) in (let TMP_84 \def (lift_lref_ge i h d0 H4) in (eq_ind_r T TMP_75
116 TMP_76 TMP_81 TMP_83 TMP_84))))))))))))) in (lt_le_e i d0 TMP_13 TMP_73
117 TMP_85)))))))))))))))))) in (let TMP_162 \def (\lambda (c: C).(\lambda (d:
118 C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl i c (CHead d (Bind
119 Abst) u))).(\lambda (a0: A).(\lambda (H1: (arity g d u (asucc g
120 a0))).(\lambda (H2: ((\forall (c1: C).(\forall (h: nat).(\forall (d0:
121 nat).((drop h d0 c1 d) \to (arity g c1 (lift h d0 u) (asucc g
122 a0)))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d0: nat).(\lambda
123 (H3: (drop h d0 c1 c)).(let TMP_87 \def (TLRef i) in (let TMP_88 \def (lift h
124 d0 TMP_87) in (let TMP_89 \def (arity g c1 TMP_88 a0) in (let TMP_149 \def
125 (\lambda (H4: (lt i d0)).(let TMP_90 \def (TLRef i) in (let TMP_91 \def
126 (\lambda (t0: T).(arity g c1 t0 a0)) in (let TMP_92 \def (S i) in (let TMP_93
127 \def (S d0) in (let TMP_94 \def (S i) in (let TMP_95 \def (S TMP_94) in (let
128 TMP_96 \def (S d0) in (let TMP_97 \def (S i) in (let TMP_98 \def (le_n_S
129 TMP_97 d0 H4) in (let TMP_99 \def (le_S TMP_95 TMP_96 TMP_98) in (let TMP_100
130 \def (le_S_n TMP_92 TMP_93 TMP_99) in (let TMP_101 \def (le_S_n i d0 TMP_100)
131 in (let TMP_102 \def (Bind Abst) in (let TMP_103 \def (CHead d TMP_102 u) in
132 (let H5 \def (drop_getl_trans_le i d0 TMP_101 c1 c h H3 TMP_103 H0) in (let
133 TMP_104 \def (\lambda (e0: C).(\lambda (_: C).(drop i O c1 e0))) in (let
134 TMP_106 \def (\lambda (e0: C).(\lambda (e1: C).(let TMP_105 \def (minus d0 i)
135 in (drop h TMP_105 e0 e1)))) in (let TMP_109 \def (\lambda (_: C).(\lambda
136 (e1: C).(let TMP_107 \def (Bind Abst) in (let TMP_108 \def (CHead d TMP_107
137 u) in (clear e1 TMP_108))))) in (let TMP_110 \def (TLRef i) in (let TMP_111
138 \def (arity g c1 TMP_110 a0) in (let TMP_144 \def (\lambda (x0: C).(\lambda
139 (x1: C).(\lambda (H6: (drop i O c1 x0)).(\lambda (H7: (drop h (minus d0 i) x0
140 x1)).(\lambda (H8: (clear x1 (CHead d (Bind Abst) u))).(let TMP_112 \def
141 (minus d0 i) in (let TMP_113 \def (\lambda (n: nat).(drop h n x0 x1)) in (let
142 TMP_114 \def (S i) in (let TMP_115 \def (minus d0 TMP_114) in (let TMP_116
143 \def (S TMP_115) in (let TMP_117 \def (minus_x_Sy d0 i H4) in (let H9 \def
144 (eq_ind nat TMP_112 TMP_113 H7 TMP_116 TMP_117) in (let TMP_118 \def (S i) in
145 (let TMP_119 \def (minus d0 TMP_118) in (let H10 \def (drop_clear_S x1 x0 h
146 TMP_119 H9 Abst d u H8) in (let TMP_125 \def (\lambda (c3: C).(let TMP_120
147 \def (Bind Abst) in (let TMP_121 \def (S i) in (let TMP_122 \def (minus d0
148 TMP_121) in (let TMP_123 \def (lift h TMP_122 u) in (let TMP_124 \def (CHead
149 c3 TMP_120 TMP_123) in (clear x0 TMP_124))))))) in (let TMP_128 \def (\lambda
150 (c3: C).(let TMP_126 \def (S i) in (let TMP_127 \def (minus d0 TMP_126) in
151 (drop h TMP_127 c3 d)))) in (let TMP_129 \def (TLRef i) in (let TMP_130 \def
152 (arity g c1 TMP_129 a0) in (let TMP_143 \def (\lambda (x: C).(\lambda (H11:
153 (clear x0 (CHead x (Bind Abst) (lift h (minus d0 (S i)) u)))).(\lambda (H12:
154 (drop h (minus d0 (S i)) x d)).(let TMP_131 \def (S i) in (let TMP_132 \def
155 (minus d0 TMP_131) in (let TMP_133 \def (lift h TMP_132 u) in (let TMP_134
156 \def (Bind Abst) in (let TMP_135 \def (S i) in (let TMP_136 \def (minus d0
157 TMP_135) in (let TMP_137 \def (lift h TMP_136 u) in (let TMP_138 \def (CHead
158 x TMP_134 TMP_137) in (let TMP_139 \def (getl_intro i c1 TMP_138 x0 H6 H11)
159 in (let TMP_140 \def (S i) in (let TMP_141 \def (minus d0 TMP_140) in (let
160 TMP_142 \def (H2 x h TMP_141 H12) in (arity_abst g c1 x TMP_133 i TMP_139 a0
161 TMP_142)))))))))))))))) in (ex2_ind C TMP_125 TMP_128 TMP_130 TMP_143
162 H10))))))))))))))))))))) in (let TMP_145 \def (ex3_2_ind C C TMP_104 TMP_106
163 TMP_109 TMP_111 TMP_144 H5) in (let TMP_146 \def (TLRef i) in (let TMP_147
164 \def (lift h d0 TMP_146) in (let TMP_148 \def (lift_lref_lt i h d0 H4) in
165 (eq_ind_r T TMP_90 TMP_91 TMP_145 TMP_147 TMP_148)))))))))))))))))))))))))))
166 in (let TMP_161 \def (\lambda (H4: (le d0 i)).(let TMP_150 \def (plus i h) in
167 (let TMP_151 \def (TLRef TMP_150) in (let TMP_152 \def (\lambda (t0:
168 T).(arity g c1 t0 a0)) in (let TMP_153 \def (plus i h) in (let TMP_154 \def
169 (Bind Abst) in (let TMP_155 \def (CHead d TMP_154 u) in (let TMP_156 \def
170 (drop_getl_trans_ge i c1 c d0 h H3 TMP_155 H0 H4) in (let TMP_157 \def
171 (arity_abst g c1 d u TMP_153 TMP_156 a0 H1) in (let TMP_158 \def (TLRef i) in
172 (let TMP_159 \def (lift h d0 TMP_158) in (let TMP_160 \def (lift_lref_ge i h
173 d0 H4) in (eq_ind_r T TMP_151 TMP_152 TMP_157 TMP_159 TMP_160))))))))))))) in
174 (lt_le_e i d0 TMP_89 TMP_149 TMP_161)))))))))))))))))) in (let TMP_188 \def
175 (\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c: C).(\lambda
176 (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u a1)).(\lambda (H2:
177 ((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
178 (arity g c1 (lift h d u) a1))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda
179 (_: (arity g (CHead c (Bind b) u) t0 a2)).(\lambda (H4: ((\forall (c1:
180 C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 (CHead c (Bind b) u))
181 \to (arity g c1 (lift h d t0) a2))))))).(\lambda (c1: C).(\lambda (h:
182 nat).(\lambda (d: nat).(\lambda (H5: (drop h d c1 c)).(let TMP_163 \def (Bind
183 b) in (let TMP_164 \def (lift h d u) in (let TMP_165 \def (Bind b) in (let
184 TMP_166 \def (s TMP_165 d) in (let TMP_167 \def (lift h TMP_166 t0) in (let
185 TMP_168 \def (THead TMP_163 TMP_164 TMP_167) in (let TMP_169 \def (\lambda
186 (t1: T).(arity g c1 t1 a2)) in (let TMP_170 \def (lift h d u) in (let TMP_171
187 \def (H2 c1 h d H5) in (let TMP_172 \def (Bind b) in (let TMP_173 \def (s
188 TMP_172 d) in (let TMP_174 \def (lift h TMP_173 t0) in (let TMP_175 \def
