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/sc3/defs.ma".
19 include "basic_1/sn3/lift1.ma".
21 include "basic_1/nf2/lift1.ma".
23 include "basic_1/csuba/arity.ma".
25 include "basic_1/arity/lift1.ma".
27 include "basic_1/arity/aprem.ma".
29 include "basic_1/llt/props.ma".
31 include "basic_1/llt/fwd.ma".
33 include "basic_1/drop1/getl.ma".
35 include "basic_1/drop1/props.ma".
37 include "basic_1/lift1/drop1.ma".
39 theorem sc3_arity_gen:
40 \forall (g: G).(\forall (c: C).(\forall (t: T).(\forall (a: A).((sc3 g a c
41 t) \to (arity g c t a)))))
43 \lambda (g: G).(\lambda (c: C).(\lambda (t: T).(\lambda (a: A).(let TMP_1
44 \def (\lambda (a0: A).((sc3 g a0 c t) \to (arity g c t a0))) in (let TMP_8
45 \def (\lambda (n: nat).(\lambda (n0: nat).(\lambda (H: (land (arity g c t
46 (ASort n n0)) (sn3 c t))).(let H0 \def H in (let TMP_2 \def (ASort n n0) in
47 (let TMP_3 \def (arity g c t TMP_2) in (let TMP_4 \def (sn3 c t) in (let
48 TMP_5 \def (ASort n n0) in (let TMP_6 \def (arity g c t TMP_5) in (let TMP_7
49 \def (\lambda (H1: (arity g c t (ASort n n0))).(\lambda (_: (sn3 c t)).H1))
50 in (land_ind TMP_3 TMP_4 TMP_6 TMP_7 H0))))))))))) in (let TMP_18 \def
51 (\lambda (a0: A).(\lambda (_: (((sc3 g a0 c t) \to (arity g c t
52 a0)))).(\lambda (a1: A).(\lambda (_: (((sc3 g a1 c t) \to (arity g c t
53 a1)))).(\lambda (H1: (land (arity g c t (AHead a0 a1)) (\forall (d:
54 C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c)
55 \to (sc3 g a1 d (THead (Flat Appl) w (lift1 is t)))))))))).(let H2 \def H1 in
56 (let TMP_9 \def (AHead a0 a1) in (let TMP_10 \def (arity g c t TMP_9) in (let
57 TMP_14 \def (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is:
58 PList).((drop1 is d c) \to (let TMP_11 \def (Flat Appl) in (let TMP_12 \def
59 (lift1 is t) in (let TMP_13 \def (THead TMP_11 w TMP_12) in (sc3 g a1 d
60 TMP_13))))))))) in (let TMP_15 \def (AHead a0 a1) in (let TMP_16 \def (arity
61 g c t TMP_15) in (let TMP_17 \def (\lambda (H3: (arity g c t (AHead a0
62 a1))).(\lambda (_: ((\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to
63 (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
64 (lift1 is t)))))))))).H3)) in (land_ind TMP_10 TMP_14 TMP_16 TMP_17
65 H2))))))))))))) in (A_ind TMP_1 TMP_8 TMP_18 a))))))).
68 \forall (g: G).(\forall (a1: A).(\forall (c: C).(\forall (t: T).((sc3 g a1 c
69 t) \to (\forall (a2: A).((leq g a1 a2) \to (sc3 g a2 c t)))))))
71 \lambda (g: G).(\lambda (a1: A).(let TMP_1 \def (\lambda (a: A).(\forall (c:
72 C).(\forall (t: T).((sc3 g a c t) \to (\forall (a2: A).((leq g a a2) \to (sc3
73 g a2 c t))))))) in (let TMP_73 \def (\lambda (a2: A).(let TMP_2 \def (\lambda
74 (a: A).(((\forall (a3: A).((llt a3 a) \to (\forall (c: C).(\forall (t:
75 T).((sc3 g a3 c t) \to (\forall (a4: A).((leq g a3 a4) \to (sc3 g a4 c
76 t))))))))) \to (\forall (c: C).(\forall (t: T).((sc3 g a c t) \to (\forall
77 (a3: A).((leq g a a3) \to (sc3 g a3 c t)))))))) in (let TMP_28 \def (\lambda
78 (n: nat).(\lambda (n0: nat).(\lambda (_: ((\forall (a3: A).((llt a3 (ASort n
79 n0)) \to (\forall (c: C).(\forall (t: T).((sc3 g a3 c t) \to (\forall (a4:
80 A).((leq g a3 a4) \to (sc3 g a4 c t)))))))))).(\lambda (c: C).(\lambda (t:
81 T).(\lambda (H0: (land (arity g c t (ASort n n0)) (sn3 c t))).(\lambda (a3:
82 A).(\lambda (H1: (leq g (ASort n n0) a3)).(let H2 \def H0 in (let TMP_3 \def
83 (ASort n n0) in (let TMP_4 \def (arity g c t TMP_3) in (let TMP_5 \def (sn3 c
84 t) in (let TMP_6 \def (sc3 g a3 c t) in (let TMP_27 \def (\lambda (H3: (arity
85 g c t (ASort n n0))).(\lambda (H4: (sn3 c t)).(let TMP_7 \def (ASort n n0) in
86 (let H_y \def (arity_repl g c t TMP_7 H3 a3 H1) in (let H_x \def
87 (leq_gen_sort1 g n n0 a3 H1) in (let H5 \def H_x in (let TMP_12 \def (\lambda
88 (n2: nat).(\lambda (h2: nat).(\lambda (k: nat).(let TMP_8 \def (ASort n n0)
89 in (let TMP_9 \def (aplus g TMP_8 k) in (let TMP_10 \def (ASort h2 n2) in
90 (let TMP_11 \def (aplus g TMP_10 k) in (eq A TMP_9 TMP_11)))))))) in (let
91 TMP_14 \def (\lambda (n2: nat).(\lambda (h2: nat).(\lambda (_: nat).(let
92 TMP_13 \def (ASort h2 n2) in (eq A a3 TMP_13))))) in (let TMP_15 \def (sc3 g
93 a3 c t) in (let TMP_26 \def (\lambda (x0: nat).(\lambda (x1: nat).(\lambda
94 (x2: nat).(\lambda (_: (eq A (aplus g (ASort n n0) x2) (aplus g (ASort x1 x0)
95 x2))).(\lambda (H7: (eq A a3 (ASort x1 x0))).(let TMP_16 \def (\lambda (e:
96 A).e) in (let TMP_17 \def (ASort x1 x0) in (let H8 \def (f_equal A A TMP_16
97 a3 TMP_17 H7) in (let TMP_18 \def (\lambda (a: A).(arity g c t a)) in (let
98 TMP_19 \def (ASort x1 x0) in (let H9 \def (eq_ind A a3 TMP_18 H_y TMP_19 H8)
99 in (let TMP_20 \def (ASort x1 x0) in (let TMP_21 \def (\lambda (a: A).(sc3 g
100 a c t)) in (let TMP_22 \def (ASort x1 x0) in (let TMP_23 \def (arity g c t
101 TMP_22) in (let TMP_24 \def (sn3 c t) in (let TMP_25 \def (conj TMP_23 TMP_24
102 H9 H4) in (eq_ind_r A TMP_20 TMP_21 TMP_25 a3 H8)))))))))))))))))) in
103 (ex2_3_ind nat nat nat TMP_12 TMP_14 TMP_15 TMP_26 H5))))))))))) in (land_ind
104 TMP_4 TMP_5 TMP_6 TMP_27 H2))))))))))))))) in (let TMP_72 \def (\lambda (a:
105 A).(\lambda (_: ((((\forall (a3: A).((llt a3 a) \to (\forall (c: C).(\forall
106 (t: T).((sc3 g a3 c t) \to (\forall (a4: A).((leq g a3 a4) \to (sc3 g a4 c
107 t))))))))) \to (\forall (c: C).(\forall (t: T).((sc3 g a c t) \to (\forall
108 (a3: A).((leq g a a3) \to (sc3 g a3 c t))))))))).(\lambda (a0: A).(\lambda
109 (H0: ((((\forall (a3: A).((llt a3 a0) \to (\forall (c: C).(\forall (t:
110 T).((sc3 g a3 c t) \to (\forall (a4: A).((leq g a3 a4) \to (sc3 g a4 c
111 t))))))))) \to (\forall (c: C).(\forall (t: T).((sc3 g a0 c t) \to (\forall
112 (a3: A).((leq g a0 a3) \to (sc3 g a3 c t))))))))).(\lambda (H1: ((\forall
113 (a3: A).((llt a3 (AHead a a0)) \to (\forall (c: C).(\forall (t: T).((sc3 g a3
114 c t) \to (\forall (a4: A).((leq g a3 a4) \to (sc3 g a4 c t)))))))))).(\lambda
115 (c: C).(\lambda (t: T).(\lambda (H2: (land (arity g c t (AHead a a0))
116 (\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall (is:
117 PList).((drop1 is d c) \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is
118 t)))))))))).(\lambda (a3: A).(\lambda (H3: (leq g (AHead a a0) a3)).(let H4
119 \def H2 in (let TMP_29 \def (AHead a a0) in (let TMP_30 \def (arity g c t
120 TMP_29) in (let TMP_34 \def (\forall (d: C).(\forall (w: T).((sc3 g a d w)
121 \to (\forall (is: PList).((drop1 is d c) \to (let TMP_31 \def (Flat Appl) in
122 (let TMP_32 \def (lift1 is t) in (let TMP_33 \def (THead TMP_31 w TMP_32) in
123 (sc3 g a0 d TMP_33))))))))) in (let TMP_35 \def (sc3 g a3 c t) in (let TMP_71
124 \def (\lambda (H5: (arity g c t (AHead a a0))).(\lambda (H6: ((\forall (d:
125 C).(\forall (w: T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c)
126 \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is t)))))))))).(let H_x \def
127 (leq_gen_head1 g a a0 a3 H3) in (let H7 \def H_x in (let TMP_36 \def (\lambda
128 (a4: A).(\lambda (_: A).(leq g a a4))) in (let TMP_37 \def (\lambda (_:
129 A).(\lambda (a5: A).(leq g a0 a5))) in (let TMP_39 \def (\lambda (a4:
130 A).(\lambda (a5: A).(let TMP_38 \def (AHead a4 a5) in (eq A a3 TMP_38)))) in
131 (let TMP_40 \def (sc3 g a3 c t) in (let TMP_70 \def (\lambda (x0: A).(\lambda
132 (x1: A).(\lambda (H8: (leq g a x0)).(\lambda (H9: (leq g a0 x1)).(\lambda
133 (H10: (eq A a3 (AHead x0 x1))).(let TMP_41 \def (\lambda (e: A).e) in (let
134 TMP_42 \def (AHead x0 x1) in (let H11 \def (f_equal A A TMP_41 a3 TMP_42 H10)
135 in (let TMP_43 \def (AHead x0 x1) in (let TMP_44 \def (\lambda (a4: A).(sc3 g
136 a4 c t)) in (let TMP_45 \def (AHead x0 x1) in (let TMP_46 \def (arity g c t
137 TMP_45) in (let TMP_50 \def (\forall (d: C).(\forall (w: T).((sc3 g x0 d w)
138 \to (\forall (is: PList).((drop1 is d c) \to (let TMP_47 \def (Flat Appl) in
139 (let TMP_48 \def (lift1 is t) in (let TMP_49 \def (THead TMP_47 w TMP_48) in
140 (sc3 g x1 d TMP_49))))))))) in (let TMP_51 \def (AHead a a0) in (let TMP_52
141 \def (AHead x0 x1) in (let TMP_53 \def (leq_head g a x0 H8 a0 x1 H9) in (let
142 TMP_54 \def (arity_repl g c t TMP_51 H5 TMP_52 TMP_53) in (let TMP_68 \def
143 (\lambda (d: C).(\lambda (w: T).(\lambda (H12: (sc3 g x0 d w)).(\lambda (is:
144 PList).(\lambda (H13: (drop1 is d c)).(let TMP_58 \def (\lambda (a4:
145 A).(\lambda (H14: (llt a4 a0)).(\lambda (c0: C).(\lambda (t0: T).(\lambda
146 (H15: (sc3 g a4 c0 t0)).(\lambda (a5: A).(\lambda (H16: (leq g a4 a5)).(let
147 TMP_55 \def (AHead a a0) in (let TMP_56 \def (llt_head_dx a a0) in (let
148 TMP_57 \def (llt_trans a4 a0 TMP_55 H14 TMP_56) in (H1 a4 TMP_57 c0 t0 H15 a5
149 H16))))))))))) in (let TMP_59 \def (Flat Appl) in (let TMP_60 \def (lift1 is
150 t) in (let TMP_61 \def (THead TMP_59 w TMP_60) in (let TMP_62 \def (AHead a
151 a0) in (let TMP_63 \def (llt_head_sx a a0) in (let TMP_64 \def (llt_repl g a
152 x0 H8 TMP_62 TMP_63) in (let TMP_65 \def (leq_sym g a x0 H8) in (let TMP_66
153 \def (H1 x0 TMP_64 d w H12 a TMP_65) in (let TMP_67 \def (H6 d w TMP_66 is
154 H13) in (H0 TMP_58 d TMP_61 TMP_67 x1 H9)))))))))))))))) in (let TMP_69 \def
155 (conj TMP_46 TMP_50 TMP_54 TMP_68) in (eq_ind_r A TMP_43 TMP_44 TMP_69 a3
156 H11)))))))))))))))))))) in (ex3_2_ind A A TMP_36 TMP_37 TMP_39 TMP_40 TMP_70
157 H7)))))))))) in (land_ind TMP_30 TMP_34 TMP_35 TMP_71 H4))))))))))))))))) in
158 (A_ind TMP_2 TMP_28 TMP_72 a2))))) in (llt_wf_ind TMP_1 TMP_73 a1)))).