189 (Bind b) in (let TMP_176 \def (lift h d u) in (let TMP_177 \def (CHead c1
190 TMP_175 TMP_176) in (let TMP_178 \def (Bind b) in (let TMP_179 \def (s
191 TMP_178 d) in (let TMP_180 \def (drop_skip_bind h d c1 c H5 b u) in (let
192 TMP_181 \def (H4 TMP_177 h TMP_179 TMP_180) in (let TMP_182 \def (arity_bind
193 g b H0 c1 TMP_170 a1 TMP_171 TMP_174 a2 TMP_181) in (let TMP_183 \def (Bind
194 b) in (let TMP_184 \def (THead TMP_183 u t0) in (let TMP_185 \def (lift h d
195 TMP_184) in (let TMP_186 \def (Bind b) in (let TMP_187 \def (lift_head
196 TMP_186 u t0 h d) in (eq_ind_r T TMP_168 TMP_169 TMP_182 TMP_185
197 TMP_187))))))))))))))))))))))))))))))))))))))))) in (let TMP_215 \def
198 (\lambda (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
199 (asucc g a1))).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
200 nat).((drop h d c1 c) \to (arity g c1 (lift h d u) (asucc g
201 a1)))))))).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g (CHead c
202 (Bind Abst) u) t0 a2)).(\lambda (H3: ((\forall (c1: C).(\forall (h:
203 nat).(\forall (d: nat).((drop h d c1 (CHead c (Bind Abst) u)) \to (arity g c1
204 (lift h d t0) a2))))))).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d:
205 nat).(\lambda (H4: (drop h d c1 c)).(let TMP_189 \def (Bind Abst) in (let
206 TMP_190 \def (lift h d u) in (let TMP_191 \def (Bind Abst) in (let TMP_192
207 \def (s TMP_191 d) in (let TMP_193 \def (lift h TMP_192 t0) in (let TMP_194
208 \def (THead TMP_189 TMP_190 TMP_193) in (let TMP_196 \def (\lambda (t1:
209 T).(let TMP_195 \def (AHead a1 a2) in (arity g c1 t1 TMP_195))) in (let
210 TMP_197 \def (lift h d u) in (let TMP_198 \def (H1 c1 h d H4) in (let TMP_199
211 \def (Bind Abst) in (let TMP_200 \def (s TMP_199 d) in (let TMP_201 \def
212 (lift h TMP_200 t0) in (let TMP_202 \def (Bind Abst) in (let TMP_203 \def
213 (lift h d u) in (let TMP_204 \def (CHead c1 TMP_202 TMP_203) in (let TMP_205
214 \def (Bind Abst) in (let TMP_206 \def (s TMP_205 d) in (let TMP_207 \def
215 (drop_skip_bind h d c1 c H4 Abst u) in (let TMP_208 \def (H3 TMP_204 h
216 TMP_206 TMP_207) in (let TMP_209 \def (arity_head g c1 TMP_197 a1 TMP_198
217 TMP_201 a2 TMP_208) in (let TMP_210 \def (Bind Abst) in (let TMP_211 \def
218 (THead TMP_210 u t0) in (let TMP_212 \def (lift h d TMP_211) in (let TMP_213
219 \def (Bind Abst) in (let TMP_214 \def (lift_head TMP_213 u t0 h d) in
220 (eq_ind_r T TMP_194 TMP_196 TMP_209 TMP_212
221 TMP_214))))))))))))))))))))))))))))))))))))))) in (let TMP_237 \def (\lambda
222 (c: C).(\lambda (u: T).(\lambda (a1: A).(\lambda (_: (arity g c u
223 a1)).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
224 nat).((drop h d c1 c) \to (arity g c1 (lift h d u) a1))))))).(\lambda (t0:
225 T).(\lambda (a2: A).(\lambda (_: (arity g c t0 (AHead a1 a2))).(\lambda (H3:
226 ((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
227 (arity g c1 (lift h d t0) (AHead a1 a2)))))))).(\lambda (c1: C).(\lambda (h:
228 nat).(\lambda (d: nat).(\lambda (H4: (drop h d c1 c)).(let TMP_216 \def (Flat
229 Appl) in (let TMP_217 \def (lift h d u) in (let TMP_218 \def (Flat Appl) in
230 (let TMP_219 \def (s TMP_218 d) in (let TMP_220 \def (lift h TMP_219 t0) in
231 (let TMP_221 \def (THead TMP_216 TMP_217 TMP_220) in (let TMP_222 \def
232 (\lambda (t1: T).(arity g c1 t1 a2)) in (let TMP_223 \def (lift h d u) in
233 (let TMP_224 \def (H1 c1 h d H4) in (let TMP_225 \def (Flat Appl) in (let
234 TMP_226 \def (s TMP_225 d) in (let TMP_227 \def (lift h TMP_226 t0) in (let
235 TMP_228 \def (Flat Appl) in (let TMP_229 \def (s TMP_228 d) in (let TMP_230
236 \def (H3 c1 h TMP_229 H4) in (let TMP_231 \def (arity_appl g c1 TMP_223 a1
237 TMP_224 TMP_227 a2 TMP_230) in (let TMP_232 \def (Flat Appl) in (let TMP_233
238 \def (THead TMP_232 u t0) in (let TMP_234 \def (lift h d TMP_233) in (let
239 TMP_235 \def (Flat Appl) in (let TMP_236 \def (lift_head TMP_235 u t0 h d) in
240 (eq_ind_r T TMP_221 TMP_222 TMP_231 TMP_234
241 TMP_236))))))))))))))))))))))))))))))))))) in (let TMP_259 \def (\lambda (c:
242 C).(\lambda (u: T).(\lambda (a0: A).(\lambda (_: (arity g c u (asucc g
243 a0))).(\lambda (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d:
244 nat).((drop h d c1 c) \to (arity g c1 (lift h d u) (asucc g
245 a0)))))))).(\lambda (t0: T).(\lambda (_: (arity g c t0 a0)).(\lambda (H3:
246 ((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c) \to
247 (arity g c1 (lift h d t0) a0))))))).(\lambda (c1: C).(\lambda (h:
248 nat).(\lambda (d: nat).(\lambda (H4: (drop h d c1 c)).(let TMP_238 \def (Flat
249 Cast) in (let TMP_239 \def (lift h d u) in (let TMP_240 \def (Flat Cast) in
250 (let TMP_241 \def (s TMP_240 d) in (let TMP_242 \def (lift h TMP_241 t0) in
251 (let TMP_243 \def (THead TMP_238 TMP_239 TMP_242) in (let TMP_244 \def
252 (\lambda (t1: T).(arity g c1 t1 a0)) in (let TMP_245 \def (lift h d u) in
253 (let TMP_246 \def (H1 c1 h d H4) in (let TMP_247 \def (Flat Cast) in (let
254 TMP_248 \def (s TMP_247 d) in (let TMP_249 \def (lift h TMP_248 t0) in (let
255 TMP_250 \def (Flat Cast) in (let TMP_251 \def (s TMP_250 d) in (let TMP_252
256 \def (H3 c1 h TMP_251 H4) in (let TMP_253 \def (arity_cast g c1 TMP_245 a0
257 TMP_246 TMP_249 TMP_252) in (let TMP_254 \def (Flat Cast) in (let TMP_255
258 \def (THead TMP_254 u t0) in (let TMP_256 \def (lift h d TMP_255) in (let
259 TMP_257 \def (Flat Cast) in (let TMP_258 \def (lift_head TMP_257 u t0 h d) in
260 (eq_ind_r T TMP_243 TMP_244 TMP_253 TMP_256
261 TMP_258)))))))))))))))))))))))))))))))))) in (let TMP_262 \def (\lambda (c:
262 C).(\lambda (t0: T).(\lambda (a1: A).(\lambda (_: (arity g c t0 a1)).(\lambda
263 (H1: ((\forall (c1: C).(\forall (h: nat).(\forall (d: nat).((drop h d c1 c)
264 \to (arity g c1 (lift h d t0) a1))))))).(\lambda (a2: A).(\lambda (H2: (leq g
265 a1 a2)).(\lambda (c1: C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H3:
266 (drop h d c1 c)).(let TMP_260 \def (lift h d t0) in (let TMP_261 \def (H1 c1
267 h d H3) in (arity_repl g c1 TMP_260 a1 TMP_261 a2 H2)))))))))))))) in
268 (arity_ind g TMP_2 TMP_10 TMP_86 TMP_162 TMP_188 TMP_215 TMP_237 TMP_259
269 TMP_262 c2 t a H)))))))))))))).
272 \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a1: A).((arity g c
273 t a1) \to (\forall (a2: A).((arity g c t a2) \to (leq g a1 a2)))))))
275 \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a1: A).(\lambda (H:
276 (arity g c t a1)).(let TMP_1 \def (\lambda (c0: C).(\lambda (t0: T).(\lambda
277 (a: A).(\forall (a2: A).((arity g c0 t0 a2) \to (leq g a a2)))))) in (let
278 TMP_4 \def (\lambda (c0: C).(\lambda (n: nat).(\lambda (a2: A).(\lambda (H0:
279 (arity g c0 (TSort n) a2)).(let TMP_2 \def (ASort O n) in (let TMP_3 \def
280 (arity_gen_sort g c0 n a2 H0) in (leq_sym g a2 TMP_2 TMP_3))))))) in (let
281 TMP_92 \def (\lambda (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i:
282 nat).(\lambda (H0: (getl i c0 (CHead d (Bind Abbr) u))).(\lambda (a:
283 A).(\lambda (_: (arity g d u a)).(\lambda (H2: ((\forall (a2: A).((arity g d
284 u a2) \to (leq g a a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef
285 i) a2)).(let H4 \def (arity_gen_lref g c0 i a2 H3) in (let TMP_7 \def
286 (\lambda (d0: C).(\lambda (u0: T).(let TMP_5 \def (Bind Abbr) in (let TMP_6
287 \def (CHead d0 TMP_5 u0) in (getl i c0 TMP_6))))) in (let TMP_8 \def (\lambda
288 (d0: C).(\lambda (u0: T).(arity g d0 u0 a2))) in (let TMP_9 \def (ex2_2 C T
289 TMP_7 TMP_8) in (let TMP_12 \def (\lambda (d0: C).(\lambda (u0: T).(let
290 TMP_10 \def (Bind Abst) in (let TMP_11 \def (CHead d0 TMP_10 u0) in (getl i
291 c0 TMP_11))))) in (let TMP_14 \def (\lambda (d0: C).(\lambda (u0: T).(let
292 TMP_13 \def (asucc g a2) in (arity g d0 u0 TMP_13)))) in (let TMP_15 \def
293 (ex2_2 C T TMP_12 TMP_14) in (let TMP_16 \def (leq g a a2) in (let TMP_62
294 \def (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
295 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
296 a2))))).(let TMP_19 \def (\lambda (d0: C).(\lambda (u0: T).(let TMP_17 \def
297 (Bind Abbr) in (let TMP_18 \def (CHead d0 TMP_17 u0) in (getl i c0
298 TMP_18))))) in (let TMP_20 \def (\lambda (d0: C).(\lambda (u0: T).(arity g d0
299 u0 a2))) in (let TMP_21 \def (leq g a a2) in (let TMP_61 \def (\lambda (x0:
300 C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind Abbr)
301 x1))).(\lambda (H7: (arity g x0 x1 a2)).(let TMP_22 \def (Bind Abbr) in (let
302 TMP_23 \def (CHead d TMP_22 u) in (let TMP_24 \def (\lambda (c1: C).(getl i
303 c0 c1)) in (let TMP_25 \def (Bind Abbr) in (let TMP_26 \def (CHead x0 TMP_25
304 x1) in (let TMP_27 \def (Bind Abbr) in (let TMP_28 \def (CHead d TMP_27 u) in
305 (let TMP_29 \def (Bind Abbr) in (let TMP_30 \def (CHead x0 TMP_29 x1) in (let
306 TMP_31 \def (getl_mono c0 TMP_28 i H0 TMP_30 H6) in (let H8 \def (eq_ind C
307 TMP_23 TMP_24 H0 TMP_26 TMP_31) in (let TMP_32 \def (\lambda (e: C).(match e
308 with [(CSort _) \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) in (let
309 TMP_33 \def (Bind Abbr) in (let TMP_34 \def (CHead d TMP_33 u) in (let TMP_35
310 \def (Bind Abbr) in (let TMP_36 \def (CHead x0 TMP_35 x1) in (let TMP_37 \def
311 (Bind Abbr) in (let TMP_38 \def (CHead d TMP_37 u) in (let TMP_39 \def (Bind
312 Abbr) in (let TMP_40 \def (CHead x0 TMP_39 x1) in (let TMP_41 \def (getl_mono
313 c0 TMP_38 i H0 TMP_40 H6) in (let H9 \def (f_equal C C TMP_32 TMP_34 TMP_36
314 TMP_41) in (let TMP_42 \def (\lambda (e: C).(match e with [(CSort _)
315 \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_43 \def (Bind
316 Abbr) in (let TMP_44 \def (CHead d TMP_43 u) in (let TMP_45 \def (Bind Abbr)
317 in (let TMP_46 \def (CHead x0 TMP_45 x1) in (let TMP_47 \def (Bind Abbr) in
318 (let TMP_48 \def (CHead d TMP_47 u) in (let TMP_49 \def (Bind Abbr) in (let
319 TMP_50 \def (CHead x0 TMP_49 x1) in (let TMP_51 \def (getl_mono c0 TMP_48 i
320 H0 TMP_50 H6) in (let H10 \def (f_equal C T TMP_42 TMP_44 TMP_46 TMP_51) in
321 (let TMP_60 \def (\lambda (H11: (eq C d x0)).(let TMP_54 \def (\lambda (t0:
322 T).(let TMP_52 \def (Bind Abbr) in (let TMP_53 \def (CHead x0 TMP_52 t0) in
323 (getl i c0 TMP_53)))) in (let H12 \def (eq_ind_r T x1 TMP_54 H8 u H10) in
324 (let TMP_55 \def (\lambda (t0: T).(arity g x0 t0 a2)) in (let H13 \def
325 (eq_ind_r T x1 TMP_55 H7 u H10) in (let TMP_58 \def (\lambda (c1: C).(let
326 TMP_56 \def (Bind Abbr) in (let TMP_57 \def (CHead c1 TMP_56 u) in (getl i c0
327 TMP_57)))) in (let H14 \def (eq_ind_r C x0 TMP_58 H12 d H11) in (let TMP_59
328 \def (\lambda (c1: C).(arity g c1 u a2)) in (let H15 \def (eq_ind_r C x0
329 TMP_59 H13 d H11) in (H2 a2 H15)))))))))) in (TMP_60
330 H9))))))))))))))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_19 TMP_20
331 TMP_21 TMP_61 H5)))))) in (let TMP_91 \def (\lambda (H5: (ex2_2 C T (\lambda