161 \forall (g: G).(\forall (a: A).(\forall (e: C).(\forall (t: T).((sc3 g a e
162 t) \to (\forall (c: C).(\forall (h: nat).(\forall (d: nat).((drop h d c e)
163 \to (sc3 g a c (lift h d t))))))))))
165 \lambda (g: G).(\lambda (a: A).(let TMP_2 \def (\lambda (a0: A).(\forall (e:
166 C).(\forall (t: T).((sc3 g a0 e t) \to (\forall (c: C).(\forall (h:
167 nat).(\forall (d: nat).((drop h d c e) \to (let TMP_1 \def (lift h d t) in
168 (sc3 g a0 c TMP_1)))))))))) in (let TMP_21 \def (\lambda (n: nat).(\lambda
169 (n0: nat).(\lambda (e: C).(\lambda (t: T).(\lambda (H: (land (arity g e t
170 (ASort n n0)) (sn3 e t))).(\lambda (c: C).(\lambda (h: nat).(\lambda (d:
171 nat).(\lambda (H0: (drop h d c e)).(let H1 \def H in (let TMP_3 \def (ASort n
172 n0) in (let TMP_4 \def (arity g e t TMP_3) in (let TMP_5 \def (sn3 e t) in
173 (let TMP_6 \def (lift h d t) in (let TMP_7 \def (ASort n n0) in (let TMP_8
174 \def (arity g c TMP_6 TMP_7) in (let TMP_9 \def (lift h d t) in (let TMP_10
175 \def (sn3 c TMP_9) in (let TMP_11 \def (land TMP_8 TMP_10) in (let TMP_20
176 \def (\lambda (H2: (arity g e t (ASort n n0))).(\lambda (H3: (sn3 e t)).(let
177 TMP_12 \def (lift h d t) in (let TMP_13 \def (ASort n n0) in (let TMP_14 \def
178 (arity g c TMP_12 TMP_13) in (let TMP_15 \def (lift h d t) in (let TMP_16
179 \def (sn3 c TMP_15) in (let TMP_17 \def (ASort n n0) in (let TMP_18 \def
180 (arity_lift g e t TMP_17 H2 c h d H0) in (let TMP_19 \def (sn3_lift e t H3 c
181 h d H0) in (conj TMP_14 TMP_16 TMP_18 TMP_19))))))))))) in (land_ind TMP_4
182 TMP_5 TMP_11 TMP_20 H1))))))))))))))))))))) in (let TMP_60 \def (\lambda (a0:
183 A).(\lambda (_: ((\forall (e: C).(\forall (t: T).((sc3 g a0 e t) \to (\forall
184 (c: C).(\forall (h: nat).(\forall (d: nat).((drop h d c e) \to (sc3 g a0 c
185 (lift h d t))))))))))).(\lambda (a1: A).(\lambda (_: ((\forall (e:
186 C).(\forall (t: T).((sc3 g a1 e t) \to (\forall (c: C).(\forall (h:
187 nat).(\forall (d: nat).((drop h d c e) \to (sc3 g a1 c (lift h d
188 t))))))))))).(\lambda (e: C).(\lambda (t: T).(\lambda (H1: (land (arity g e t
189 (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall
190 (is: PList).((drop1 is d e) \to (sc3 g a1 d (THead (Flat Appl) w (lift1 is
191 t)))))))))).(\lambda (c: C).(\lambda (h: nat).(\lambda (d: nat).(\lambda (H2:
192 (drop h d c e)).(let H3 \def H1 in (let TMP_22 \def (AHead a0 a1) in (let
193 TMP_23 \def (arity g e t TMP_22) in (let TMP_27 \def (\forall (d0:
194 C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 e)
195 \to (let TMP_24 \def (Flat Appl) in (let TMP_25 \def (lift1 is t) in (let
196 TMP_26 \def (THead TMP_24 w TMP_25) in (sc3 g a1 d0 TMP_26))))))))) in (let
197 TMP_28 \def (lift h d t) in (let TMP_29 \def (AHead a0 a1) in (let TMP_30
198 \def (arity g c TMP_28 TMP_29) in (let TMP_35 \def (\forall (d0: C).(\forall
199 (w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 c) \to (let
200 TMP_31 \def (Flat Appl) in (let TMP_32 \def (lift h d t) in (let TMP_33 \def
201 (lift1 is TMP_32) in (let TMP_34 \def (THead TMP_31 w TMP_33) in (sc3 g a1 d0
202 TMP_34)))))))))) in (let TMP_36 \def (land TMP_30 TMP_35) in (let TMP_59 \def
203 (\lambda (H4: (arity g e t (AHead a0 a1))).(\lambda (H5: ((\forall (d0:
204 C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 e)
205 \to (sc3 g a1 d0 (THead (Flat Appl) w (lift1 is t)))))))))).(let TMP_37 \def
206 (lift h d t) in (let TMP_38 \def (AHead a0 a1) in (let TMP_39 \def (arity g c
207 TMP_37 TMP_38) in (let TMP_44 \def (\forall (d0: C).(\forall (w: T).((sc3 g
208 a0 d0 w) \to (\forall (is: PList).((drop1 is d0 c) \to (let TMP_40 \def (Flat
209 Appl) in (let TMP_41 \def (lift h d t) in (let TMP_42 \def (lift1 is TMP_41)
210 in (let TMP_43 \def (THead TMP_40 w TMP_42) in (sc3 g a1 d0 TMP_43))))))))))
211 in (let TMP_45 \def (AHead a0 a1) in (let TMP_46 \def (arity_lift g e t
212 TMP_45 H4 c h d H2) in (let TMP_58 \def (\lambda (d0: C).(\lambda (w:
213 T).(\lambda (H6: (sc3 g a0 d0 w)).(\lambda (is: PList).(\lambda (H7: (drop1
214 is d0 c)).(let TMP_47 \def (PConsTail is h d) in (let H_y \def (H5 d0 w H6
215 TMP_47) in (let TMP_48 \def (PConsTail is h d) in (let TMP_49 \def (lift1
216 TMP_48 t) in (let TMP_52 \def (\lambda (t0: T).(let TMP_50 \def (Flat Appl)
217 in (let TMP_51 \def (THead TMP_50 w t0) in (sc3 g a1 d0 TMP_51)))) in (let
218 TMP_53 \def (drop1_cons_tail c e h d H2 is d0 H7) in (let TMP_54 \def (H_y
219 TMP_53) in (let TMP_55 \def (lift h d t) in (let TMP_56 \def (lift1 is
220 TMP_55) in (let TMP_57 \def (lift1_cons_tail t h d is) in (eq_ind T TMP_49
221 TMP_52 TMP_54 TMP_56 TMP_57)))))))))))))))) in (conj TMP_39 TMP_44 TMP_46
222 TMP_58)))))))))) in (land_ind TMP_23 TMP_27 TMP_36 TMP_59
223 H3)))))))))))))))))))))) in (A_ind TMP_2 TMP_21 TMP_60 a))))).
226 \forall (g: G).(\forall (e: C).(\forall (a: A).(\forall (hds:
227 PList).(\forall (c: C).(\forall (t: T).((sc3 g a e t) \to ((drop1 hds c e)
228 \to (sc3 g a c (lift1 hds t)))))))))
230 \lambda (g: G).(\lambda (e: C).(\lambda (a: A).(\lambda (hds: PList).(let
231 TMP_2 \def (\lambda (p: PList).(\forall (c: C).(\forall (t: T).((sc3 g a e t)
232 \to ((drop1 p c e) \to (let TMP_1 \def (lift1 p t) in (sc3 g a c TMP_1)))))))
233 in (let TMP_4 \def (\lambda (c: C).(\lambda (t: T).(\lambda (H: (sc3 g a e
234 t)).(\lambda (H0: (drop1 PNil c e)).(let H_y \def (drop1_gen_pnil c e H0) in
235 (let TMP_3 \def (\lambda (c0: C).(sc3 g a c0 t)) in (eq_ind_r C e TMP_3 H c
236 H_y))))))) in (let TMP_13 \def (\lambda (n: nat).(\lambda (n0: nat).(\lambda
237 (p: PList).(\lambda (H: ((\forall (c: C).(\forall (t: T).((sc3 g a e t) \to
238 ((drop1 p c e) \to (sc3 g a c (lift1 p t)))))))).(\lambda (c: C).(\lambda (t:
239 T).(\lambda (H0: (sc3 g a e t)).(\lambda (H1: (drop1 (PCons n n0 p) c
240 e)).(let H_x \def (drop1_gen_pcons c e p n n0 H1) in (let H2 \def H_x in (let
241 TMP_5 \def (\lambda (c2: C).(drop n n0 c c2)) in (let TMP_6 \def (\lambda
242 (c2: C).(drop1 p c2 e)) in (let TMP_7 \def (lift1 p t) in (let TMP_8 \def
243 (lift n n0 TMP_7) in (let TMP_9 \def (sc3 g a c TMP_8) in (let TMP_12 \def
244 (\lambda (x: C).(\lambda (H3: (drop n n0 c x)).(\lambda (H4: (drop1 p x
245 e)).(let TMP_10 \def (lift1 p t) in (let TMP_11 \def (H x t H0 H4) in
246 (sc3_lift g a x TMP_10 TMP_11 c n n0 H3)))))) in (ex2_ind C TMP_5 TMP_6 TMP_9
247 TMP_12 H2))))))))))))))))) in (PList_ind TMP_2 TMP_4 TMP_13 hds))))))).
250 \forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (i:
251 nat).(\forall (d: C).(\forall (v: T).(\forall (c: C).((sc3 g a c (THeads
252 (Flat Appl) vs (lift (S i) O v))) \to ((getl i c (CHead d (Bind Abbr) v)) \to
253 (sc3 g a c (THeads (Flat Appl) vs (TLRef i)))))))))))
255 \lambda (g: G).(\lambda (a: A).(let TMP_4 \def (\lambda (a0: A).(\forall
256 (vs: TList).(\forall (i: nat).(\forall (d: C).(\forall (v: T).(\forall (c:
257 C).((sc3 g a0 c (THeads (Flat Appl) vs (lift (S i) O v))) \to ((getl i c
258 (CHead d (Bind Abbr) v)) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def
259 (TLRef i) in (let TMP_3 \def (THeads TMP_1 vs TMP_2) in (sc3 g a0 c
260 TMP_3)))))))))))) in (let TMP_39 \def (\lambda (n: nat).(\lambda (n0:
261 nat).(\lambda (vs: TList).(\lambda (i: nat).(\lambda (d: C).(\lambda (v:
262 T).(\lambda (c: C).(\lambda (H: (land (arity g c (THeads (Flat Appl) vs (lift
263 (S i) O v)) (ASort n n0)) (sn3 c (THeads (Flat Appl) vs (lift (S i) O
264 v))))).(\lambda (H0: (getl i c (CHead d (Bind Abbr) v))).(let H1 \def H in
265 (let TMP_5 \def (Flat Appl) in (let TMP_6 \def (S i) in (let TMP_7 \def (lift
266 TMP_6 O v) in (let TMP_8 \def (THeads TMP_5 vs TMP_7) in (let TMP_9 \def
267 (ASort n n0) in (let TMP_10 \def (arity g c TMP_8 TMP_9) in (let TMP_11 \def
268 (Flat Appl) in (let TMP_12 \def (S i) in (let TMP_13 \def (lift TMP_12 O v)
269 in (let TMP_14 \def (THeads TMP_11 vs TMP_13) in (let TMP_15 \def (sn3 c
270 TMP_14) in (let TMP_16 \def (Flat Appl) in (let TMP_17 \def (TLRef i) in (let
271 TMP_18 \def (THeads TMP_16 vs TMP_17) in (let TMP_19 \def (ASort n n0) in
272 (let TMP_20 \def (arity g c TMP_18 TMP_19) in (let TMP_21 \def (Flat Appl) in
273 (let TMP_22 \def (TLRef i) in (let TMP_23 \def (THeads TMP_21 vs TMP_22) in
274 (let TMP_24 \def (sn3 c TMP_23) in (let TMP_25 \def (land TMP_20 TMP_24) in
275 (let TMP_38 \def (\lambda (H2: (arity g c (THeads (Flat Appl) vs (lift (S i)
276 O v)) (ASort n n0))).(\lambda (H3: (sn3 c (THeads (Flat Appl) vs (lift (S i)
277 O v)))).(let TMP_26 \def (Flat Appl) in (let TMP_27 \def (TLRef i) in (let
278 TMP_28 \def (THeads TMP_26 vs TMP_27) in (let TMP_29 \def (ASort n n0) in
279 (let TMP_30 \def (arity g c TMP_28 TMP_29) in (let TMP_31 \def (Flat Appl) in
280 (let TMP_32 \def (TLRef i) in (let TMP_33 \def (THeads TMP_31 vs TMP_32) in
281 (let TMP_34 \def (sn3 c TMP_33) in (let TMP_35 \def (ASort n n0) in (let
282 TMP_36 \def (arity_appls_abbr g c d v i H0 vs TMP_35 H2) in (let TMP_37 \def
283 (sn3_appls_abbr c d v i H0 vs H3) in (conj TMP_30 TMP_34 TMP_36
284 TMP_37))))))))))))))) in (land_ind TMP_10 TMP_15 TMP_25 TMP_38
285 H1))))))))))))))))))))))))))))))))) in (let TMP_166 \def (\lambda (a0:
286 A).(\lambda (_: ((\forall (vs: TList).(\forall (i: nat).(\forall (d:
287 C).(\forall (v: T).(\forall (c: C).((sc3 g a0 c (THeads (Flat Appl) vs (lift
288 (S i) O v))) \to ((getl i c (CHead d (Bind Abbr) v)) \to (sc3 g a0 c (THeads
289 (Flat Appl) vs (TLRef i)))))))))))).(\lambda (a1: A).(\lambda (H0: ((\forall
290 (vs: TList).(\forall (i: nat).(\forall (d: C).(\forall (v: T).(\forall (c:
291 C).((sc3 g a1 c (THeads (Flat Appl) vs (lift (S i) O v))) \to ((getl i c
292 (CHead d (Bind Abbr) v)) \to (sc3 g a1 c (THeads (Flat Appl) vs (TLRef
293 i)))))))))))).(\lambda (vs: TList).(\lambda (i: nat).(\lambda (d: C).(\lambda
294 (v: T).(\lambda (c: C).(\lambda (H1: (land (arity g c (THeads (Flat Appl) vs
295 (lift (S i) O v)) (AHead a0 a1)) (\forall (d0: C).(\forall (w: T).((sc3 g a0
296 d0 w) \to (\forall (is: PList).((drop1 is d0 c) \to (sc3 g a1 d0 (THead (Flat
297 Appl) w (lift1 is (THeads (Flat Appl) vs (lift (S i) O v)))))))))))).(\lambda
298 (H2: (getl i c (CHead d (Bind Abbr) v))).(let H3 \def H1 in (let TMP_40 \def
299 (Flat Appl) in (let TMP_41 \def (S i) in (let TMP_42 \def (lift TMP_41 O v)
300 in (let TMP_43 \def (THeads TMP_40 vs TMP_42) in (let TMP_44 \def (AHead a0
301 a1) in (let TMP_45 \def (arity g c TMP_43 TMP_44) in (let TMP_53 \def
302 (\forall (d0: C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is:
303 PList).((drop1 is d0 c) \to (let TMP_46 \def (Flat Appl) in (let TMP_47 \def
304 (Flat Appl) in (let TMP_48 \def (S i) in (let TMP_49 \def (lift TMP_48 O v)
305 in (let TMP_50 \def (THeads TMP_47 vs TMP_49) in (let TMP_51 \def (lift1 is
306 TMP_50) in (let TMP_52 \def (THead TMP_46 w TMP_51) in (sc3 g a1 d0
307 TMP_52))))))))))))) in (let TMP_54 \def (Flat Appl) in (let TMP_55 \def
308 (TLRef i) in (let TMP_56 \def (THeads TMP_54 vs TMP_55) in (let TMP_57 \def
309 (AHead a0 a1) in (let TMP_58 \def (arity g c TMP_56 TMP_57) in (let TMP_65
310 \def (\forall (d0: C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is:
311 PList).((drop1 is d0 c) \to (let TMP_59 \def (Flat Appl) in (let TMP_60 \def
312 (Flat Appl) in (let TMP_61 \def (TLRef i) in (let TMP_62 \def (THeads TMP_60
313 vs TMP_61) in (let TMP_63 \def (lift1 is TMP_62) in (let TMP_64 \def (THead
314 TMP_59 w TMP_63) in (sc3 g a1 d0 TMP_64)))))))))))) in (let TMP_66 \def (land
315 TMP_58 TMP_65) in (let TMP_165 \def (\lambda (H4: (arity g c (THeads (Flat
316 Appl) vs (lift (S i) O v)) (AHead a0 a1))).(\lambda (H5: ((\forall (d0:
317 C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is: PList).((drop1 is d0 c)
318 \to (sc3 g a1 d0 (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs (lift
319 (S i) O v)))))))))))).(let TMP_67 \def (Flat Appl) in (let TMP_68 \def (TLRef
320 i) in (let TMP_69 \def (THeads TMP_67 vs TMP_68) in (let TMP_70 \def (AHead
321 a0 a1) in (let TMP_71 \def (arity g c TMP_69 TMP_70) in (let TMP_78 \def
322 (\forall (d0: C).(\forall (w: T).((sc3 g a0 d0 w) \to (\forall (is:
323 PList).((drop1 is d0 c) \to (let TMP_72 \def (Flat Appl) in (let TMP_73 \def
324 (Flat Appl) in (let TMP_74 \def (TLRef i) in (let TMP_75 \def (THeads TMP_73
325 vs TMP_74) in (let TMP_76 \def (lift1 is TMP_75) in (let TMP_77 \def (THead
326 TMP_72 w TMP_76) in (sc3 g a1 d0 TMP_77)))))))))))) in (let TMP_79 \def
327 (AHead a0 a1) in (let TMP_80 \def (arity_appls_abbr g c d v i H2 vs TMP_79
328 H4) in (let TMP_164 \def (\lambda (d0: C).(\lambda (w: T).(\lambda (H6: (sc3
329 g a0 d0 w)).(\lambda (is: PList).(\lambda (H7: (drop1 is d0 c)).(let H_x \def
330 (drop1_getl_trans is c d0 H7 Abbr d v i H2) in (let H8 \def H_x in (let
331 TMP_82 \def (\lambda (e2: C).(let TMP_81 \def (ptrans is i) in (drop1 TMP_81
332 e2 d))) in (let TMP_88 \def (\lambda (e2: C).(let TMP_83 \def (trans is i) in
333 (let TMP_84 \def (Bind Abbr) in (let TMP_85 \def (ptrans is i) in (let TMP_86
334 \def (lift1 TMP_85 v) in (let TMP_87 \def (CHead e2 TMP_84 TMP_86) in (getl
335 TMP_83 d0 TMP_87))))))) in (let TMP_89 \def (Flat Appl) in (let TMP_90 \def
336 (Flat Appl) in (let TMP_91 \def (TLRef i) in (let TMP_92 \def (THeads TMP_90
337 vs TMP_91) in (let TMP_93 \def (lift1 is TMP_92) in (let TMP_94 \def (THead
338 TMP_89 w TMP_93) in (let TMP_95 \def (sc3 g a1 d0 TMP_94) in (let TMP_163
339 \def (\lambda (x: C).(\lambda (_: (drop1 (ptrans is i) x d)).(\lambda (H10:
340 (getl (trans is i) d0 (CHead x (Bind Abbr) (lift1 (ptrans is i) v)))).(let
341 TMP_96 \def (lifts1 is vs) in (let TMP_97 \def (TCons w TMP_96) in (let H_y
342 \def (H0 TMP_97) in (let TMP_98 \def (Flat Appl) in (let TMP_99 \def (lifts1
343 is vs) in (let TMP_100 \def (TLRef i) in (let TMP_101 \def (lift1 is TMP_100)
344 in (let TMP_102 \def (THeads TMP_98 TMP_99 TMP_101) in (let TMP_105 \def
345 (\lambda (t: T).(let TMP_103 \def (Flat Appl) in (let TMP_104 \def (THead
346 TMP_103 w t) in (sc3 g a1 d0 TMP_104)))) in (let TMP_106 \def (trans is i) in
347 (let TMP_107 \def (TLRef TMP_106) in (let TMP_113 \def (\lambda (t: T).(let
348 TMP_108 \def (Flat Appl) in (let TMP_109 \def (Flat Appl) in (let TMP_110
349 \def (lifts1 is vs) in (let TMP_111 \def (THeads TMP_109 TMP_110 t) in (let
350 TMP_112 \def (THead TMP_108 w TMP_111) in (sc3 g a1 d0 TMP_112))))))) in (let
351 TMP_114 \def (trans is i) in (let TMP_115 \def (ptrans is i) in (let TMP_116
352 \def (lift1 TMP_115 v) in (let TMP_117 \def (S i) in (let TMP_118 \def (lift
353 TMP_117 O v) in (let TMP_119 \def (lift1 is TMP_118) in (let TMP_125 \def
354 (\lambda (t: T).(let TMP_120 \def (Flat Appl) in (let TMP_121 \def (Flat
355 Appl) in (let TMP_122 \def (lifts1 is vs) in (let TMP_123 \def (THeads
356 TMP_121 TMP_122 t) in (let TMP_124 \def (THead TMP_120 w TMP_123) in (sc3 g
357 a1 d0 TMP_124))))))) in (let TMP_126 \def (Flat Appl) in (let TMP_127 \def (S
358 i) in (let TMP_128 \def (lift TMP_127 O v) in (let TMP_129 \def (THeads
359 TMP_126 vs TMP_128) in (let TMP_130 \def (lift1 is TMP_129) in (let TMP_133
360 \def (\lambda (t: T).(let TMP_131 \def (Flat Appl) in (let TMP_132 \def
361 (THead TMP_131 w t) in (sc3 g a1 d0 TMP_132)))) in (let TMP_134 \def (H5 d0 w
362 H6 is H7) in (let TMP_135 \def (Flat Appl) in (let TMP_136 \def (lifts1 is
363 vs) in (let TMP_137 \def (S i) in (let TMP_138 \def (lift TMP_137 O v) in
364 (let TMP_139 \def (lift1 is TMP_138) in (let TMP_140 \def (THeads TMP_135
365 TMP_136 TMP_139) in (let TMP_141 \def (S i) in (let TMP_142 \def (lift
366 TMP_141 O v) in (let TMP_143 \def (lifts1_flat Appl is TMP_142 vs) in (let
367 TMP_144 \def (eq_ind T TMP_130 TMP_133 TMP_134 TMP_140 TMP_143) in (let
368 TMP_145 \def (trans is i) in (let TMP_146 \def (S TMP_145) in (let TMP_147
369 \def (ptrans is i) in (let TMP_148 \def (lift1 TMP_147 v) in (let TMP_149
370 \def (lift TMP_146 O TMP_148) in (let TMP_150 \def (lift1_free is i v) in
371 (let TMP_151 \def (eq_ind T TMP_119 TMP_125 TMP_144 TMP_149 TMP_150) in (let
372 TMP_152 \def (H_y TMP_114 x TMP_116 d0 TMP_151 H10) in (let TMP_153 \def
373 (TLRef i) in (let TMP_154 \def (lift1 is TMP_153) in (let TMP_155 \def
374 (lift1_lref is i) in (let TMP_156 \def (eq_ind_r T TMP_107 TMP_113 TMP_152
375 TMP_154 TMP_155) in (let TMP_157 \def (Flat Appl) in (let TMP_158 \def (TLRef
376 i) in (let TMP_159 \def (THeads TMP_157 vs TMP_158) in (let TMP_160 \def
377 (lift1 is TMP_159) in (let TMP_161 \def (TLRef i) in (let TMP_162 \def
378 (lifts1_flat Appl is TMP_161 vs) in (eq_ind_r T TMP_102 TMP_105 TMP_156
379 TMP_160 TMP_162)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) in
380 (ex2_ind C TMP_82 TMP_88 TMP_95 TMP_163 H8)))))))))))))))))) in (conj TMP_71
381 TMP_78 TMP_80 TMP_164)))))))))))) in (land_ind TMP_45 TMP_53 TMP_66 TMP_165
382 H3)))))))))))))))))))))))))))) in (A_ind TMP_4 TMP_39 TMP_166 a))))).
385 \forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (c: C).(\forall
386 (u: T).((sc3 g (asucc g a) c (THeads (Flat Appl) vs u)) \to (\forall (t:
387 T).((sc3 g a c (THeads (Flat Appl) vs t)) \to (sc3 g a c (THeads (Flat Appl)
388 vs (THead (Flat Cast) u t))))))))))
390 \lambda (g: G).(\lambda (a: A).(let TMP_5 \def (\lambda (a0: A).(\forall
391 (vs: TList).(\forall (c: C).(\forall (u: T).((sc3 g (asucc g a0) c (THeads
392 (Flat Appl) vs u)) \to (\forall (t: T).((sc3 g a0 c (THeads (Flat Appl) vs
393 t)) \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def (Flat Cast) in (let
394 TMP_3 \def (THead TMP_2 u t) in (let TMP_4 \def (THeads TMP_1 vs TMP_3) in
395 (sc3 g a0 c TMP_4)))))))))))) in (let TMP_134 \def (\lambda (n: nat).(\lambda
396 (n0: nat).(\lambda (vs: TList).(\lambda (c: C).(\lambda (u: T).(\lambda (H:
397 (sc3 g (match n with [O \Rightarrow (ASort O (next g n0)) | (S h) \Rightarrow
398 (ASort h n0)]) c (THeads (Flat Appl) vs u))).(\lambda (t: T).(\lambda (H0:
399 (land (arity g c (THeads (Flat Appl) vs t) (ASort n n0)) (sn3 c (THeads (Flat
400 Appl) vs t)))).(let TMP_17 \def (\lambda (n1: nat).((sc3 g (match n1 with [O
401 \Rightarrow (ASort O (next g n0)) | (S h) \Rightarrow (ASort h n0)]) c
402 (THeads (Flat Appl) vs u)) \to ((land (arity g c (THeads (Flat Appl) vs t)
403 (ASort n1 n0)) (sn3 c (THeads (Flat Appl) vs t))) \to (let TMP_6 \def (Flat
404 Appl) in (let TMP_7 \def (Flat Cast) in (let TMP_8 \def (THead TMP_7 u t) in
405 (let TMP_9 \def (THeads TMP_6 vs TMP_8) in (let TMP_10 \def (ASort n1 n0) in
406 (let TMP_11 \def (arity g c TMP_9 TMP_10) in (let TMP_12 \def (Flat Appl) in
407 (let TMP_13 \def (Flat Cast) in (let TMP_14 \def (THead TMP_13 u t) in (let
408 TMP_15 \def (THeads TMP_12 vs TMP_14) in (let TMP_16 \def (sn3 c TMP_15) in
409 (land TMP_11 TMP_16))))))))))))))) in (let TMP_73 \def (\lambda (H1: (sc3 g
410 (ASort O (next g n0)) c (THeads (Flat Appl) vs u))).(\lambda (H2: (land
411 (arity g c (THeads (Flat Appl) vs t) (ASort O n0)) (sn3 c (THeads (Flat Appl)
412 vs t)))).(let H3 \def H1 in (let TMP_18 \def (Flat Appl) in (let TMP_19 \def
413 (THeads TMP_18 vs u) in (let TMP_20 \def (next g n0) in (let TMP_21 \def
414 (ASort O TMP_20) in (let TMP_22 \def (arity g c TMP_19 TMP_21) in (let TMP_23
415 \def (Flat Appl) in (let TMP_24 \def (THeads TMP_23 vs u) in (let TMP_25 \def
416 (sn3 c TMP_24) in (let TMP_26 \def (Flat Appl) in (let TMP_27 \def (Flat
417 Cast) in (let TMP_28 \def (THead TMP_27 u t) in (let TMP_29 \def (THeads
418 TMP_26 vs TMP_28) in (let TMP_30 \def (ASort O n0) in (let TMP_31 \def (arity
419 g c TMP_29 TMP_30) in (let TMP_32 \def (Flat Appl) in (let TMP_33 \def (Flat
420 Cast) in (let TMP_34 \def (THead TMP_33 u t) in (let TMP_35 \def (THeads
421 TMP_32 vs TMP_34) in (let TMP_36 \def (sn3 c TMP_35) in (let TMP_37 \def
422 (land TMP_31 TMP_36) in (let TMP_72 \def (\lambda (H4: (arity g c (THeads
423 (Flat Appl) vs u) (ASort O (next g n0)))).(\lambda (H5: (sn3 c (THeads (Flat
424 Appl) vs u))).(let H6 \def H2 in (let TMP_38 \def (Flat Appl) in (let TMP_39
425 \def (THeads TMP_38 vs t) in (let TMP_40 \def (ASort O n0) in (let TMP_41
426 \def (arity g c TMP_39 TMP_40) in (let TMP_42 \def (Flat Appl) in (let TMP_43
427 \def (THeads TMP_42 vs t) in (let TMP_44 \def (sn3 c TMP_43) in (let TMP_45
428 \def (Flat Appl) in (let TMP_46 \def (Flat Cast) in (let TMP_47 \def (THead
429 TMP_46 u t) in (let TMP_48 \def (THeads TMP_45 vs TMP_47) in (let TMP_49 \def
430 (ASort O n0) in (let TMP_50 \def (arity g c TMP_48 TMP_49) in (let TMP_51
431 \def (Flat Appl) in (let TMP_52 \def (Flat Cast) in (let TMP_53 \def (THead
432 TMP_52 u t) in (let TMP_54 \def (THeads TMP_51 vs TMP_53) in (let TMP_55 \def
433 (sn3 c TMP_54) in (let TMP_56 \def (land TMP_50 TMP_55) in (let TMP_71 \def
434 (\lambda (H7: (arity g c (THeads (Flat Appl) vs t) (ASort O n0))).(\lambda
435 (H8: (sn3 c (THeads (Flat Appl) vs t))).(let TMP_57 \def (Flat Appl) in (let
436 TMP_58 \def (Flat Cast) in (let TMP_59 \def (THead TMP_58 u t) in (let TMP_60
437 \def (THeads TMP_57 vs TMP_59) in (let TMP_61 \def (ASort O n0) in (let
438 TMP_62 \def (arity g c TMP_60 TMP_61) in (let TMP_63 \def (Flat Appl) in (let
439 TMP_64 \def (Flat Cast) in (let TMP_65 \def (THead TMP_64 u t) in (let TMP_66
440 \def (THeads TMP_63 vs TMP_65) in (let TMP_67 \def (sn3 c TMP_66) in (let
441 TMP_68 \def (ASort O n0) in (let TMP_69 \def (arity_appls_cast g c u t vs
442 TMP_68 H4 H7) in (let TMP_70 \def (sn3_appls_cast c vs u H5 t H8) in (conj
443 TMP_62 TMP_67 TMP_69 TMP_70))))))))))))))))) in (land_ind TMP_41 TMP_44
444 TMP_56 TMP_71 H6)))))))))))))))))))))))) in (land_ind TMP_22 TMP_25 TMP_37
445 TMP_72 H3))))))))))))))))))))))))) in (let TMP_133 \def (\lambda (n1:
446 nat).(\lambda (_: (((sc3 g (match n1 with [O \Rightarrow (ASort O (next g