332 (d0: C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda
333 (d0: C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))))).(let TMP_65 \def
334 (\lambda (d0: C).(\lambda (u0: T).(let TMP_63 \def (Bind Abst) in (let TMP_64
335 \def (CHead d0 TMP_63 u0) in (getl i c0 TMP_64))))) in (let TMP_67 \def
336 (\lambda (d0: C).(\lambda (u0: T).(let TMP_66 \def (asucc g a2) in (arity g
337 d0 u0 TMP_66)))) in (let TMP_68 \def (leq g a a2) in (let TMP_90 \def
338 (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind
339 Abst) x1))).(\lambda (_: (arity g x0 x1 (asucc g a2))).(let TMP_69 \def (Bind
340 Abbr) in (let TMP_70 \def (CHead d TMP_69 u) in (let TMP_71 \def (\lambda
341 (c1: C).(getl i c0 c1)) in (let TMP_72 \def (Bind Abst) in (let TMP_73 \def
342 (CHead x0 TMP_72 x1) in (let TMP_74 \def (Bind Abbr) in (let TMP_75 \def
343 (CHead d TMP_74 u) in (let TMP_76 \def (Bind Abst) in (let TMP_77 \def (CHead
344 x0 TMP_76 x1) in (let TMP_78 \def (getl_mono c0 TMP_75 i H0 TMP_77 H6) in
345 (let H8 \def (eq_ind C TMP_70 TMP_71 H0 TMP_73 TMP_78) in (let TMP_79 \def
346 (Bind Abbr) in (let TMP_80 \def (CHead d TMP_79 u) in (let TMP_81 \def
347 (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _ k _)
348 \Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
349 \Rightarrow True | Abst \Rightarrow False | Void \Rightarrow False]) | (Flat
350 _) \Rightarrow False])])) in (let TMP_82 \def (Bind Abst) in (let TMP_83 \def
351 (CHead x0 TMP_82 x1) in (let TMP_84 \def (Bind Abbr) in (let TMP_85 \def
352 (CHead d TMP_84 u) in (let TMP_86 \def (Bind Abst) in (let TMP_87 \def (CHead
353 x0 TMP_86 x1) in (let TMP_88 \def (getl_mono c0 TMP_85 i H0 TMP_87 H6) in
354 (let H9 \def (eq_ind C TMP_80 TMP_81 I TMP_83 TMP_88) in (let TMP_89 \def
355 (leq g a a2) in (False_ind TMP_89 H9)))))))))))))))))))))))))))) in
356 (ex2_2_ind C T TMP_65 TMP_67 TMP_68 TMP_90 H5)))))) in (or_ind TMP_9 TMP_15
357 TMP_16 TMP_62 TMP_91 H4))))))))))))))))))))) in (let TMP_184 \def (\lambda
358 (c0: C).(\lambda (d: C).(\lambda (u: T).(\lambda (i: nat).(\lambda (H0: (getl
359 i c0 (CHead d (Bind Abst) u))).(\lambda (a: A).(\lambda (_: (arity g d u
360 (asucc g a))).(\lambda (H2: ((\forall (a2: A).((arity g d u a2) \to (leq g
361 (asucc g a) a2))))).(\lambda (a2: A).(\lambda (H3: (arity g c0 (TLRef i)
362 a2)).(let H4 \def (arity_gen_lref g c0 i a2 H3) in (let TMP_95 \def (\lambda
363 (d0: C).(\lambda (u0: T).(let TMP_93 \def (Bind Abbr) in (let TMP_94 \def
364 (CHead d0 TMP_93 u0) in (getl i c0 TMP_94))))) in (let TMP_96 \def (\lambda
365 (d0: C).(\lambda (u0: T).(arity g d0 u0 a2))) in (let TMP_97 \def (ex2_2 C T
366 TMP_95 TMP_96) in (let TMP_100 \def (\lambda (d0: C).(\lambda (u0: T).(let
367 TMP_98 \def (Bind Abst) in (let TMP_99 \def (CHead d0 TMP_98 u0) in (getl i
368 c0 TMP_99))))) in (let TMP_102 \def (\lambda (d0: C).(\lambda (u0: T).(let
369 TMP_101 \def (asucc g a2) in (arity g d0 u0 TMP_101)))) in (let TMP_103 \def
370 (ex2_2 C T TMP_100 TMP_102) in (let TMP_104 \def (leq g a a2) in (let TMP_132
371 \def (\lambda (H5: (ex2_2 C T (\lambda (d0: C).(\lambda (u0: T).(getl i c0
372 (CHead d0 (Bind Abbr) u0)))) (\lambda (d0: C).(\lambda (u0: T).(arity g d0 u0
373 a2))))).(let TMP_107 \def (\lambda (d0: C).(\lambda (u0: T).(let TMP_105 \def
374 (Bind Abbr) in (let TMP_106 \def (CHead d0 TMP_105 u0) in (getl i c0
375 TMP_106))))) in (let TMP_108 \def (\lambda (d0: C).(\lambda (u0: T).(arity g
376 d0 u0 a2))) in (let TMP_109 \def (leq g a a2) in (let TMP_131 \def (\lambda
377 (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0 (Bind Abbr)
378 x1))).(\lambda (_: (arity g x0 x1 a2)).(let TMP_110 \def (Bind Abst) in (let
379 TMP_111 \def (CHead d TMP_110 u) in (let TMP_112 \def (\lambda (c1: C).(getl
380 i c0 c1)) in (let TMP_113 \def (Bind Abbr) in (let TMP_114 \def (CHead x0
381 TMP_113 x1) in (let TMP_115 \def (Bind Abst) in (let TMP_116 \def (CHead d
382 TMP_115 u) in (let TMP_117 \def (Bind Abbr) in (let TMP_118 \def (CHead x0
383 TMP_117 x1) in (let TMP_119 \def (getl_mono c0 TMP_116 i H0 TMP_118 H6) in
384 (let H8 \def (eq_ind C TMP_111 TMP_112 H0 TMP_114 TMP_119) in (let TMP_120
385 \def (Bind Abst) in (let TMP_121 \def (CHead d TMP_120 u) in (let TMP_122
386 \def (\lambda (ee: C).(match ee with [(CSort _) \Rightarrow False | (CHead _
387 k _) \Rightarrow (match k with [(Bind b) \Rightarrow (match b with [Abbr
388 \Rightarrow False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat
389 _) \Rightarrow False])])) in (let TMP_123 \def (Bind Abbr) in (let TMP_124
390 \def (CHead x0 TMP_123 x1) in (let TMP_125 \def (Bind Abst) in (let TMP_126
391 \def (CHead d TMP_125 u) in (let TMP_127 \def (Bind Abbr) in (let TMP_128
392 \def (CHead x0 TMP_127 x1) in (let TMP_129 \def (getl_mono c0 TMP_126 i H0
393 TMP_128 H6) in (let H9 \def (eq_ind C TMP_121 TMP_122 I TMP_124 TMP_129) in
394 (let TMP_130 \def (leq g a a2) in (False_ind TMP_130
395 H9)))))))))))))))))))))))))))) in (ex2_2_ind C T TMP_107 TMP_108 TMP_109
396 TMP_131 H5)))))) in (let TMP_183 \def (\lambda (H5: (ex2_2 C T (\lambda (d0:
397 C).(\lambda (u0: T).(getl i c0 (CHead d0 (Bind Abst) u0)))) (\lambda (d0:
398 C).(\lambda (u0: T).(arity g d0 u0 (asucc g a2)))))).(let TMP_135 \def
399 (\lambda (d0: C).(\lambda (u0: T).(let TMP_133 \def (Bind Abst) in (let
400 TMP_134 \def (CHead d0 TMP_133 u0) in (getl i c0 TMP_134))))) in (let TMP_137
401 \def (\lambda (d0: C).(\lambda (u0: T).(let TMP_136 \def (asucc g a2) in
402 (arity g d0 u0 TMP_136)))) in (let TMP_138 \def (leq g a a2) in (let TMP_182
403 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda (H6: (getl i c0 (CHead x0
404 (Bind Abst) x1))).(\lambda (H7: (arity g x0 x1 (asucc g a2))).(let TMP_139
405 \def (Bind Abst) in (let TMP_140 \def (CHead d TMP_139 u) in (let TMP_141
406 \def (\lambda (c1: C).(getl i c0 c1)) in (let TMP_142 \def (Bind Abst) in
407 (let TMP_143 \def (CHead x0 TMP_142 x1) in (let TMP_144 \def (Bind Abst) in
408 (let TMP_145 \def (CHead d TMP_144 u) in (let TMP_146 \def (Bind Abst) in
409 (let TMP_147 \def (CHead x0 TMP_146 x1) in (let TMP_148 \def (getl_mono c0
410 TMP_145 i H0 TMP_147 H6) in (let H8 \def (eq_ind C TMP_140 TMP_141 H0 TMP_143
411 TMP_148) in (let TMP_149 \def (\lambda (e: C).(match e with [(CSort _)
412 \Rightarrow d | (CHead c1 _ _) \Rightarrow c1])) in (let TMP_150 \def (Bind
413 Abst) in (let TMP_151 \def (CHead d TMP_150 u) in (let TMP_152 \def (Bind
414 Abst) in (let TMP_153 \def (CHead x0 TMP_152 x1) in (let TMP_154 \def (Bind
415 Abst) in (let TMP_155 \def (CHead d TMP_154 u) in (let TMP_156 \def (Bind
416 Abst) in (let TMP_157 \def (CHead x0 TMP_156 x1) in (let TMP_158 \def
417 (getl_mono c0 TMP_155 i H0 TMP_157 H6) in (let H9 \def (f_equal C C TMP_149
418 TMP_151 TMP_153 TMP_158) in (let TMP_159 \def (\lambda (e: C).(match e with
419 [(CSort _) \Rightarrow u | (CHead _ _ t0) \Rightarrow t0])) in (let TMP_160
420 \def (Bind Abst) in (let TMP_161 \def (CHead d TMP_160 u) in (let TMP_162
421 \def (Bind Abst) in (let TMP_163 \def (CHead x0 TMP_162 x1) in (let TMP_164
422 \def (Bind Abst) in (let TMP_165 \def (CHead d TMP_164 u) in (let TMP_166
423 \def (Bind Abst) in (let TMP_167 \def (CHead x0 TMP_166 x1) in (let TMP_168
424 \def (getl_mono c0 TMP_165 i H0 TMP_167 H6) in (let H10 \def (f_equal C T
425 TMP_159 TMP_161 TMP_163 TMP_168) in (let TMP_181 \def (\lambda (H11: (eq C d
426 x0)).(let TMP_171 \def (\lambda (t0: T).(let TMP_169 \def (Bind Abst) in (let
427 TMP_170 \def (CHead x0 TMP_169 t0) in (getl i c0 TMP_170)))) in (let H12 \def
428 (eq_ind_r T x1 TMP_171 H8 u H10) in (let TMP_173 \def (\lambda (t0: T).(let
429 TMP_172 \def (asucc g a2) in (arity g x0 t0 TMP_172))) in (let H13 \def
430 (eq_ind_r T x1 TMP_173 H7 u H10) in (let TMP_176 \def (\lambda (c1: C).(let
431 TMP_174 \def (Bind Abst) in (let TMP_175 \def (CHead c1 TMP_174 u) in (getl i
432 c0 TMP_175)))) in (let H14 \def (eq_ind_r C x0 TMP_176 H12 d H11) in (let
433 TMP_178 \def (\lambda (c1: C).(let TMP_177 \def (asucc g a2) in (arity g c1 u
434 TMP_177))) in (let H15 \def (eq_ind_r C x0 TMP_178 H13 d H11) in (let TMP_179
435 \def (asucc g a2) in (let TMP_180 \def (H2 TMP_179 H15) in (asucc_inj g a a2
436 TMP_180)))))))))))) in (TMP_181 H9))))))))))))))))))))))))))))))))))))))) in
437 (ex2_2_ind C T TMP_135 TMP_137 TMP_138 TMP_182 H5)))))) in (or_ind TMP_97
438 TMP_103 TMP_104 TMP_132 TMP_183 H4))))))))))))))))))))) in (let TMP_191 \def
439 (\lambda (b: B).(\lambda (H0: (not (eq B b Abst))).(\lambda (c0: C).(\lambda
440 (u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_:
441 ((\forall (a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0:
442 T).(\lambda (a3: A).(\lambda (_: (arity g (CHead c0 (Bind b) u) t0
443 a3)).(\lambda (H4: ((\forall (a4: A).((arity g (CHead c0 (Bind b) u) t0 a4)
444 \to (leq g a3 a4))))).(\lambda (a0: A).(\lambda (H5: (arity g c0 (THead (Bind
445 b) u t0) a0)).(let H6 \def (arity_gen_bind b H0 g c0 u t0 a0 H5) in (let
446 TMP_185 \def (\lambda (a4: A).(arity g c0 u a4)) in (let TMP_188 \def
447 (\lambda (_: A).(let TMP_186 \def (Bind b) in (let TMP_187 \def (CHead c0
448 TMP_186 u) in (arity g TMP_187 t0 a0)))) in (let TMP_189 \def (leq g a3 a0)
449 in (let TMP_190 \def (\lambda (x: A).(\lambda (_: (arity g c0 u x)).(\lambda
450 (H8: (arity g (CHead c0 (Bind b) u) t0 a0)).(H4 a0 H8)))) in (ex2_ind A
451 TMP_185 TMP_188 TMP_189 TMP_190 H6))))))))))))))))))) in (let TMP_210 \def
452 (\lambda (c0: C).(\lambda (u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u
453 (asucc g a2))).(\lambda (H1: ((\forall (a3: A).((arity g c0 u a3) \to (leq g
454 (asucc g a2) a3))))).(\lambda (t0: T).(\lambda (a3: A).(\lambda (_: (arity g
455 (CHead c0 (Bind Abst) u) t0 a3)).(\lambda (H3: ((\forall (a4: A).((arity g