447 n0)) | (S h) \Rightarrow (ASort h n0)]) c (THeads (Flat Appl) vs u)) \to
448 ((land (arity g c (THeads (Flat Appl) vs t) (ASort n1 n0)) (sn3 c (THeads
449 (Flat Appl) vs t))) \to (land (arity g c (THeads (Flat Appl) vs (THead (Flat
450 Cast) u t)) (ASort n1 n0)) (sn3 c (THeads (Flat Appl) vs (THead (Flat Cast) u
451 t)))))))).(\lambda (H1: (sc3 g (ASort n1 n0) c (THeads (Flat Appl) vs
452 u))).(\lambda (H2: (land (arity g c (THeads (Flat Appl) vs t) (ASort (S n1)
453 n0)) (sn3 c (THeads (Flat Appl) vs t)))).(let H3 \def H1 in (let TMP_74 \def
454 (Flat Appl) in (let TMP_75 \def (THeads TMP_74 vs u) in (let TMP_76 \def
455 (ASort n1 n0) in (let TMP_77 \def (arity g c TMP_75 TMP_76) in (let TMP_78
456 \def (Flat Appl) in (let TMP_79 \def (THeads TMP_78 vs u) in (let TMP_80 \def
457 (sn3 c TMP_79) in (let TMP_81 \def (Flat Appl) in (let TMP_82 \def (Flat
458 Cast) in (let TMP_83 \def (THead TMP_82 u t) in (let TMP_84 \def (THeads
459 TMP_81 vs TMP_83) in (let TMP_85 \def (S n1) in (let TMP_86 \def (ASort
460 TMP_85 n0) in (let TMP_87 \def (arity g c TMP_84 TMP_86) in (let TMP_88 \def
461 (Flat Appl) in (let TMP_89 \def (Flat Cast) in (let TMP_90 \def (THead TMP_89
462 u t) in (let TMP_91 \def (THeads TMP_88 vs TMP_90) in (let TMP_92 \def (sn3 c
463 TMP_91) in (let TMP_93 \def (land TMP_87 TMP_92) in (let TMP_132 \def
464 (\lambda (H4: (arity g c (THeads (Flat Appl) vs u) (ASort n1 n0))).(\lambda
465 (H5: (sn3 c (THeads (Flat Appl) vs u))).(let H6 \def H2 in (let TMP_94 \def
466 (Flat Appl) in (let TMP_95 \def (THeads TMP_94 vs t) in (let TMP_96 \def (S
467 n1) in (let TMP_97 \def (ASort TMP_96 n0) in (let TMP_98 \def (arity g c
468 TMP_95 TMP_97) in (let TMP_99 \def (Flat Appl) in (let TMP_100 \def (THeads
469 TMP_99 vs t) in (let TMP_101 \def (sn3 c TMP_100) in (let TMP_102 \def (Flat
470 Appl) in (let TMP_103 \def (Flat Cast) in (let TMP_104 \def (THead TMP_103 u
471 t) in (let TMP_105 \def (THeads TMP_102 vs TMP_104) in (let TMP_106 \def (S
472 n1) in (let TMP_107 \def (ASort TMP_106 n0) in (let TMP_108 \def (arity g c
473 TMP_105 TMP_107) in (let TMP_109 \def (Flat Appl) in (let TMP_110 \def (Flat
474 Cast) in (let TMP_111 \def (THead TMP_110 u t) in (let TMP_112 \def (THeads
475 TMP_109 vs TMP_111) in (let TMP_113 \def (sn3 c TMP_112) in (let TMP_114 \def
476 (land TMP_108 TMP_113) in (let TMP_131 \def (\lambda (H7: (arity g c (THeads
477 (Flat Appl) vs t) (ASort (S n1) n0))).(\lambda (H8: (sn3 c (THeads (Flat
478 Appl) vs t))).(let TMP_115 \def (Flat Appl) in (let TMP_116 \def (Flat Cast)
479 in (let TMP_117 \def (THead TMP_116 u t) in (let TMP_118 \def (THeads TMP_115
480 vs TMP_117) in (let TMP_119 \def (S n1) in (let TMP_120 \def (ASort TMP_119
481 n0) in (let TMP_121 \def (arity g c TMP_118 TMP_120) in (let TMP_122 \def
482 (Flat Appl) in (let TMP_123 \def (Flat Cast) in (let TMP_124 \def (THead
483 TMP_123 u t) in (let TMP_125 \def (THeads TMP_122 vs TMP_124) in (let TMP_126
484 \def (sn3 c TMP_125) in (let TMP_127 \def (S n1) in (let TMP_128 \def (ASort
485 TMP_127 n0) in (let TMP_129 \def (arity_appls_cast g c u t vs TMP_128 H4 H7)
486 in (let TMP_130 \def (sn3_appls_cast c vs u H5 t H8) in (conj TMP_121 TMP_126
487 TMP_129 TMP_130))))))))))))))))))) in (land_ind TMP_98 TMP_101 TMP_114
488 TMP_131 H6)))))))))))))))))))))))))) in (land_ind TMP_77 TMP_80 TMP_93
489 TMP_132 H3))))))))))))))))))))))))))) in (nat_ind TMP_17 TMP_73 TMP_133 n H
490 H0)))))))))))) in (let TMP_270 \def (\lambda (a0: A).(\lambda (_: ((\forall
491 (vs: TList).(\forall (c: C).(\forall (u: T).((sc3 g (asucc g a0) c (THeads
492 (Flat Appl) vs u)) \to (\forall (t: T).((sc3 g a0 c (THeads (Flat Appl) vs
493 t)) \to (sc3 g a0 c (THeads (Flat Appl) vs (THead (Flat Cast) u
494 t))))))))))).(\lambda (a1: A).(\lambda (H0: ((\forall (vs: TList).(\forall
495 (c: C).(\forall (u: T).((sc3 g (asucc g a1) c (THeads (Flat Appl) vs u)) \to
496 (\forall (t: T).((sc3 g a1 c (THeads (Flat Appl) vs t)) \to (sc3 g a1 c
497 (THeads (Flat Appl) vs (THead (Flat Cast) u t))))))))))).(\lambda (vs:
498 TList).(\lambda (c: C).(\lambda (u: T).(\lambda (H1: (land (arity g c (THeads
499 (Flat Appl) vs u) (AHead a0 (asucc g a1))) (\forall (d: C).(\forall (w:
500 T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g (asucc
501 g a1) d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs
502 u))))))))))).(\lambda (t: T).(\lambda (H2: (land (arity g c (THeads (Flat
503 Appl) vs t) (AHead a0 a1)) (\forall (d: C).(\forall (w: T).((sc3 g a0 d w)
504 \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d (THead (Flat Appl) w
505 (lift1 is (THeads (Flat Appl) vs t))))))))))).(let H3 \def H1 in (let TMP_135
506 \def (Flat Appl) in (let TMP_136 \def (THeads TMP_135 vs u) in (let TMP_137
507 \def (asucc g a1) in (let TMP_138 \def (AHead a0 TMP_137) in (let TMP_139
508 \def (arity g c TMP_136 TMP_138) in (let TMP_146 \def (\forall (d:
509 C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c)
510 \to (let TMP_140 \def (asucc g a1) in (let TMP_141 \def (Flat Appl) in (let
511 TMP_142 \def (Flat Appl) in (let TMP_143 \def (THeads TMP_142 vs u) in (let
512 TMP_144 \def (lift1 is TMP_143) in (let TMP_145 \def (THead TMP_141 w
513 TMP_144) in (sc3 g TMP_140 d TMP_145)))))))))))) in (let TMP_147 \def (Flat
514 Appl) in (let TMP_148 \def (Flat Cast) in (let TMP_149 \def (THead TMP_148 u
515 t) in (let TMP_150 \def (THeads TMP_147 vs TMP_149) in (let TMP_151 \def
516 (AHead a0 a1) in (let TMP_152 \def (arity g c TMP_150 TMP_151) in (let
517 TMP_160 \def (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall
518 (is: PList).((drop1 is d c) \to (let TMP_153 \def (Flat Appl) in (let TMP_154
519 \def (Flat Appl) in (let TMP_155 \def (Flat Cast) in (let TMP_156 \def (THead
520 TMP_155 u t) in (let TMP_157 \def (THeads TMP_154 vs TMP_156) in (let TMP_158
521 \def (lift1 is TMP_157) in (let TMP_159 \def (THead TMP_153 w TMP_158) in
522 (sc3 g a1 d TMP_159))))))))))))) in (let TMP_161 \def (land TMP_152 TMP_160)
523 in (let TMP_269 \def (\lambda (H4: (arity g c (THeads (Flat Appl) vs u)
524 (AHead a0 (asucc g a1)))).(\lambda (H5: ((\forall (d: C).(\forall (w:
525 T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g (asucc
526 g a1) d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs
527 u))))))))))).(let H6 \def H2 in (let TMP_162 \def (Flat Appl) in (let TMP_163
528 \def (THeads TMP_162 vs t) in (let TMP_164 \def (AHead a0 a1) in (let TMP_165
529 \def (arity g c TMP_163 TMP_164) in (let TMP_171 \def (\forall (d:
530 C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c)
531 \to (let TMP_166 \def (Flat Appl) in (let TMP_167 \def (Flat Appl) in (let
532 TMP_168 \def (THeads TMP_167 vs t) in (let TMP_169 \def (lift1 is TMP_168) in
533 (let TMP_170 \def (THead TMP_166 w TMP_169) in (sc3 g a1 d TMP_170)))))))))))
534 in (let TMP_172 \def (Flat Appl) in (let TMP_173 \def (Flat Cast) in (let
535 TMP_174 \def (THead TMP_173 u t) in (let TMP_175 \def (THeads TMP_172 vs
536 TMP_174) in (let TMP_176 \def (AHead a0 a1) in (let TMP_177 \def (arity g c
537 TMP_175 TMP_176) in (let TMP_185 \def (\forall (d: C).(\forall (w: T).((sc3 g
538 a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (let TMP_178 \def (Flat
539 Appl) in (let TMP_179 \def (Flat Appl) in (let TMP_180 \def (Flat Cast) in
540 (let TMP_181 \def (THead TMP_180 u t) in (let TMP_182 \def (THeads TMP_179 vs
541 TMP_181) in (let TMP_183 \def (lift1 is TMP_182) in (let TMP_184 \def (THead
542 TMP_178 w TMP_183) in (sc3 g a1 d TMP_184))))))))))))) in (let TMP_186 \def
543 (land TMP_177 TMP_185) in (let TMP_268 \def (\lambda (H7: (arity g c (THeads
544 (Flat Appl) vs t) (AHead a0 a1))).(\lambda (H8: ((\forall (d: C).(\forall (w:
545 T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1 d
546 (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs t))))))))))).(let
547 TMP_187 \def (Flat Appl) in (let TMP_188 \def (Flat Cast) in (let TMP_189
548 \def (THead TMP_188 u t) in (let TMP_190 \def (THeads TMP_187 vs TMP_189) in
549 (let TMP_191 \def (AHead a0 a1) in (let TMP_192 \def (arity g c TMP_190
550 TMP_191) in (let TMP_200 \def (\forall (d: C).(\forall (w: T).((sc3 g a0 d w)
551 \to (\forall (is: PList).((drop1 is d c) \to (let TMP_193 \def (Flat Appl) in
552 (let TMP_194 \def (Flat Appl) in (let TMP_195 \def (Flat Cast) in (let
553 TMP_196 \def (THead TMP_195 u t) in (let TMP_197 \def (THeads TMP_194 vs
554 TMP_196) in (let TMP_198 \def (lift1 is TMP_197) in (let TMP_199 \def (THead
555 TMP_193 w TMP_198) in (sc3 g a1 d TMP_199))))))))))))) in (let TMP_201 \def
556 (AHead a0 a1) in (let TMP_202 \def (arity_appls_cast g c u t vs TMP_201 H4
557 H7) in (let TMP_267 \def (\lambda (d: C).(\lambda (w: T).(\lambda (H9: (sc3 g
558 a0 d w)).(\lambda (is: PList).(\lambda (H10: (drop1 is d c)).(let TMP_203
559 \def (lifts1 is vs) in (let TMP_204 \def (TCons w TMP_203) in (let H_y \def
560 (H0 TMP_204) in (let TMP_205 \def (Flat Appl) in (let TMP_206 \def (lifts1 is
561 vs) in (let TMP_207 \def (Flat Cast) in (let TMP_208 \def (THead TMP_207 u t)
562 in (let TMP_209 \def (lift1 is TMP_208) in (let TMP_210 \def (THeads TMP_205
563 TMP_206 TMP_209) in (let TMP_213 \def (\lambda (t0: T).(let TMP_211 \def
564 (Flat Appl) in (let TMP_212 \def (THead TMP_211 w t0) in (sc3 g a1 d
565 TMP_212)))) in (let TMP_214 \def (Flat Cast) in (let TMP_215 \def (lift1 is
566 u) in (let TMP_216 \def (lift1 is t) in (let TMP_217 \def (THead TMP_214
567 TMP_215 TMP_216) in (let TMP_223 \def (\lambda (t0: T).(let TMP_218 \def
568 (Flat Appl) in (let TMP_219 \def (Flat Appl) in (let TMP_220 \def (lifts1 is
569 vs) in (let TMP_221 \def (THeads TMP_219 TMP_220 t0) in (let TMP_222 \def
570 (THead TMP_218 w TMP_221) in (sc3 g a1 d TMP_222))))))) in (let TMP_224 \def
571 (lift1 is u) in (let TMP_225 \def (Flat Appl) in (let TMP_226 \def (THeads
572 TMP_225 vs u) in (let TMP_227 \def (lift1 is TMP_226) in (let TMP_231 \def
573 (\lambda (t0: T).(let TMP_228 \def (asucc g a1) in (let TMP_229 \def (Flat
574 Appl) in (let TMP_230 \def (THead TMP_229 w t0) in (sc3 g TMP_228 d
575 TMP_230))))) in (let TMP_232 \def (H5 d w H9 is H10) in (let TMP_233 \def
576 (Flat Appl) in (let TMP_234 \def (lifts1 is vs) in (let TMP_235 \def (lift1
577 is u) in (let TMP_236 \def (THeads TMP_233 TMP_234 TMP_235) in (let TMP_237
578 \def (lifts1_flat Appl is u vs) in (let TMP_238 \def (eq_ind T TMP_227
579 TMP_231 TMP_232 TMP_236 TMP_237) in (let TMP_239 \def (lift1 is t) in (let
580 TMP_240 \def (Flat Appl) in (let TMP_241 \def (THeads TMP_240 vs t) in (let
581 TMP_242 \def (lift1 is TMP_241) in (let TMP_245 \def (\lambda (t0: T).(let
582 TMP_243 \def (Flat Appl) in (let TMP_244 \def (THead TMP_243 w t0) in (sc3 g
583 a1 d TMP_244)))) in (let TMP_246 \def (H8 d w H9 is H10) in (let TMP_247 \def