456 (CHead c0 (Bind Abst) u) t0 a4) \to (leq g a3 a4))))).(\lambda (a0:
457 A).(\lambda (H4: (arity g c0 (THead (Bind Abst) u t0) a0)).(let H5 \def
458 (arity_gen_abst g c0 u t0 a0 H4) in (let TMP_193 \def (\lambda (a4:
459 A).(\lambda (a5: A).(let TMP_192 \def (AHead a4 a5) in (eq A a0 TMP_192))))
460 in (let TMP_195 \def (\lambda (a4: A).(\lambda (_: A).(let TMP_194 \def
461 (asucc g a4) in (arity g c0 u TMP_194)))) in (let TMP_198 \def (\lambda (_:
462 A).(\lambda (a5: A).(let TMP_196 \def (Bind Abst) in (let TMP_197 \def (CHead
463 c0 TMP_196 u) in (arity g TMP_197 t0 a5))))) in (let TMP_199 \def (AHead a2
464 a3) in (let TMP_200 \def (leq g TMP_199 a0) in (let TMP_209 \def (\lambda
465 (x0: A).(\lambda (x1: A).(\lambda (H6: (eq A a0 (AHead x0 x1))).(\lambda (H7:
466 (arity g c0 u (asucc g x0))).(\lambda (H8: (arity g (CHead c0 (Bind Abst) u)
467 t0 x1)).(let TMP_201 \def (AHead x0 x1) in (let TMP_203 \def (\lambda (a:
468 A).(let TMP_202 \def (AHead a2 a3) in (leq g TMP_202 a))) in (let TMP_204
469 \def (asucc g x0) in (let TMP_205 \def (H1 TMP_204 H7) in (let TMP_206 \def
470 (asucc_inj g a2 x0 TMP_205) in (let TMP_207 \def (H3 x1 H8) in (let TMP_208
471 \def (leq_head g a2 x0 TMP_206 a3 x1 TMP_207) in (eq_ind_r A TMP_201 TMP_203
472 TMP_208 a0 H6))))))))))))) in (ex3_2_ind A A TMP_193 TMP_195 TMP_198 TMP_200
473 TMP_209 H5))))))))))))))))))) in (let TMP_218 \def (\lambda (c0: C).(\lambda
474 (u: T).(\lambda (a2: A).(\lambda (_: (arity g c0 u a2)).(\lambda (_:
475 ((\forall (a3: A).((arity g c0 u a3) \to (leq g a2 a3))))).(\lambda (t0:
476 T).(\lambda (a3: A).(\lambda (_: (arity g c0 t0 (AHead a2 a3))).(\lambda (H3:
477 ((\forall (a4: A).((arity g c0 t0 a4) \to (leq g (AHead a2 a3)
478 a4))))).(\lambda (a0: A).(\lambda (H4: (arity g c0 (THead (Flat Appl) u t0)
479 a0)).(let H5 \def (arity_gen_appl g c0 u t0 a0 H4) in (let TMP_211 \def
480 (\lambda (a4: A).(arity g c0 u a4)) in (let TMP_213 \def (\lambda (a4:
481 A).(let TMP_212 \def (AHead a4 a0) in (arity g c0 t0 TMP_212))) in (let
482 TMP_214 \def (leq g a3 a0) in (let TMP_217 \def (\lambda (x: A).(\lambda (_:
483 (arity g c0 u x)).(\lambda (H7: (arity g c0 t0 (AHead x a0))).(let TMP_215
484 \def (AHead x a0) in (let TMP_216 \def (H3 TMP_215 H7) in (ahead_inj_snd g a2
485 a3 x a0 TMP_216)))))) in (ex2_ind A TMP_211 TMP_213 TMP_214 TMP_217
486 H5))))))))))))))))) in (let TMP_224 \def (\lambda (c0: C).(\lambda (u:
487 T).(\lambda (a: A).(\lambda (_: (arity g c0 u (asucc g a))).(\lambda (_:
488 ((\forall (a2: A).((arity g c0 u a2) \to (leq g (asucc g a) a2))))).(\lambda
489 (t0: T).(\lambda (_: (arity g c0 t0 a)).(\lambda (H3: ((\forall (a2:
490 A).((arity g c0 t0 a2) \to (leq g a a2))))).(\lambda (a2: A).(\lambda (H4:
491 (arity g c0 (THead (Flat Cast) u t0) a2)).(let H5 \def (arity_gen_cast g c0 u
492 t0 a2 H4) in (let TMP_219 \def (asucc g a2) in (let TMP_220 \def (arity g c0
493 u TMP_219) in (let TMP_221 \def (arity g c0 t0 a2) in (let TMP_222 \def (leq
494 g a a2) in (let TMP_223 \def (\lambda (_: (arity g c0 u (asucc g
495 a2))).(\lambda (H7: (arity g c0 t0 a2)).(H3 a2 H7))) in (land_ind TMP_220
496 TMP_221 TMP_222 TMP_223 H5))))))))))))))))) in (let TMP_227 \def (\lambda
497 (c0: C).(\lambda (t0: T).(\lambda (a2: A).(\lambda (_: (arity g c0 t0
498 a2)).(\lambda (H1: ((\forall (a3: A).((arity g c0 t0 a3) \to (leq g a2
499 a3))))).(\lambda (a3: A).(\lambda (H2: (leq g a2 a3)).(\lambda (a0:
500 A).(\lambda (H3: (arity g c0 t0 a0)).(let TMP_225 \def (leq_sym g a2 a3 H2)
501 in (let TMP_226 \def (H1 a0 H3) in (leq_trans g a3 a2 TMP_225 a0
502 TMP_226)))))))))))) in (arity_ind g TMP_1 TMP_4 TMP_92 TMP_184 TMP_191
503 TMP_210 TMP_218 TMP_224 TMP_227 c t a1 H)))))))))))))).
505 theorem arity_repellent:
506 \forall (g: G).(\forall (c: C).(\forall (w: T).(\forall (t: T).(\forall (a1:
507 A).((arity g (CHead c (Bind Abst) w) t a1) \to (\forall (a2: A).((arity g c
508 (THead (Bind Abst) w t) a2) \to ((leq g a1 a2) \to (\forall (P:
511 \lambda (g: G).(\lambda (c: C).(\lambda (w: T).(\lambda (t: T).(\lambda (a1:
512 A).(\lambda (H: (arity g (CHead c (Bind Abst) w) t a1)).(\lambda (a2:
513 A).(\lambda (H0: (arity g c (THead (Bind Abst) w t) a2)).(\lambda (H1: (leq g
514 a1 a2)).(\lambda (P: Prop).(let TMP_1 \def (Bind Abst) in (let TMP_2 \def
515 (CHead c TMP_1 w) in (let H_y \def (arity_repl g TMP_2 t a1 H a2 H1) in (let
516 H2 \def (arity_gen_abst g c w t a2 H0) in (let TMP_4 \def (\lambda (a3:
517 A).(\lambda (a4: A).(let TMP_3 \def (AHead a3 a4) in (eq A a2 TMP_3)))) in
518 (let TMP_6 \def (\lambda (a3: A).(\lambda (_: A).(let TMP_5 \def (asucc g a3)
519 in (arity g c w TMP_5)))) in (let TMP_9 \def (\lambda (_: A).(\lambda (a4:
520 A).(let TMP_7 \def (Bind Abst) in (let TMP_8 \def (CHead c TMP_7 w) in (arity
521 g TMP_8 t a4))))) in (let TMP_18 \def (\lambda (x0: A).(\lambda (x1:
522 A).(\lambda (H3: (eq A a2 (AHead x0 x1))).(\lambda (_: (arity g c w (asucc g
523 x0))).(\lambda (H5: (arity g (CHead c (Bind Abst) w) t x1)).(let TMP_12 \def
524 (\lambda (a: A).(let TMP_10 \def (Bind Abst) in (let TMP_11 \def (CHead c
525 TMP_10 w) in (arity g TMP_11 t a)))) in (let TMP_13 \def (AHead x0 x1) in
526 (let H6 \def (eq_ind A a2 TMP_12 H_y TMP_13 H3) in (let TMP_14 \def (Bind
527 Abst) in (let TMP_15 \def (CHead c TMP_14 w) in (let TMP_16 \def (AHead x0
528 x1) in (let TMP_17 \def (arity_mono g TMP_15 t TMP_16 H6 x1 H5) in
529 (leq_ahead_false_2 g x1 x0 TMP_17 P))))))))))))) in (ex3_2_ind A A TMP_4
530 TMP_6 TMP_9 P TMP_18 H2)))))))))))))))))).
532 theorem arity_appls_cast:
533 \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t: T).(\forall (vs:
534 TList).(\forall (a: A).((arity g c (THeads (Flat Appl) vs u) (asucc g a)) \to
535 ((arity g c (THeads (Flat Appl) vs t) a) \to (arity g c (THeads (Flat Appl)
536 vs (THead (Flat Cast) u t)) a))))))))
538 \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (t: T).(\lambda (vs:
539 TList).(let TMP_5 \def (\lambda (t0: TList).(\forall (a: A).((arity g c
540 (THeads (Flat Appl) t0 u) (asucc g a)) \to ((arity g c (THeads (Flat Appl) t0
541 t) a) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def (Flat Cast) in (let
542 TMP_3 \def (THead TMP_2 u t) in (let TMP_4 \def (THeads TMP_1 t0 TMP_3) in
543 (arity g c TMP_4 a))))))))) in (let TMP_6 \def (\lambda (a: A).(\lambda (H:
544 (arity g c u (asucc g a))).(\lambda (H0: (arity g c t a)).(arity_cast g c u a
545 H t H0)))) in (let TMP_68 \def (\lambda (t0: T).(\lambda (t1: TList).(\lambda
546 (H: ((\forall (a: A).((arity g c (THeads (Flat Appl) t1 u) (asucc g a)) \to
547 ((arity g c (THeads (Flat Appl) t1 t) a) \to (arity g c (THeads (Flat Appl)
548 t1 (THead (Flat Cast) u t)) a)))))).(\lambda (a: A).(\lambda (H0: (arity g c
549 (THead (Flat Appl) t0 (THeads (Flat Appl) t1 u)) (asucc g a))).(\lambda (H1:
550 (arity g c (THead (Flat Appl) t0 (THeads (Flat Appl) t1 t)) a)).(let TMP_7
551 \def (Flat Appl) in (let TMP_8 \def (THeads TMP_7 t1 t) in (let H2 \def
552 (arity_gen_appl g c t0 TMP_8 a H1) in (let TMP_9 \def (\lambda (a1: A).(arity
553 g c t0 a1)) in (let TMP_13 \def (\lambda (a1: A).(let TMP_10 \def (Flat Appl)
554 in (let TMP_11 \def (THeads TMP_10 t1 t) in (let TMP_12 \def (AHead a1 a) in
555 (arity g c TMP_11 TMP_12))))) in (let TMP_14 \def (Flat Appl) in (let TMP_15
556 \def (Flat Appl) in (let TMP_16 \def (Flat Cast) in (let TMP_17 \def (THead
557 TMP_16 u t) in (let TMP_18 \def (THeads TMP_15 t1 TMP_17) in (let TMP_19 \def
558 (THead TMP_14 t0 TMP_18) in (let TMP_20 \def (arity g c TMP_19 a) in (let
559 TMP_67 \def (\lambda (x: A).(\lambda (H3: (arity g c t0 x)).(\lambda (H4:
560 (arity g c (THeads (Flat Appl) t1 t) (AHead x a))).(let TMP_21 \def (Flat
561 Appl) in (let TMP_22 \def (THeads TMP_21 t1 u) in (let TMP_23 \def (asucc g
562 a) in (let H5 \def (arity_gen_appl g c t0 TMP_22 TMP_23 H0) in (let TMP_24
563 \def (\lambda (a1: A).(arity g c t0 a1)) in (let TMP_29 \def (\lambda (a1:
564 A).(let TMP_25 \def (Flat Appl) in (let TMP_26 \def (THeads TMP_25 t1 u) in
565 (let TMP_27 \def (asucc g a) in (let TMP_28 \def (AHead a1 TMP_27) in (arity
566 g c TMP_26 TMP_28)))))) in (let TMP_30 \def (Flat Appl) in (let TMP_31 \def
567 (Flat Appl) in (let TMP_32 \def (Flat Cast) in (let TMP_33 \def (THead TMP_32
568 u t) in (let TMP_34 \def (THeads TMP_31 t1 TMP_33) in (let TMP_35 \def (THead
569 TMP_30 t0 TMP_34) in (let TMP_36 \def (arity g c TMP_35 a) in (let TMP_66
570 \def (\lambda (x0: A).(\lambda (H6: (arity g c t0 x0)).(\lambda (H7: (arity g
571 c (THeads (Flat Appl) t1 u) (AHead x0 (asucc g a)))).(let TMP_37 \def (Flat
572 Appl) in (let TMP_38 \def (Flat Cast) in (let TMP_39 \def (THead TMP_38 u t)
573 in (let TMP_40 \def (THeads TMP_37 t1 TMP_39) in (let TMP_41 \def (AHead x a)
574 in (let TMP_42 \def (Flat Appl) in (let TMP_43 \def (THeads TMP_42 t1 u) in
575 (let TMP_44 \def (asucc g a) in (let TMP_45 \def (AHead x TMP_44) in (let
576 TMP_46 \def (Flat Appl) in (let TMP_47 \def (THeads TMP_46 t1 u) in (let
577 TMP_48 \def (asucc g a) in (let TMP_49 \def (AHead x0 TMP_48) in (let TMP_50
578 \def (asucc g a) in (let TMP_51 \def (AHead x TMP_50) in (let TMP_52 \def
579 (arity_mono g c t0 x0 H6 x H3) in (let TMP_53 \def (asucc g a) in (let TMP_54
580 \def (asucc g a) in (let TMP_55 \def (asucc g a) in (let TMP_56 \def
581 (leq_refl g TMP_55) in (let TMP_57 \def (leq_head g x0 x TMP_52 TMP_53 TMP_54
582 TMP_56) in (let TMP_58 \def (arity_repl g c TMP_47 TMP_49 H7 TMP_51 TMP_57)
583 in (let TMP_59 \def (AHead x a) in (let TMP_60 \def (asucc g TMP_59) in (let
584 TMP_61 \def (AHead x a) in (let TMP_62 \def (asucc g TMP_61) in (let TMP_63
585 \def (leq_refl g TMP_62) in (let TMP_64 \def (arity_repl g c TMP_43 TMP_45
586 TMP_58 TMP_60 TMP_63) in (let TMP_65 \def (H TMP_41 TMP_64 H4) in (arity_appl
587 g c t0 x H3 TMP_40 a TMP_65))))))))))))))))))))))))))))))))) in (ex2_ind A
588 TMP_24 TMP_29 TMP_36 TMP_66 H5)))))))))))))))))) in (ex2_ind A TMP_9 TMP_13
589 TMP_20 TMP_67 H2)))))))))))))))))))) in (TList_ind TMP_5 TMP_6 TMP_68
592 theorem arity_appls_abbr:
593 \forall (g: G).(\forall (c: C).(\forall (d: C).(\forall (v: T).(\forall (i:
594 nat).((getl i c (CHead d (Bind Abbr) v)) \to (\forall (vs: TList).(\forall
595 (a: A).((arity g c (THeads (Flat Appl) vs (lift (S i) O v)) a) \to (arity g c
596 (THeads (Flat Appl) vs (TLRef i)) a)))))))))
598 \lambda (g: G).(\lambda (c: C).(\lambda (d: C).(\lambda (v: T).(\lambda (i:
599 nat).(\lambda (H: (getl i c (CHead d (Bind Abbr) v))).(\lambda (vs:
600 TList).(let TMP_4 \def (\lambda (t: TList).(\forall (a: A).((arity g c
601 (THeads (Flat Appl) t (lift (S i) O v)) a) \to (let TMP_1 \def (Flat Appl) in
602 (let TMP_2 \def (TLRef i) in (let TMP_3 \def (THeads TMP_1 t TMP_2) in (arity
603 g c TMP_3 a))))))) in (let TMP_8 \def (\lambda (a: A).(\lambda (H0: (arity g
604 c (lift (S i) O v) a)).(let TMP_5 \def (S i) in (let TMP_6 \def (getl_drop
605 Abbr c d v i H) in (let TMP_7 \def (arity_gen_lift g c v a TMP_5 O H0 d
606 TMP_6) in (arity_abbr g c d v i H a TMP_7)))))) in (let TMP_32 \def (\lambda
607 (t: T).(\lambda (t0: TList).(\lambda (H0: ((\forall (a: A).((arity g c
608 (THeads (Flat Appl) t0 (lift (S i) O v)) a) \to (arity g c (THeads (Flat
609 Appl) t0 (TLRef i)) a))))).(\lambda (a: A).(\lambda (H1: (arity g c (THead
610 (Flat Appl) t (THeads (Flat Appl) t0 (lift (S i) O v))) a)).(let TMP_9 \def
611 (Flat Appl) in (let TMP_10 \def (S i) in (let TMP_11 \def (lift TMP_10 O v)
612 in (let TMP_12 \def (THeads TMP_9 t0 TMP_11) in (let H2 \def (arity_gen_appl
613 g c t TMP_12 a H1) in (let TMP_13 \def (\lambda (a1: A).(arity g c t a1)) in
614 (let TMP_19 \def (\lambda (a1: A).(let TMP_14 \def (Flat Appl) in (let TMP_15
615 \def (S i) in (let TMP_16 \def (lift TMP_15 O v) in (let TMP_17 \def (THeads
616 TMP_14 t0 TMP_16) in (let TMP_18 \def (AHead a1 a) in (arity g c TMP_17
617 TMP_18))))))) in (let TMP_20 \def (Flat Appl) in (let TMP_21 \def (Flat Appl)
618 in (let TMP_22 \def (TLRef i) in (let TMP_23 \def (THeads TMP_21 t0 TMP_22)
619 in (let TMP_24 \def (THead TMP_20 t TMP_23) in (let TMP_25 \def (arity g c
620 TMP_24 a) in (let TMP_31 \def (\lambda (x: A).(\lambda (H3: (arity g c t
621 x)).(\lambda (H4: (arity g c (THeads (Flat Appl) t0 (lift (S i) O v)) (AHead
622 x a))).(let TMP_26 \def (Flat Appl) in (let TMP_27 \def (TLRef i) in (let
623 TMP_28 \def (THeads TMP_26 t0 TMP_27) in (let TMP_29 \def (AHead x a) in (let
624 TMP_30 \def (H0 TMP_29 H4) in (arity_appl g c t x H3 TMP_28 a TMP_30)))))))))
625 in (ex2_ind A TMP_13 TMP_19 TMP_25 TMP_31 H2)))))))))))))))))))) in
626 (TList_ind TMP_4 TMP_8 TMP_32 vs)))))))))).
628 theorem arity_appls_bind:
629 \forall (g: G).(\forall (b: B).((not (eq B b Abst)) \to (\forall (c:
630 C).(\forall (v: T).(\forall (a1: A).((arity g c v a1) \to (\forall (t:
631 T).(\forall (vs: TList).(\forall (a2: A).((arity g (CHead c (Bind b) v)
632 (THeads (Flat Appl) (lifts (S O) O vs) t) a2) \to (arity g c (THeads (Flat
633 Appl) vs (THead (Bind b) v t)) a2)))))))))))
635 \lambda (g: G).(\lambda (b: B).(\lambda (H: (not (eq B b Abst))).(\lambda
636 (c: C).(\lambda (v: T).(\lambda (a1: A).(\lambda (H0: (arity g c v
637 a1)).(\lambda (t: T).(\lambda (vs: TList).(let TMP_5 \def (\lambda (t0:
638 TList).(\forall (a2: A).((arity g (CHead c (Bind b) v) (THeads (Flat Appl)
639 (lifts (S O) O t0) t) a2) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def
640 (Bind b) in (let TMP_3 \def (THead TMP_2 v t) in (let TMP_4 \def (THeads
641 TMP_1 t0 TMP_3) in (arity g c TMP_4 a2)))))))) in (let TMP_6 \def (\lambda
642 (a2: A).(\lambda (H1: (arity g (CHead c (Bind b) v) t a2)).(arity_bind g b H
643 c v a1 H0 t a2 H1))) in (let TMP_49 \def (\lambda (t0: T).(\lambda (t1:
644 TList).(\lambda (H1: ((\forall (a2: A).((arity g (CHead c (Bind b) v) (THeads
645 (Flat Appl) (lifts (S O) O t1) t) a2) \to (arity g c (THeads (Flat Appl) t1
646 (THead (Bind b) v t)) a2))))).(\lambda (a2: A).(\lambda (H2: (arity g (CHead
647 c (Bind b) v) (THead (Flat Appl) (lift (S O) O t0) (THeads (Flat Appl) (lifts
648 (S O) O t1) t)) a2)).(let TMP_7 \def (Bind b) in (let TMP_8 \def (CHead c
649 TMP_7 v) in (let TMP_9 \def (S O) in (let TMP_10 \def (lift TMP_9 O t0) in
650 (let TMP_11 \def (Flat Appl) in (let TMP_12 \def (S O) in (let TMP_13 \def
651 (lifts TMP_12 O t1) in (let TMP_14 \def (THeads TMP_11 TMP_13 t) in (let H3
652 \def (arity_gen_appl g TMP_8 TMP_10 TMP_14 a2 H2) in (let TMP_19 \def
653 (\lambda (a3: A).(let TMP_15 \def (Bind b) in (let TMP_16 \def (CHead c
654 TMP_15 v) in (let TMP_17 \def (S O) in (let TMP_18 \def (lift TMP_17 O t0) in
655 (arity g TMP_16 TMP_18 a3)))))) in (let TMP_27 \def (\lambda (a3: A).(let
656 TMP_20 \def (Bind b) in (let TMP_21 \def (CHead c TMP_20 v) in (let TMP_22
657 \def (Flat Appl) in (let TMP_23 \def (S O) in (let TMP_24 \def (lifts TMP_23
658 O t1) in (let TMP_25 \def (THeads TMP_22 TMP_24 t) in (let TMP_26 \def (AHead
659 a3 a2) in (arity g TMP_21 TMP_25 TMP_26))))))))) in (let TMP_28 \def (Flat
660 Appl) in (let TMP_29 \def (Flat Appl) in (let TMP_30 \def (Bind b) in (let
661 TMP_31 \def (THead TMP_30 v t) in (let TMP_32 \def (THeads TMP_29 t1 TMP_31)
662 in (let TMP_33 \def (THead TMP_28 t0 TMP_32) in (let TMP_34 \def (arity g c
663 TMP_33 a2) in (let TMP_48 \def (\lambda (x: A).(\lambda (H4: (arity g (CHead
664 c (Bind b) v) (lift (S O) O t0) x)).(\lambda (H5: (arity g (CHead c (Bind b)
665 v) (THeads (Flat Appl) (lifts (S O) O t1) t) (AHead x a2))).(let TMP_35 \def
666 (Bind b) in (let TMP_36 \def (CHead c TMP_35 v) in (let TMP_37 \def (S O) in
667 (let TMP_38 \def (Bind b) in (let TMP_39 \def (drop_refl c) in (let TMP_40
668 \def (drop_drop TMP_38 O c c TMP_39 v) in (let TMP_41 \def (arity_gen_lift g
669 TMP_36 t0 x TMP_37 O H4 c TMP_40) in (let TMP_42 \def (Flat Appl) in (let
670 TMP_43 \def (Bind b) in (let TMP_44 \def (THead TMP_43 v t) in (let TMP_45
671 \def (THeads TMP_42 t1 TMP_44) in (let TMP_46 \def (AHead x a2) in (let
672 TMP_47 \def (H1 TMP_46 H5) in (arity_appl g c t0 x TMP_41 TMP_45 a2
673 TMP_47))))))))))))))))) in (ex2_ind A TMP_19 TMP_27 TMP_34 TMP_48
674 H3))))))))))))))))))))))))) in (TList_ind TMP_5 TMP_6 TMP_49 vs)))))))))))).
projects / helm.git / blob