584 (Flat Appl) in (let TMP_248 \def (lifts1 is vs) in (let TMP_249 \def (lift1
585 is t) in (let TMP_250 \def (THeads TMP_247 TMP_248 TMP_249) in (let TMP_251
586 \def (lifts1_flat Appl is t vs) in (let TMP_252 \def (eq_ind T TMP_242
587 TMP_245 TMP_246 TMP_250 TMP_251) in (let TMP_253 \def (H_y d TMP_224 TMP_238
588 TMP_239 TMP_252) in (let TMP_254 \def (Flat Cast) in (let TMP_255 \def (THead
589 TMP_254 u t) in (let TMP_256 \def (lift1 is TMP_255) in (let TMP_257 \def
590 (lift1_flat Cast is u t) in (let TMP_258 \def (eq_ind_r T TMP_217 TMP_223
591 TMP_253 TMP_256 TMP_257) in (let TMP_259 \def (Flat Appl) in (let TMP_260
592 \def (Flat Cast) in (let TMP_261 \def (THead TMP_260 u t) in (let TMP_262
593 \def (THeads TMP_259 vs TMP_261) in (let TMP_263 \def (lift1 is TMP_262) in
594 (let TMP_264 \def (Flat Cast) in (let TMP_265 \def (THead TMP_264 u t) in
595 (let TMP_266 \def (lifts1_flat Appl is TMP_265 vs) in (eq_ind_r T TMP_210
596 TMP_213 TMP_258 TMP_263
597 TMP_266))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) in (conj
598 TMP_192 TMP_200 TMP_202 TMP_267))))))))))))) in (land_ind TMP_165 TMP_171
599 TMP_186 TMP_268 H6)))))))))))))))))) in (land_ind TMP_139 TMP_146 TMP_161
600 TMP_269 H3))))))))))))))))))))))))))) in (A_ind TMP_5 TMP_134 TMP_270 a))))).
602 theorem sc3_props__sc3_sn3_abst:
603 \forall (g: G).(\forall (a: A).(land (\forall (c: C).(\forall (t: T).((sc3 g
604 a c t) \to (sn3 c t)))) (\forall (vs: TList).(\forall (i: nat).(let t \def
605 (THeads (Flat Appl) vs (TLRef i)) in (\forall (c: C).((arity g c t a) \to
606 ((nf2 c (TLRef i)) \to ((sns3 c vs) \to (sc3 g a c t))))))))))
608 \lambda (g: G).(\lambda (a: A).(let TMP_5 \def (\lambda (a0: A).(let TMP_1
609 \def (\forall (c: C).(\forall (t: T).((sc3 g a0 c t) \to (sn3 c t)))) in (let
610 TMP_4 \def (\forall (vs: TList).(\forall (i: nat).(let TMP_2 \def (Flat Appl)
611 in (let TMP_3 \def (TLRef i) in (let t \def (THeads TMP_2 vs TMP_3) in
612 (\forall (c: C).((arity g c t a0) \to ((nf2 c (TLRef i)) \to ((sns3 c vs) \to
613 (sc3 g a0 c t)))))))))) in (land TMP_1 TMP_4)))) in (let TMP_34 \def (\lambda
614 (n: nat).(\lambda (n0: nat).(let TMP_6 \def (\forall (c: C).(\forall (t:
615 T).((land (arity g c t (ASort n n0)) (sn3 c t)) \to (sn3 c t)))) in (let
616 TMP_16 \def (\forall (vs: TList).(\forall (i: nat).(\forall (c: C).((arity g
617 c (THeads (Flat Appl) vs (TLRef i)) (ASort n n0)) \to ((nf2 c (TLRef i)) \to
618 ((sns3 c vs) \to (let TMP_7 \def (Flat Appl) in (let TMP_8 \def (TLRef i) in
619 (let TMP_9 \def (THeads TMP_7 vs TMP_8) in (let TMP_10 \def (ASort n n0) in
620 (let TMP_11 \def (arity g c TMP_9 TMP_10) in (let TMP_12 \def (Flat Appl) in
621 (let TMP_13 \def (TLRef i) in (let TMP_14 \def (THeads TMP_12 vs TMP_13) in
622 (let TMP_15 \def (sn3 c TMP_14) in (land TMP_11 TMP_15)))))))))))))))) in
623 (let TMP_22 \def (\lambda (c: C).(\lambda (t: T).(\lambda (H: (land (arity g
624 c t (ASort n n0)) (sn3 c t))).(let H0 \def H in (let TMP_17 \def (ASort n n0)
625 in (let TMP_18 \def (arity g c t TMP_17) in (let TMP_19 \def (sn3 c t) in
626 (let TMP_20 \def (sn3 c t) in (let TMP_21 \def (\lambda (_: (arity g c t
627 (ASort n n0))).(\lambda (H2: (sn3 c t)).H2)) in (land_ind TMP_18 TMP_19
628 TMP_20 TMP_21 H0)))))))))) in (let TMP_33 \def (\lambda (vs: TList).(\lambda
629 (i: nat).(\lambda (c: C).(\lambda (H: (arity g c (THeads (Flat Appl) vs
630 (TLRef i)) (ASort n n0))).(\lambda (H0: (nf2 c (TLRef i))).(\lambda (H1:
631 (sns3 c vs)).(let TMP_23 \def (Flat Appl) in (let TMP_24 \def (TLRef i) in
632 (let TMP_25 \def (THeads TMP_23 vs TMP_24) in (let TMP_26 \def (ASort n n0)
633 in (let TMP_27 \def (arity g c TMP_25 TMP_26) in (let TMP_28 \def (Flat Appl)
634 in (let TMP_29 \def (TLRef i) in (let TMP_30 \def (THeads TMP_28 vs TMP_29)
635 in (let TMP_31 \def (sn3 c TMP_30) in (let TMP_32 \def (sn3_appls_lref c i H0
636 vs H1) in (conj TMP_27 TMP_31 H TMP_32))))))))))))))))) in (conj TMP_6 TMP_16
637 TMP_22 TMP_33))))))) in (let TMP_254 \def (\lambda (a0: A).(\lambda (H: (land
638 (\forall (c: C).(\forall (t: T).((sc3 g a0 c t) \to (sn3 c t)))) (\forall
639 (vs: TList).(\forall (i: nat).(\forall (c: C).((arity g c (THeads (Flat Appl)
640 vs (TLRef i)) a0) \to ((nf2 c (TLRef i)) \to ((sns3 c vs) \to (sc3 g a0 c
641 (THeads (Flat Appl) vs (TLRef i))))))))))).(\lambda (a1: A).(\lambda (H0:
642 (land (\forall (c: C).(\forall (t: T).((sc3 g a1 c t) \to (sn3 c t))))
643 (\forall (vs: TList).(\forall (i: nat).(\forall (c: C).((arity g c (THeads
644 (Flat Appl) vs (TLRef i)) a1) \to ((nf2 c (TLRef i)) \to ((sns3 c vs) \to
645 (sc3 g a1 c (THeads (Flat Appl) vs (TLRef i))))))))))).(let TMP_35 \def
646 (\forall (c: C).(\forall (t: T).((land (arity g c t (AHead a0 a1)) (\forall
647 (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d
648 c) \to (sc3 g a1 d (THead (Flat Appl) w (lift1 is t))))))))) \to (sn3 c t))))
649 in (let TMP_48 \def (\forall (vs: TList).(\forall (i: nat).(\forall (c:
650 C).((arity g c (THeads (Flat Appl) vs (TLRef i)) (AHead a0 a1)) \to ((nf2 c
651 (TLRef i)) \to ((sns3 c vs) \to (let TMP_36 \def (Flat Appl) in (let TMP_37
652 \def (TLRef i) in (let TMP_38 \def (THeads TMP_36 vs TMP_37) in (let TMP_39
653 \def (AHead a0 a1) in (let TMP_40 \def (arity g c TMP_38 TMP_39) in (let
654 TMP_47 \def (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is:
655 PList).((drop1 is d c) \to (let TMP_41 \def (Flat Appl) in (let TMP_42 \def
656 (Flat Appl) in (let TMP_43 \def (TLRef i) in (let TMP_44 \def (THeads TMP_42
657 vs TMP_43) in (let TMP_45 \def (lift1 is TMP_44) in (let TMP_46 \def (THead
658 TMP_41 w TMP_45) in (sc3 g a1 d TMP_46)))))))))))) in (land TMP_40
659 TMP_47))))))))))))) in (let TMP_130 \def (\lambda (c: C).(\lambda (t:
660 T).(\lambda (H1: (land (arity g c t (AHead a0 a1)) (\forall (d: C).(\forall
661 (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1
662 d (THead (Flat Appl) w (lift1 is t)))))))))).(let H2 \def H in (let TMP_49
663 \def (\forall (c0: C).(\forall (t0: T).((sc3 g a0 c0 t0) \to (sn3 c0 t0))))
664 in (let TMP_53 \def (\forall (vs: TList).(\forall (i: nat).(\forall (c0:
665 C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a0) \to ((nf2 c0 (TLRef i))
666 \to ((sns3 c0 vs) \to (let TMP_50 \def (Flat Appl) in (let TMP_51 \def (TLRef
667 i) in (let TMP_52 \def (THeads TMP_50 vs TMP_51) in (sc3 g a0 c0
668 TMP_52)))))))))) in (let TMP_54 \def (sn3 c t) in (let TMP_129 \def (\lambda
669 (_: ((\forall (c0: C).(\forall (t0: T).((sc3 g a0 c0 t0) \to (sn3 c0
670 t0)))))).(\lambda (H4: ((\forall (vs: TList).(\forall (i: nat).(\forall (c0:
671 C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a0) \to ((nf2 c0 (TLRef i))
672 \to ((sns3 c0 vs) \to (sc3 g a0 c0 (THeads (Flat Appl) vs (TLRef
673 i))))))))))).(let H5 \def H0 in (let TMP_55 \def (\forall (c0: C).(\forall
674 (t0: T).((sc3 g a1 c0 t0) \to (sn3 c0 t0)))) in (let TMP_59 \def (\forall
675 (vs: TList).(\forall (i: nat).(\forall (c0: C).((arity g c0 (THeads (Flat
676 Appl) vs (TLRef i)) a1) \to ((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to (let
677 TMP_56 \def (Flat Appl) in (let TMP_57 \def (TLRef i) in (let TMP_58 \def
678 (THeads TMP_56 vs TMP_57) in (sc3 g a1 c0 TMP_58)))))))))) in (let TMP_60
679 \def (sn3 c t) in (let TMP_128 \def (\lambda (H6: ((\forall (c0: C).(\forall
680 (t0: T).((sc3 g a1 c0 t0) \to (sn3 c0 t0)))))).(\lambda (_: ((\forall (vs:
681 TList).(\forall (i: nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl) vs
682 (TLRef i)) a1) \to ((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to (sc3 g a1 c0
683 (THeads (Flat Appl) vs (TLRef i))))))))))).(let H8 \def H1 in (let TMP_61
684 \def (AHead a0 a1) in (let TMP_62 \def (arity g c t TMP_61) in (let TMP_66
685 \def (\forall (d: C).(\forall (w: T).((sc3 g a0 d w) \to (\forall (is:
686 PList).((drop1 is d c) \to (let TMP_63 \def (Flat Appl) in (let TMP_64 \def
687 (lift1 is t) in (let TMP_65 \def (THead TMP_63 w TMP_64) in (sc3 g a1 d
688 TMP_65))))))))) in (let TMP_67 \def (sn3 c t) in (let TMP_127 \def (\lambda
689 (H9: (arity g c t (AHead a0 a1))).(\lambda (H10: ((\forall (d: C).(\forall
690 (w: T).((sc3 g a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (sc3 g a1
691 d (THead (Flat Appl) w (lift1 is t)))))))))).(let TMP_68 \def (AHead a0 a1)
692 in (let H_y \def (arity_aprem g c t TMP_68 H9 O a0) in (let TMP_69 \def
693 (aprem_zero a0 a1) in (let H11 \def (H_y TMP_69) in (let TMP_70 \def (\lambda
694 (d: C).(\lambda (_: T).(\lambda (j: nat).(drop j O d c)))) in (let TMP_72
695 \def (\lambda (d: C).(\lambda (u: T).(\lambda (_: nat).(let TMP_71 \def
696 (asucc g a0) in (arity g d u TMP_71))))) in (let TMP_73 \def (sn3 c t) in
697 (let TMP_126 \def (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2:
698 nat).(\lambda (H12: (drop x2 O x0 c)).(\lambda (H13: (arity g x0 x1 (asucc g
699 a0))).(let TMP_74 \def (Bind Abst) in (let TMP_75 \def (CHead x0 TMP_74 x1)
700 in (let TMP_76 \def (TLRef O) in (let TMP_77 \def (Bind Abst) in (let TMP_78
701 \def (CHead x0 TMP_77 x1) in (let TMP_79 \def (Bind Abst) in (let TMP_80 \def
702 (CHead x0 TMP_79 x1) in (let TMP_81 \def (getl_refl Abst x0 x1) in (let
703 TMP_82 \def (arity_abst g TMP_80 x0 x1 O TMP_81 a0 H13) in (let TMP_83 \def
704 (Bind Abst) in (let TMP_84 \def (CHead x0 TMP_83 x1) in (let TMP_85 \def
705 (getl_refl Abst x0 x1) in (let TMP_86 \def (nf2_lref_abst TMP_84 x0 x1 O
706 TMP_85) in (let TMP_87 \def (H4 TNil O TMP_78 TMP_82 TMP_86 I) in (let TMP_88
707 \def (S x2) in (let TMP_89 \def (PCons TMP_88 O PNil) in (let H_y0 \def (H10
708 TMP_75 TMP_76 TMP_87 TMP_89) in (let TMP_90 \def (Bind Abst) in (let TMP_91
709 \def (CHead x0 TMP_90 x1) in (let TMP_92 \def (Flat Appl) in (let TMP_93 \def
710 (TLRef O) in (let TMP_94 \def (S x2) in (let TMP_95 \def (lift TMP_94 O t) in
711 (let TMP_96 \def (THead TMP_92 TMP_93 TMP_95) in (let TMP_97 \def (Bind Abst)
712 in (let TMP_98 \def (CHead x0 TMP_97 x1) in (let TMP_99 \def (S x2) in (let
713 TMP_100 \def (Bind Abst) in (let TMP_101 \def (drop_drop TMP_100 x2 x0 c H12
714 x1) in (let TMP_102 \def (drop1_nil c) in (let TMP_103 \def (drop1_cons
715 TMP_98 c TMP_99 O TMP_101 c PNil TMP_102) in (let TMP_104 \def (H_y0 TMP_103)
716 in (let H_y1 \def (H6 TMP_91 TMP_96 TMP_104) in (let TMP_105 \def (Bind Abst)
717 in (let TMP_106 \def (CHead x0 TMP_105 x1) in (let TMP_107 \def (TLRef O) in
718 (let TMP_108 \def (S x2) in (let TMP_109 \def (lift TMP_108 O t) in (let H_x
719 \def (sn3_gen_flat Appl TMP_106 TMP_107 TMP_109 H_y1) in (let H14 \def H_x in
720 (let TMP_110 \def (Bind Abst) in (let TMP_111 \def (CHead x0 TMP_110 x1) in
721 (let TMP_112 \def (TLRef O) in (let TMP_113 \def (sn3 TMP_111 TMP_112) in
722 (let TMP_114 \def (Bind Abst) in (let TMP_115 \def (CHead x0 TMP_114 x1) in
723 (let TMP_116 \def (S x2) in (let TMP_117 \def (lift TMP_116 O t) in (let
724 TMP_118 \def (sn3 TMP_115 TMP_117) in (let TMP_119 \def (sn3 c t) in (let
725 TMP_125 \def (\lambda (_: (sn3 (CHead x0 (Bind Abst) x1) (TLRef O))).(\lambda
726 (H16: (sn3 (CHead x0 (Bind Abst) x1) (lift (S x2) O t))).(let TMP_120 \def
727 (Bind Abst) in (let TMP_121 \def (CHead x0 TMP_120 x1) in (let TMP_122 \def
728 (S x2) in (let TMP_123 \def (Bind Abst) in (let TMP_124 \def (drop_drop
729 TMP_123 x2 x0 c H12 x1) in (sn3_gen_lift TMP_121 t TMP_122 O H16 c
730 TMP_124)))))))) in (land_ind TMP_113 TMP_118 TMP_119 TMP_125
731 H14))))))))))))))))))))))))))))))))))))))))))))))))))))))))) in (ex2_3_ind C
732 T nat TMP_70 TMP_72 TMP_73 TMP_126 H11))))))))))) in (land_ind TMP_62 TMP_66
733 TMP_67 TMP_127 H8))))))))) in (land_ind TMP_55 TMP_59 TMP_60 TMP_128
734 H5)))))))) in (land_ind TMP_49 TMP_53 TMP_54 TMP_129 H2))))))))) in (let
735 TMP_253 \def (\lambda (vs: TList).(\lambda (i: nat).(\lambda (c: C).(\lambda
736 (H1: (arity g c (THeads (Flat Appl) vs (TLRef i)) (AHead a0 a1))).(\lambda
737 (H2: (nf2 c (TLRef i))).(\lambda (H3: (sns3 c vs)).(let TMP_131 \def (Flat
738 Appl) in (let TMP_132 \def (TLRef i) in (let TMP_133 \def (THeads TMP_131 vs
739 TMP_132) in (let TMP_134 \def (AHead a0 a1) in (let TMP_135 \def (arity g c
740 TMP_133 TMP_134) in (let TMP_142 \def (\forall (d: C).(\forall (w: T).((sc3 g
741 a0 d w) \to (\forall (is: PList).((drop1 is d c) \to (let TMP_136 \def (Flat
742 Appl) in (let TMP_137 \def (Flat Appl) in (let TMP_138 \def (TLRef i) in (let
743 TMP_139 \def (THeads TMP_137 vs TMP_138) in (let TMP_140 \def (lift1 is
744 TMP_139) in (let TMP_141 \def (THead TMP_136 w TMP_140) in (sc3 g a1 d
745 TMP_141)))))))))))) in (let TMP_252 \def (\lambda (d: C).(\lambda (w:
746 T).(\lambda (H4: (sc3 g a0 d w)).(\lambda (is: PList).(\lambda (H5: (drop1 is
747 d c)).(let H6 \def H in (let TMP_143 \def (\forall (c0: C).(\forall (t:
748 T).((sc3 g a0 c0 t) \to (sn3 c0 t)))) in (let TMP_147 \def (\forall (vs0:
749 TList).(\forall (i0: nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl)
750 vs0 (TLRef i0)) a0) \to ((nf2 c0 (TLRef i0)) \to ((sns3 c0 vs0) \to (let
751 TMP_144 \def (Flat Appl) in (let TMP_145 \def (TLRef i0) in (let TMP_146 \def
752 (THeads TMP_144 vs0 TMP_145) in (sc3 g a0 c0 TMP_146)))))))))) in (let
753 TMP_148 \def (Flat Appl) in (let TMP_149 \def (Flat Appl) in (let TMP_150
754 \def (TLRef i) in (let TMP_151 \def (THeads TMP_149 vs TMP_150) in (let
755 TMP_152 \def (lift1 is TMP_151) in (let TMP_153 \def (THead TMP_148 w
756 TMP_152) in (let TMP_154 \def (sc3 g a1 d TMP_153) in (let TMP_251 \def
757 (\lambda (H7: ((\forall (c0: C).(\forall (t: T).((sc3 g a0 c0 t) \to (sn3 c0
758 t)))))).(\lambda (_: ((\forall (vs0: TList).(\forall (i0: nat).(\forall (c0:
759 C).((arity g c0 (THeads (Flat Appl) vs0 (TLRef i0)) a0) \to ((nf2 c0 (TLRef
760 i0)) \to ((sns3 c0 vs0) \to (sc3 g a0 c0 (THeads (Flat Appl) vs0 (TLRef
761 i0))))))))))).(let H9 \def H0 in (let TMP_155 \def (\forall (c0: C).(\forall
762 (t: T).((sc3 g a1 c0 t) \to (sn3 c0 t)))) in (let TMP_159 \def (\forall (vs0:
763 TList).(\forall (i0: nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl)
764 vs0 (TLRef i0)) a1) \to ((nf2 c0 (TLRef i0)) \to ((sns3 c0 vs0) \to (let
765 TMP_156 \def (Flat Appl) in (let TMP_157 \def (TLRef i0) in (let TMP_158 \def
766 (THeads TMP_156 vs0 TMP_157) in (sc3 g a1 c0 TMP_158)))))))))) in (let
767 TMP_160 \def (Flat Appl) in (let TMP_161 \def (Flat Appl) in (let TMP_162
768 \def (TLRef i) in (let TMP_163 \def (THeads TMP_161 vs TMP_162) in (let
769 TMP_164 \def (lift1 is TMP_163) in (let TMP_165 \def (THead TMP_160 w
770 TMP_164) in (let TMP_166 \def (sc3 g a1 d TMP_165) in (let TMP_250 \def
771 (\lambda (_: ((\forall (c0: C).(\forall (t: T).((sc3 g a1 c0 t) \to (sn3 c0
772 t)))))).(\lambda (H11: ((\forall (vs0: TList).(\forall (i0: nat).(\forall
773 (c0: C).((arity g c0 (THeads (Flat Appl) vs0 (TLRef i0)) a1) \to ((nf2 c0
774 (TLRef i0)) \to ((sns3 c0 vs0) \to (sc3 g a1 c0 (THeads (Flat Appl) vs0
775 (TLRef i0))))))))))).(let TMP_167 \def (lifts1 is vs) in (let TMP_168 \def
776 (TCons w TMP_167) in (let H_y \def (H11 TMP_168) in (let TMP_169 \def (Flat
777 Appl) in (let TMP_170 \def (lifts1 is vs) in (let TMP_171 \def (TLRef i) in
778 (let TMP_172 \def (lift1 is TMP_171) in (let TMP_173 \def (THeads TMP_169
779 TMP_170 TMP_172) in (let TMP_176 \def (\lambda (t: T).(let TMP_174 \def (Flat
780 Appl) in (let TMP_175 \def (THead TMP_174 w t) in (sc3 g a1 d TMP_175)))) in
781 (let TMP_177 \def (trans is i) in (let TMP_178 \def (TLRef TMP_177) in (let
782 TMP_184 \def (\lambda (t: T).(let TMP_179 \def (Flat Appl) in (let TMP_180
783 \def (Flat Appl) in (let TMP_181 \def (lifts1 is vs) in (let TMP_182 \def
784 (THeads TMP_180 TMP_181 t) in (let TMP_183 \def (THead TMP_179 w TMP_182) in
785 (sc3 g a1 d TMP_183))))))) in (let TMP_185 \def (trans is i) in (let TMP_186
786 \def (TLRef i) in (let TMP_187 \def (lift1 is TMP_186) in (let TMP_193 \def
787 (\lambda (t: T).(let TMP_188 \def (Flat Appl) in (let TMP_189 \def (Flat
788 Appl) in (let TMP_190 \def (lifts1 is vs) in (let TMP_191 \def (THeads
789 TMP_189 TMP_190 t) in (let TMP_192 \def (THead TMP_188 w TMP_191) in (arity g
790 d TMP_192 a1))))))) in (let TMP_194 \def (Flat Appl) in (let TMP_195 \def
791 (TLRef i) in (let TMP_196 \def (THeads TMP_194 vs TMP_195) in (let TMP_197
792 \def (lift1 is TMP_196) in (let TMP_200 \def (\lambda (t: T).(let TMP_198
793 \def (Flat Appl) in (let TMP_199 \def (THead TMP_198 w t) in (arity g d
794 TMP_199 a1)))) in (let TMP_201 \def (sc3_arity_gen g d w a0 H4) in (let
795 TMP_202 \def (Flat Appl) in (let TMP_203 \def (TLRef i) in (let TMP_204 \def
796 (THeads TMP_202 vs TMP_203) in (let TMP_205 \def (lift1 is TMP_204) in (let
797 TMP_206 \def (AHead a0 a1) in (let TMP_207 \def (Flat Appl) in (let TMP_208
798 \def (TLRef i) in (let TMP_209 \def (THeads TMP_207 vs TMP_208) in (let
799 TMP_210 \def (arity_lift1 g TMP_206 c is d TMP_209 H5 H1) in (let TMP_211
800 \def (arity_appl g d w a0 TMP_201 TMP_205 a1 TMP_210) in (let TMP_212 \def
801 (Flat Appl) in (let TMP_213 \def (lifts1 is vs) in (let TMP_214 \def (TLRef
802 i) in (let TMP_215 \def (lift1 is TMP_214) in (let TMP_216 \def (THeads
803 TMP_212 TMP_213 TMP_215) in (let TMP_217 \def (TLRef i) in (let TMP_218 \def
804 (lifts1_flat Appl is TMP_217 vs) in (let TMP_219 \def (eq_ind T TMP_197
805 TMP_200 TMP_211 TMP_216 TMP_218) in (let TMP_220 \def (trans is i) in (let
806 TMP_221 \def (TLRef TMP_220) in (let TMP_222 \def (lift1_lref is i) in (let
807 TMP_223 \def (eq_ind T TMP_187 TMP_193 TMP_219 TMP_221 TMP_222) in (let
808 TMP_224 \def (TLRef i) in (let TMP_225 \def (lift1 is TMP_224) in (let
809 TMP_226 \def (\lambda (t: T).(nf2 d t)) in (let TMP_227 \def (TLRef i) in
810 (let TMP_228 \def (nf2_lift1 c is d TMP_227 H5 H2) in (let TMP_229 \def
811 (trans is i) in (let TMP_230 \def (TLRef TMP_229) in (let TMP_231 \def
812 (lift1_lref is i) in (let TMP_232 \def (eq_ind T TMP_225 TMP_226 TMP_228
813 TMP_230 TMP_231) in (let TMP_233 \def (sn3 d w) in (let TMP_234 \def (lifts1
814 is vs) in (let TMP_235 \def (sns3 d TMP_234) in (let TMP_236 \def (H7 d w H4)
815 in (let TMP_237 \def (sns3_lifts1 c is d H5 vs H3) in (let TMP_238 \def (conj
816 TMP_233 TMP_235 TMP_236 TMP_237) in (let TMP_239 \def (H_y TMP_185 d TMP_223
817 TMP_232 TMP_238) in (let TMP_240 \def (TLRef i) in (let TMP_241 \def (lift1
818 is TMP_240) in (let TMP_242 \def (lift1_lref is i) in (let TMP_243 \def
819 (eq_ind_r T TMP_178 TMP_184 TMP_239 TMP_241 TMP_242) in (let TMP_244 \def
820 (Flat Appl) in (let TMP_245 \def (TLRef i) in (let TMP_246 \def (THeads
821 TMP_244 vs TMP_245) in (let TMP_247 \def (lift1 is TMP_246) in (let TMP_248
822 \def (TLRef i) in (let TMP_249 \def (lifts1_flat Appl is TMP_248 vs) in
823 (eq_ind_r T TMP_173 TMP_176 TMP_243 TMP_247
824 TMP_249)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
825 )) in (land_ind TMP_155 TMP_159 TMP_166 TMP_250 H9)))))))))))))) in (land_ind
826 TMP_143 TMP_147 TMP_154 TMP_251 H6))))))))))))))))) in (conj TMP_135 TMP_142
827 H1 TMP_252)))))))))))))) in (conj TMP_35 TMP_48 TMP_130 TMP_253))))))))) in
828 (A_ind TMP_5 TMP_34 TMP_254 a))))).
831 \forall (g: G).(\forall (a: A).(\forall (c: C).(\forall (t: T).((sc3 g a c
834 \lambda (g: G).(\lambda (a: A).(\lambda (c: C).(\lambda (t: T).(\lambda (H:
835 (sc3 g a c t)).(let H_x \def (sc3_props__sc3_sn3_abst g a) in (let H0 \def
836 H_x in (let TMP_1 \def (\forall (c0: C).(\forall (t0: T).((sc3 g a c0 t0) \to
837 (sn3 c0 t0)))) in (let TMP_5 \def (\forall (vs: TList).(\forall (i:
838 nat).(\forall (c0: C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a) \to
839 ((nf2 c0 (TLRef i)) \to ((sns3 c0 vs) \to (let TMP_2 \def (Flat Appl) in (let
840 TMP_3 \def (TLRef i) in (let TMP_4 \def (THeads TMP_2 vs TMP_3) in (sc3 g a
841 c0 TMP_4)))))))))) in (let TMP_6 \def (sn3 c t) in (let TMP_7 \def (\lambda
842 (H1: ((\forall (c0: C).(\forall (t0: T).((sc3 g a c0 t0) \to (sn3 c0
843 t0)))))).(\lambda (_: ((\forall (vs: TList).(\forall (i: nat).(\forall (c0:
844 C).((arity g c0 (THeads (Flat Appl) vs (TLRef i)) a) \to ((nf2 c0 (TLRef i))
845 \to ((sns3 c0 vs) \to (sc3 g a c0 (THeads (Flat Appl) vs (TLRef
846 i))))))))))).(H1 c t H))) in (land_ind TMP_1 TMP_5 TMP_6 TMP_7 H0))))))))))).
849 \forall (g: G).(\forall (a: A).(\forall (vs: TList).(\forall (c: C).(\forall
850 (i: nat).((arity g c (THeads (Flat Appl) vs (TLRef i)) a) \to ((nf2 c (TLRef
851 i)) \to ((sns3 c vs) \to (sc3 g a c (THeads (Flat Appl) vs (TLRef i))))))))))
853 \lambda (g: G).(\lambda (a: A).(\lambda (vs: TList).(\lambda (c: C).(\lambda
854 (i: nat).(\lambda (H: (arity g c (THeads (Flat Appl) vs (TLRef i))
855 a)).(\lambda (H0: (nf2 c (TLRef i))).(\lambda (H1: (sns3 c vs)).(let H_x \def
856 (sc3_props__sc3_sn3_abst g a) in (let H2 \def H_x in (let TMP_1 \def (\forall
857 (c0: C).(\forall (t: T).((sc3 g a c0 t) \to (sn3 c0 t)))) in (let TMP_5 \def
858 (\forall (vs0: TList).(\forall (i0: nat).(\forall (c0: C).((arity g c0
859 (THeads (Flat Appl) vs0 (TLRef i0)) a) \to ((nf2 c0 (TLRef i0)) \to ((sns3 c0
860 vs0) \to (let TMP_2 \def (Flat Appl) in (let TMP_3 \def (TLRef i0) in (let
861 TMP_4 \def (THeads TMP_2 vs0 TMP_3) in (sc3 g a c0 TMP_4)))))))))) in (let
862 TMP_6 \def (Flat Appl) in (let TMP_7 \def (TLRef i) in (let TMP_8 \def
863 (THeads TMP_6 vs TMP_7) in (let TMP_9 \def (sc3 g a c TMP_8) in (let TMP_10
864 \def (\lambda (_: ((\forall (c0: C).(\forall (t: T).((sc3 g a c0 t) \to (sn3
865 c0 t)))))).(\lambda (H4: ((\forall (vs0: TList).(\forall (i0: nat).(\forall
866 (c0: C).((arity g c0 (THeads (Flat Appl) vs0 (TLRef i0)) a) \to ((nf2 c0
867 (TLRef i0)) \to ((sns3 c0 vs0) \to (sc3 g a c0 (THeads (Flat Appl) vs0 (TLRef
868 i0))))))))))).(H4 vs i c H H0 H1))) in (land_ind TMP_1 TMP_5 TMP_9 TMP_10
872 \forall (g: G).(\forall (b: B).((not (eq B b Abst)) \to (\forall (a1:
873 A).(\forall (a2: A).(\forall (vs: TList).(\forall (c: C).(\forall (v:
874 T).(\forall (t: T).((sc3 g a2 (CHead c (Bind b) v) (THeads (Flat Appl) (lifts
875 (S O) O vs) t)) \to ((sc3 g a1 c v) \to (sc3 g a2 c (THeads (Flat Appl) vs
876 (THead (Bind b) v t)))))))))))))
878 \lambda (g: G).(\lambda (b: B).(\lambda (H: (not (eq B b Abst))).(\lambda
879 (a1: A).(\lambda (a2: A).(let TMP_5 \def (\lambda (a: A).(\forall (vs:
880 TList).(\forall (c: C).(\forall (v: T).(\forall (t: T).((sc3 g a (CHead c
881 (Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t)) \to ((sc3 g a1 c v)
882 \to (let TMP_1 \def (Flat Appl) in (let TMP_2 \def (Bind b) in (let TMP_3
883 \def (THead TMP_2 v t) in (let TMP_4 \def (THeads TMP_1 vs TMP_3) in (sc3 g a
884 c TMP_4)))))))))))) in (let TMP_50 \def (\lambda (n: nat).(\lambda (n0:
885 nat).(\lambda (vs: TList).(\lambda (c: C).(\lambda (v: T).(\lambda (t:
886 T).(\lambda (H0: (land (arity g (CHead c (Bind b) v) (THeads (Flat Appl)
887 (lifts (S O) O vs) t) (ASort n n0)) (sn3 (CHead c (Bind b) v) (THeads (Flat
888 Appl) (lifts (S O) O vs) t)))).(\lambda (H1: (sc3 g a1 c v)).(let H2 \def H0
889 in (let TMP_6 \def (Bind b) in (let TMP_7 \def (CHead c TMP_6 v) in (let
890 TMP_8 \def (Flat Appl) in (let TMP_9 \def (S O) in (let TMP_10 \def (lifts
891 TMP_9 O vs) in (let TMP_11 \def (THeads TMP_8 TMP_10 t) in (let TMP_12 \def
892 (ASort n n0) in (let TMP_13 \def (arity g TMP_7 TMP_11 TMP_12) in (let TMP_14
893 \def (Bind b) in (let TMP_15 \def (CHead c TMP_14 v) in (let TMP_16 \def
894 (Flat Appl) in (let TMP_17 \def (S O) in (let TMP_18 \def (lifts TMP_17 O vs)
895 in (let TMP_19 \def (THeads TMP_16 TMP_18 t) in (let TMP_20 \def (sn3 TMP_15
896 TMP_19) in (let TMP_21 \def (Flat Appl) in (let TMP_22 \def (Bind b) in (let
897 TMP_23 \def (THead TMP_22 v t) in (let TMP_24 \def (THeads TMP_21 vs TMP_23)
898 in (let TMP_25 \def (ASort n n0) in (let TMP_26 \def (arity g c TMP_24
899 TMP_25) in (let TMP_27 \def (Flat Appl) in (let TMP_28 \def (Bind b) in (let
900 TMP_29 \def (THead TMP_28 v t) in (let TMP_30 \def (THeads TMP_27 vs TMP_29)
901 in (let TMP_31 \def (sn3 c TMP_30) in (let TMP_32 \def (land TMP_26 TMP_31)
902 in (let TMP_49 \def (\lambda (H3: (arity g (CHead c (Bind b) v) (THeads (Flat
903 Appl) (lifts (S O) O vs) t) (ASort n n0))).(\lambda (H4: (sn3 (CHead c (Bind
904 b) v) (THeads (Flat Appl) (lifts (S O) O vs) t))).(let TMP_33 \def (Flat
905 Appl) in (let TMP_34 \def (Bind b) in (let TMP_35 \def (THead TMP_34 v t) in
906 (let TMP_36 \def (THeads TMP_33 vs TMP_35) in (let TMP_37 \def (ASort n n0)
907 in (let TMP_38 \def (arity g c TMP_36 TMP_37) in (let TMP_39 \def (Flat Appl)
908 in (let TMP_40 \def (Bind b) in (let TMP_41 \def (THead TMP_40 v t) in (let
909 TMP_42 \def (THeads TMP_39 vs TMP_41) in (let TMP_43 \def (sn3 c TMP_42) in
910 (let TMP_44 \def (sc3_arity_gen g c v a1 H1) in (let TMP_45 \def (ASort n n0)
911 in (let TMP_46 \def (arity_appls_bind g b H c v a1 TMP_44 t vs TMP_45 H3) in
912 (let TMP_47 \def (sc3_sn3 g a1 c v H1) in (let TMP_48 \def (sn3_appls_bind b
913 H c v TMP_47 vs t H4) in (conj TMP_38 TMP_43 TMP_46 TMP_48)))))))))))))))))))
914 in (land_ind TMP_13 TMP_20 TMP_32 TMP_49
915 H2)))))))))))))))))))))))))))))))))))))) in (let TMP_206 \def (\lambda (a:
916 A).(\lambda (_: ((\forall (vs: TList).(\forall (c: C).(\forall (v:
917 T).(\forall (t: T).((sc3 g a (CHead c (Bind b) v) (THeads (Flat Appl) (lifts
918 (S O) O vs) t)) \to ((sc3 g a1 c v) \to (sc3 g a c (THeads (Flat Appl) vs
919 (THead (Bind b) v t))))))))))).(\lambda (a0: A).(\lambda (H1: ((\forall (vs:
920 TList).(\forall (c: C).(\forall (v: T).(\forall (t: T).((sc3 g a0 (CHead c
921 (Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t)) \to ((sc3 g a1 c v)
922 \to (sc3 g a0 c (THeads (Flat Appl) vs (THead (Bind b) v
923 t))))))))))).(\lambda (vs: TList).(\lambda (c: C).(\lambda (v: T).(\lambda
924 (t: T).(\lambda (H2: (land (arity g (CHead c (Bind b) v) (THeads (Flat Appl)
925 (lifts (S O) O vs) t) (AHead a a0)) (\forall (d: C).(\forall (w: T).((sc3 g a
926 d w) \to (\forall (is: PList).((drop1 is d (CHead c (Bind b) v)) \to (sc3 g
927 a0 d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs)
928 t))))))))))).(\lambda (H3: (sc3 g a1 c v)).(let H4 \def H2 in (let TMP_51
929 \def (Bind b) in (let TMP_52 \def (CHead c TMP_51 v) in (let TMP_53 \def
930 (Flat Appl) in (let TMP_54 \def (S O) in (let TMP_55 \def (lifts TMP_54 O vs)
931 in (let TMP_56 \def (THeads TMP_53 TMP_55 t) in (let TMP_57 \def (AHead a a0)
932 in (let TMP_58 \def (arity g TMP_52 TMP_56 TMP_57) in (let TMP_66 \def
933 (\forall (d: C).(\forall (w: T).((sc3 g a d w) \to (\forall (is:
934 PList).((drop1 is d (CHead c (Bind b) v)) \to (let TMP_59 \def (Flat Appl) in
935 (let TMP_60 \def (Flat Appl) in (let TMP_61 \def (S O) in (let TMP_62 \def
936 (lifts TMP_61 O vs) in (let TMP_63 \def (THeads TMP_60 TMP_62 t) in (let
937 TMP_64 \def (lift1 is TMP_63) in (let TMP_65 \def (THead TMP_59 w TMP_64) in
938 (sc3 g a0 d TMP_65))))))))))))) in (let TMP_67 \def (Flat Appl) in (let
939 TMP_68 \def (Bind b) in (let TMP_69 \def (THead TMP_68 v t) in (let TMP_70
940 \def (THeads TMP_67 vs TMP_69) in (let TMP_71 \def (AHead a a0) in (let
941 TMP_72 \def (arity g c TMP_70 TMP_71) in (let TMP_80 \def (\forall (d:
942 C).(\forall (w: T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c)
943 \to (let TMP_73 \def (Flat Appl) in (let TMP_74 \def (Flat Appl) in (let
944 TMP_75 \def (Bind b) in (let TMP_76 \def (THead TMP_75 v t) in (let TMP_77
945 \def (THeads TMP_74 vs TMP_76) in (let TMP_78 \def (lift1 is TMP_77) in (let
946 TMP_79 \def (THead TMP_73 w TMP_78) in (sc3 g a0 d TMP_79))))))))))))) in
947 (let TMP_81 \def (land TMP_72 TMP_80) in (let TMP_205 \def (\lambda (H5:
948 (arity g (CHead c (Bind b) v) (THeads (Flat Appl) (lifts (S O) O vs) t)
949 (AHead a a0))).(\lambda (H6: ((\forall (d: C).(\forall (w: T).((sc3 g a d w)
950 \to (\forall (is: PList).((drop1 is d (CHead c (Bind b) v)) \to (sc3 g a0 d
951 (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) (lifts (S O) O vs)
952 t))))))))))).(let TMP_82 \def (Flat Appl) in (let TMP_83 \def (Bind b) in
953 (let TMP_84 \def (THead TMP_83 v t) in (let TMP_85 \def (THeads TMP_82 vs
954 TMP_84) in (let TMP_86 \def (AHead a a0) in (let TMP_87 \def (arity g c
955 TMP_85 TMP_86) in (let TMP_95 \def (\forall (d: C).(\forall (w: T).((sc3 g a
956 d w) \to (\forall (is: PList).((drop1 is d c) \to (let TMP_88 \def (Flat
957 Appl) in (let TMP_89 \def (Flat Appl) in (let TMP_90 \def (Bind b) in (let
958 TMP_91 \def (THead TMP_90 v t) in (let TMP_92 \def (THeads TMP_89 vs TMP_91)
959 in (let TMP_93 \def (lift1 is TMP_92) in (let TMP_94 \def (THead TMP_88 w
960 TMP_93) in (sc3 g a0 d TMP_94))))))))))))) in (let TMP_96 \def (sc3_arity_gen
961 g c v a1 H3) in (let TMP_97 \def (AHead a a0) in (let TMP_98 \def
962 (arity_appls_bind g b H c v a1 TMP_96 t vs TMP_97 H5) in (let TMP_204 \def
963 (\lambda (d: C).(\lambda (w: T).(\lambda (H7: (sc3 g a d w)).(\lambda (is:
964 PList).(\lambda (H8: (drop1 is d c)).(let TMP_99 \def (lifts1 is vs) in (let
965 TMP_100 \def (TCons w TMP_99) in (let H_y \def (H1 TMP_100) in (let TMP_101
966 \def (Flat Appl) in (let TMP_102 \def (lifts1 is vs) in (let TMP_103 \def
967 (Bind b) in (let TMP_104 \def (THead TMP_103 v t) in (let TMP_105 \def (lift1
968 is TMP_104) in (let TMP_106 \def (THeads TMP_101 TMP_102 TMP_105) in (let
969 TMP_109 \def (\lambda (t0: T).(let TMP_107 \def (Flat Appl) in (let TMP_108
970 \def (THead TMP_107 w t0) in (sc3 g a0 d TMP_108)))) in (let TMP_110 \def
971 (Bind b) in (let TMP_111 \def (lift1 is v) in (let TMP_112 \def (Ss is) in
972 (let TMP_113 \def (lift1 TMP_112 t) in (let TMP_114 \def (THead TMP_110
973 TMP_111 TMP_113) in (let TMP_120 \def (\lambda (t0: T).(let TMP_115 \def
974 (Flat Appl) in (let TMP_116 \def (Flat Appl) in (let TMP_117 \def (lifts1 is
975 vs) in (let TMP_118 \def (THeads TMP_116 TMP_117 t0) in (let TMP_119 \def
976 (THead TMP_115 w TMP_118) in (sc3 g a0 d TMP_119))))))) in (let TMP_121 \def
977 (lift1 is v) in (let TMP_122 \def (Ss is) in (let TMP_123 \def (lift1 TMP_122
978 t) in (let TMP_124 \def (Ss is) in (let TMP_125 \def (S O) in (let TMP_126
979 \def (lifts TMP_125 O vs) in (let TMP_127 \def (lifts1 TMP_124 TMP_126) in
980 (let TMP_139 \def (\lambda (t0: TList).(let TMP_128 \def (Bind b) in (let
981 TMP_129 \def (lift1 is v) in (let TMP_130 \def (CHead d TMP_128 TMP_129) in
982 (let TMP_131 \def (Flat Appl) in (let TMP_132 \def (S O) in (let TMP_133 \def
983 (lift TMP_132 O w) in (let TMP_134 \def (Flat Appl) in (let TMP_135 \def (Ss
984 is) in (let TMP_136 \def (lift1 TMP_135 t) in (let TMP_137 \def (THeads
985 TMP_134 t0 TMP_136) in (let TMP_138 \def (THead TMP_131 TMP_133 TMP_137) in
986 (sc3 g a0 TMP_130 TMP_138))))))))))))) in (let TMP_140 \def (Ss is) in (let
987 TMP_141 \def (Flat Appl) in (let TMP_142 \def (S O) in (let TMP_143 \def
988 (lifts TMP_142 O vs) in (let TMP_144 \def (THeads TMP_141 TMP_143 t) in (let
989 TMP_145 \def (lift1 TMP_140 TMP_144) in (let TMP_153 \def (\lambda (t0:
990 T).(let TMP_146 \def (Bind b) in (let TMP_147 \def (lift1 is v) in (let
991 TMP_148 \def (CHead d TMP_146 TMP_147) in (let TMP_149 \def (Flat Appl) in
992 (let TMP_150 \def (S O) in (let TMP_151 \def (lift TMP_150 O w) in (let
993 TMP_152 \def (THead TMP_149 TMP_151 t0) in (sc3 g a0 TMP_148 TMP_152)))))))))
994 in (let TMP_154 \def (Bind b) in (let TMP_155 \def (lift1 is v) in (let
995 TMP_156 \def (CHead d TMP_154 TMP_155) in (let TMP_157 \def (S O) in (let
996 TMP_158 \def (lift TMP_157 O w) in (let TMP_159 \def (Bind b) in (let TMP_160
997 \def (lift1 is v) in (let TMP_161 \def (CHead d TMP_159 TMP_160) in (let
998 TMP_162 \def (S O) in (let TMP_163 \def (Bind b) in (let TMP_164 \def
999 (drop_refl d) in (let TMP_165 \def (lift1 is v) in (let TMP_166 \def
1000 (drop_drop TMP_163 O d d TMP_164 TMP_165) in (let TMP_167 \def (sc3_lift g a
1001 d w H7 TMP_161 TMP_162 O TMP_166) in (let TMP_168 \def (Ss is) in (let
1002 TMP_169 \def (drop1_skip_bind b c is d v H8) in (let TMP_170 \def (H6 TMP_156
1003 TMP_158 TMP_167 TMP_168 TMP_169) in (let TMP_171 \def (Flat Appl) in (let
1004 TMP_172 \def (Ss is) in (let TMP_173 \def (S O) in (let TMP_174 \def (lifts
1005 TMP_173 O vs) in (let TMP_175 \def (lifts1 TMP_172 TMP_174) in (let TMP_176
1006 \def (Ss is) in (let TMP_177 \def (lift1 TMP_176 t) in (let TMP_178 \def
1007 (THeads TMP_171 TMP_175 TMP_177) in (let TMP_179 \def (Ss is) in (let TMP_180
1008 \def (S O) in (let TMP_181 \def (lifts TMP_180 O vs) in (let TMP_182 \def
1009 (lifts1_flat Appl TMP_179 t TMP_181) in (let TMP_183 \def (eq_ind T TMP_145
1010 TMP_153 TMP_170 TMP_178 TMP_182) in (let TMP_184 \def (S O) in (let TMP_185
1011 \def (lifts1 is vs) in (let TMP_186 \def (lifts TMP_184 O TMP_185) in (let
1012 TMP_187 \def (lifts1_xhg is vs) in (let TMP_188 \def (eq_ind TList TMP_127
1013 TMP_139 TMP_183 TMP_186 TMP_187) in (let TMP_189 \def (sc3_lift1 g c a1 is d
1014 v H3 H8) in (let TMP_190 \def (H_y d TMP_121 TMP_123 TMP_188 TMP_189) in (let
1015 TMP_191 \def (Bind b) in (let TMP_192 \def (THead TMP_191 v t) in (let
1016 TMP_193 \def (lift1 is TMP_192) in (let TMP_194 \def (lift1_bind b is v t) in
1017 (let TMP_195 \def (eq_ind_r T TMP_114 TMP_120 TMP_190 TMP_193 TMP_194) in
1018 (let TMP_196 \def (Flat Appl) in (let TMP_197 \def (Bind b) in (let TMP_198
1019 \def (THead TMP_197 v t) in (let TMP_199 \def (THeads TMP_196 vs TMP_198) in
1020 (let TMP_200 \def (lift1 is TMP_199) in (let TMP_201 \def (Bind b) in (let
1021 TMP_202 \def (THead TMP_201 v t) in (let TMP_203 \def (lifts1_flat Appl is
1022 TMP_202 vs) in (eq_ind_r T TMP_106 TMP_109 TMP_195 TMP_200
1023 TMP_203)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1024 )))))))))))))))) in (conj TMP_87 TMP_95 TMP_98 TMP_204)))))))))))))) in
1025 (land_ind TMP_58 TMP_66 TMP_81 TMP_205 H4)))))))))))))))))))))))))))))) in
1026 (A_ind TMP_5 TMP_50 TMP_206 a2)))))))).
1029 \forall (g: G).(\forall (a1: A).(\forall (a2: A).(\forall (vs:
1030 TList).(\forall (c: C).(\forall (v: T).(\forall (t: T).((sc3 g a2 c (THeads
1031 (Flat Appl) vs (THead (Bind Abbr) v t))) \to ((sc3 g a1 c v) \to (\forall (w:
1032 T).((sc3 g (asucc g a1) c w) \to (sc3 g a2 c (THeads (Flat Appl) vs (THead
1033 (Flat Appl) v (THead (Bind Abst) w t))))))))))))))
1035 \lambda (g: G).(\lambda (a1: A).(\lambda (a2: A).(let TMP_7 \def (\lambda
1036 (a: A).(\forall (vs: TList).(\forall (c: C).(\forall (v: T).(\forall (t:
1037 T).((sc3 g a c (THeads (Flat Appl) vs (THead (Bind Abbr) v t))) \to ((sc3 g
1038 a1 c v) \to (\forall (w: T).((sc3 g (asucc g a1) c w) \to (let TMP_1 \def
1039 (Flat Appl) in (let TMP_2 \def (Flat Appl) in (let TMP_3 \def (Bind Abst) in
1040 (let TMP_4 \def (THead TMP_3 w t) in (let TMP_5 \def (THead TMP_2 v TMP_4) in
1041 (let TMP_6 \def (THeads TMP_1 vs TMP_5) in (sc3 g a c TMP_6))))))))))))))))
1042 in (let TMP_59 \def (\lambda (n: nat).(\lambda (n0: nat).(\lambda (vs:
1043 TList).(\lambda (c: C).(\lambda (v: T).(\lambda (t: T).(\lambda (H: (land
1044 (arity g c (THeads (Flat Appl) vs (THead (Bind Abbr) v t)) (ASort n n0)) (sn3
1045 c (THeads (Flat Appl) vs (THead (Bind Abbr) v t))))).(\lambda (H0: (sc3 g a1
1046 c v)).(\lambda (w: T).(\lambda (H1: (sc3 g (asucc g a1) c w)).(let H2 \def H
1047 in (let TMP_8 \def (Flat Appl) in (let TMP_9 \def (Bind Abbr) in (let TMP_10
1048 \def (THead TMP_9 v t) in (let TMP_11 \def (THeads TMP_8 vs TMP_10) in (let
1049 TMP_12 \def (ASort n n0) in (let TMP_13 \def (arity g c TMP_11 TMP_12) in
1050 (let TMP_14 \def (Flat Appl) in (let TMP_15 \def (Bind Abbr) in (let TMP_16
1051 \def (THead TMP_15 v t) in (let TMP_17 \def (THeads TMP_14 vs TMP_16) in (let
1052 TMP_18 \def (sn3 c TMP_17) in (let TMP_19 \def (Flat Appl) in (let TMP_20
1053 \def (Flat Appl) in (let TMP_21 \def (Bind Abst) in (let TMP_22 \def (THead
1054 TMP_21 w t) in (let TMP_23 \def (THead TMP_20 v TMP_22) in (let TMP_24 \def
1055 (THeads TMP_19 vs TMP_23) in (let TMP_25 \def (ASort n n0) in (let TMP_26
1056 \def (arity g c TMP_24 TMP_25) in (let TMP_27 \def (Flat Appl) in (let TMP_28
1057 \def (Flat Appl) in (let TMP_29 \def (Bind Abst) in (let TMP_30 \def (THead
1058 TMP_29 w t) in (let TMP_31 \def (THead TMP_28 v TMP_30) in (let TMP_32 \def
1059 (THeads TMP_27 vs TMP_31) in (let TMP_33 \def (sn3 c TMP_32) in (let TMP_34
1060 \def (land TMP_26 TMP_33) in (let TMP_58 \def (\lambda (H3: (arity g c
1061 (THeads (Flat Appl) vs (THead (Bind Abbr) v t)) (ASort n n0))).(\lambda (H4:
1062 (sn3 c (THeads (Flat Appl) vs (THead (Bind Abbr) v t)))).(let TMP_35 \def
1063 (Flat Appl) in (let TMP_36 \def (Flat Appl) in (let TMP_37 \def (Bind Abst)
1064 in (let TMP_38 \def (THead TMP_37 w t) in (let TMP_39 \def (THead TMP_36 v
1065 TMP_38) in (let TMP_40 \def (THeads TMP_35 vs TMP_39) in (let TMP_41 \def
1066 (ASort n n0) in (let TMP_42 \def (arity g c TMP_40 TMP_41) in (let TMP_43
1067 \def (Flat Appl) in (let TMP_44 \def (Flat Appl) in (let TMP_45 \def (Bind
1068 Abst) in (let TMP_46 \def (THead TMP_45 w t) in (let TMP_47 \def (THead
1069 TMP_44 v TMP_46) in (let TMP_48 \def (THeads TMP_43 vs TMP_47) in (let TMP_49
1070 \def (sn3 c TMP_48) in (let TMP_50 \def (sc3_arity_gen g c v a1 H0) in (let
1071 TMP_51 \def (asucc g a1) in (let TMP_52 \def (sc3_arity_gen g c w TMP_51 H1)
1072 in (let TMP_53 \def (ASort n n0) in (let TMP_54 \def (arity_appls_appl g c v
1073 a1 TMP_50 w TMP_52 t vs TMP_53 H3) in (let TMP_55 \def (asucc g a1) in (let
1074 TMP_56 \def (sc3_sn3 g TMP_55 c w H1) in (let TMP_57 \def (sn3_appls_beta c v
1075 t vs H4 w TMP_56) in (conj TMP_42 TMP_49 TMP_54
1076 TMP_57)))))))))))))))))))))))))) in (land_ind TMP_13 TMP_18 TMP_34 TMP_58
1077 H2)))))))))))))))))))))))))))))))))))))))) in (let TMP_226 \def (\lambda (a:
1078 A).(\lambda (_: ((\forall (vs: TList).(\forall (c: C).(\forall (v:
1079 T).(\forall (t: T).((sc3 g a c (THeads (Flat Appl) vs (THead (Bind Abbr) v
1080 t))) \to ((sc3 g a1 c v) \to (\forall (w: T).((sc3 g (asucc g a1) c w) \to
1081 (sc3 g a c (THeads (Flat Appl) vs (THead (Flat Appl) v (THead (Bind Abst) w
1082 t)))))))))))))).(\lambda (a0: A).(\lambda (H0: ((\forall (vs: TList).(\forall
1083 (c: C).(\forall (v: T).(\forall (t: T).((sc3 g a0 c (THeads (Flat Appl) vs
1084 (THead (Bind Abbr) v t))) \to ((sc3 g a1 c v) \to (\forall (w: T).((sc3 g
1085 (asucc g a1) c w) \to (sc3 g a0 c (THeads (Flat Appl) vs (THead (Flat Appl) v
1086 (THead (Bind Abst) w t)))))))))))))).(\lambda (vs: TList).(\lambda (c:
1087 C).(\lambda (v: T).(\lambda (t: T).(\lambda (H1: (land (arity g c (THeads
1088 (Flat Appl) vs (THead (Bind Abbr) v t)) (AHead a a0)) (\forall (d:
1089 C).(\forall (w: T).((sc3 g a d w) \to (\forall (is: PList).((drop1 is d c)
1090 \to (sc3 g a0 d (THead (Flat Appl) w (lift1 is (THeads (Flat Appl) vs (THead
1091 (Bind Abbr) v t)))))))))))).(\lambda (H2: (sc3 g a1 c v)).(\lambda (w:
1092 T).(\lambda (H3: (sc3 g (asucc g a1) c w)).(let H4 \def H1 in (let TMP_60
1093 \def (Flat Appl) in (let TMP_61 \def (Bind Abbr) in (let TMP_62 \def (THead
1094 TMP_61 v t) in (let TMP_63 \def (THeads TMP_60 vs TMP_62) in (let TMP_64 \def
1095 (AHead a a0) in (let TMP_65 \def (arity g c TMP_63 TMP_64) in (let TMP_73
1096 \def (\forall (d: C).(\forall (w0: T).((sc3 g a d w0) \to (\forall (is:
1097 PList).((drop1 is d c) \to (let TMP_66 \def (Flat Appl) in (let TMP_67 \def
1098 (Flat Appl) in (let TMP_68 \def (Bind Abbr) in (let TMP_69 \def (THead TMP_68
1099 v t) in (let TMP_70 \def (THeads TMP_67 vs TMP_69) in (let TMP_71 \def (lift1
1100 is TMP_70) in (let TMP_72 \def (THead TMP_66 w0 TMP_71) in (sc3 g a0 d
1101 TMP_72))))))))))))) in (let TMP_74 \def (Flat Appl) in (let TMP_75 \def (Flat
1102 Appl) in (let TMP_76 \def (Bind Abst) in (let TMP_77 \def (THead TMP_76 w t)
1103 in (let TMP_78 \def (THead TMP_75 v TMP_77) in (let TMP_79 \def (THeads
1104 TMP_74 vs TMP_78) in (let TMP_80 \def (AHead a a0) in (let TMP_81 \def (arity
1105 g c TMP_79 TMP_80) in (let TMP_91 \def (\forall (d: C).(\forall (w0: T).((sc3
1106 g a d w0) \to (\forall (is: PList).((drop1 is d c) \to (let TMP_82 \def (Flat
1107 Appl) in (let TMP_83 \def (Flat Appl) in (let TMP_84 \def (Flat Appl) in (let
1108 TMP_85 \def (Bind Abst) in (let TMP_86 \def (THead TMP_85 w t) in (let TMP_87
1109 \def (THead TMP_84 v TMP_86) in (let TMP_88 \def (THeads TMP_83 vs TMP_87) in
1110 (let TMP_89 \def (lift1 is TMP_88) in (let TMP_90 \def (THead TMP_82 w0
1111 TMP_89) in (sc3 g a0 d TMP_90))))))))))))))) in (let TMP_92 \def (land TMP_81
1112 TMP_91) in (let TMP_225 \def (\lambda (H5: (arity g c (THeads (Flat Appl) vs
1113 (THead (Bind Abbr) v t)) (AHead a a0))).(\lambda (H6: ((\forall (d:
1114 C).(\forall (w0: T).((sc3 g a d w0) \to (\forall (is: PList).((drop1 is d c)
1115 \to (sc3 g a0 d (THead (Flat Appl) w0 (lift1 is (THeads (Flat Appl) vs (THead
1116 (Bind Abbr) v t)))))))))))).(let TMP_93 \def (Flat Appl) in (let TMP_94 \def
1117 (Flat Appl) in (let TMP_95 \def (Bind Abst) in (let TMP_96 \def (THead TMP_95
1118 w t) in (let TMP_97 \def (THead TMP_94 v TMP_96) in (let TMP_98 \def (THeads
1119 TMP_93 vs TMP_97) in (let TMP_99 \def (AHead a a0) in (let TMP_100 \def
1120 (arity g c TMP_98 TMP_99) in (let TMP_110 \def (\forall (d: C).(\forall (w0:
1121 T).((sc3 g a d w0) \to (\forall (is: PList).((drop1 is d c) \to (let TMP_101
1122 \def (Flat Appl) in (let TMP_102 \def (Flat Appl) in (let TMP_103 \def (Flat
1123 Appl) in (let TMP_104 \def (Bind Abst) in (let TMP_105 \def (THead TMP_104 w
1124 t) in (let TMP_106 \def (THead TMP_103 v TMP_105) in (let TMP_107 \def
1125 (THeads TMP_102 vs TMP_106) in (let TMP_108 \def (lift1 is TMP_107) in (let
1126 TMP_109 \def (THead TMP_101 w0 TMP_108) in (sc3 g a0 d TMP_109)))))))))))))))
1127 in (let TMP_111 \def (sc3_arity_gen g c v a1 H2) in (let TMP_112 \def (asucc
1128 g a1) in (let TMP_113 \def (sc3_arity_gen g c w TMP_112 H3) in (let TMP_114
1129 \def (AHead a a0) in (let TMP_115 \def (arity_appls_appl g c v a1 TMP_111 w
1130 TMP_113 t vs TMP_114 H5) in (let TMP_224 \def (\lambda (d: C).(\lambda (w0:
1131 T).(\lambda (H7: (sc3 g a d w0)).(\lambda (is: PList).(\lambda (H8: (drop1 is
1132 d c)).(let TMP_116 \def (Flat Appl) in (let TMP_117 \def (lifts1 is vs) in
1133 (let TMP_118 \def (Flat Appl) in (let TMP_119 \def (Bind Abst) in (let
1134 TMP_120 \def (THead TMP_119 w t) in (let TMP_121 \def (THead TMP_118 v
1135 TMP_120) in (let TMP_122 \def (lift1 is TMP_121) in (let TMP_123 \def (THeads
1136 TMP_116 TMP_117 TMP_122) in (let TMP_126 \def (\lambda (t0: T).(let TMP_124
1137 \def (Flat Appl) in (let TMP_125 \def (THead TMP_124 w0 t0) in (sc3 g a0 d
1138 TMP_125)))) in (let TMP_127 \def (Flat Appl) in (let TMP_128 \def (lift1 is
1139 v) in (let TMP_129 \def (Bind Abst) in (let TMP_130 \def (THead TMP_129 w t)
1140 in (let TMP_131 \def (lift1 is TMP_130) in (let TMP_132 \def (THead TMP_127
1141 TMP_128 TMP_131) in (let TMP_138 \def (\lambda (t0: T).(let TMP_133 \def
1142 (Flat Appl) in (let TMP_134 \def (Flat Appl) in (let TMP_135 \def (lifts1 is
1143 vs) in (let TMP_136 \def (THeads TMP_134 TMP_135 t0) in (let TMP_137 \def
1144 (THead TMP_133 w0 TMP_136) in (sc3 g a0 d TMP_137))))))) in (let TMP_139 \def
1145 (Bind Abst) in (let TMP_140 \def (lift1 is w) in (let TMP_141 \def (Ss is) in
1146 (let TMP_142 \def (lift1 TMP_141 t) in (let TMP_143 \def (THead TMP_139
1147 TMP_140 TMP_142) in (let TMP_152 \def (\lambda (t0: T).(let TMP_144 \def
1148 (Flat Appl) in (let TMP_145 \def (Flat Appl) in (let TMP_146 \def (lifts1 is
1149 vs) in (let TMP_147 \def (Flat Appl) in (let TMP_148 \def (lift1 is v) in
1150 (let TMP_149 \def (THead TMP_147 TMP_148 t0) in (let TMP_150 \def (THeads
1151 TMP_145 TMP_146 TMP_149) in (let TMP_151 \def (THead TMP_144 w0 TMP_150) in
1152 (sc3 g a0 d TMP_151)))))))))) in (let TMP_153 \def (lifts1 is vs) in (let
1153 TMP_154 \def (TCons w0 TMP_153) in (let H_y \def (H0 TMP_154) in (let TMP_155
1154 \def (lift1 is v) in (let TMP_156 \def (Ss is) in (let TMP_157 \def (lift1
1155 TMP_156 t) in (let TMP_158 \def (Bind Abbr) in (let TMP_159 \def (THead
1156 TMP_158 v t) in (let TMP_160 \def (lift1 is TMP_159) in (let TMP_166 \def
1157 (\lambda (t0: T).(let TMP_161 \def (Flat Appl) in (let TMP_162 \def (Flat
1158 Appl) in (let TMP_163 \def (lifts1 is vs) in (let TMP_164 \def (THeads
1159 TMP_162 TMP_163 t0) in (let TMP_165 \def (THead TMP_161 w0 TMP_164) in (sc3 g
1160 a0 d TMP_165))))))) in (let TMP_167 \def (Flat Appl) in (let TMP_168 \def
1161 (Bind Abbr) in (let TMP_169 \def (THead TMP_168 v t) in (let TMP_170 \def
1162 (THeads TMP_167 vs TMP_169) in (let TMP_171 \def (lift1 is TMP_170) in (let
1163 TMP_174 \def (\lambda (t0: T).(let TMP_172 \def (Flat Appl) in (let TMP_173
1164 \def (THead TMP_172 w0 t0) in (sc3 g a0 d TMP_173)))) in (let TMP_175 \def
1165 (H6 d w0 H7 is H8) in (let TMP_176 \def (Flat Appl) in (let TMP_177 \def
1166 (lifts1 is vs) in (let TMP_178 \def (Bind Abbr) in (let TMP_179 \def (THead
1167 TMP_178 v t) in (let TMP_180 \def (lift1 is TMP_179) in (let TMP_181 \def
1168 (THeads TMP_176 TMP_177 TMP_180) in (let TMP_182 \def (Bind Abbr) in (let
1169 TMP_183 \def (THead TMP_182 v t) in (let TMP_184 \def (lifts1_flat Appl is
1170 TMP_183 vs) in (let TMP_185 \def (eq_ind T TMP_171 TMP_174 TMP_175 TMP_181
1171 TMP_184) in (let TMP_186 \def (Bind Abbr) in (let TMP_187 \def (lift1 is v)
1172 in (let TMP_188 \def (Ss is) in (let TMP_189 \def (lift1 TMP_188 t) in (let
1173 TMP_190 \def (THead TMP_186 TMP_187 TMP_189) in (let TMP_191 \def (lift1_bind
1174 Abbr is v t) in (let TMP_192 \def (eq_ind T TMP_160 TMP_166 TMP_185 TMP_190
1175 TMP_191) in (let TMP_193 \def (sc3_lift1 g c a1 is d v H2 H8) in (let TMP_194
1176 \def (lift1 is w) in (let TMP_195 \def (asucc g a1) in (let TMP_196 \def
1177 (sc3_lift1 g c TMP_195 is d w H3 H8) in (let TMP_197 \def (H_y d TMP_155
1178 TMP_157 TMP_192 TMP_193 TMP_194 TMP_196) in (let TMP_198 \def (Bind Abst) in
1179 (let TMP_199 \def (THead TMP_198 w t) in (let TMP_200 \def (lift1 is TMP_199)
1180 in (let TMP_201 \def (lift1_bind Abst is w t) in (let TMP_202 \def (eq_ind_r
1181 T TMP_143 TMP_152 TMP_197 TMP_200 TMP_201) in (let TMP_203 \def (Flat Appl)
1182 in (let TMP_204 \def (Bind Abst) in (let TMP_205 \def (THead TMP_204 w t) in
1183 (let TMP_206 \def (THead TMP_203 v TMP_205) in (let TMP_207 \def (lift1 is
1184 TMP_206) in (let TMP_208 \def (Bind Abst) in (let TMP_209 \def (THead TMP_208
1185 w t) in (let TMP_210 \def (lift1_flat Appl is v TMP_209) in (let TMP_211 \def
1186 (eq_ind_r T TMP_132 TMP_138 TMP_202 TMP_207 TMP_210) in (let TMP_212 \def
1187 (Flat Appl) in (let TMP_213 \def (Flat Appl) in (let TMP_214 \def (Bind Abst)
1188 in (let TMP_215 \def (THead TMP_214 w t) in (let TMP_216 \def (THead TMP_213
1189 v TMP_215) in (let TMP_217 \def (THeads TMP_212 vs TMP_216) in (let TMP_218
1190 \def (lift1 is TMP_217) in (let TMP_219 \def (Flat Appl) in (let TMP_220 \def
1191 (Bind Abst) in (let TMP_221 \def (THead TMP_220 w t) in (let TMP_222 \def
1192 (THead TMP_219 v TMP_221) in (let TMP_223 \def (lifts1_flat Appl is TMP_222
1193 vs) in (eq_ind_r T TMP_123 TMP_126 TMP_211 TMP_218
1194 TMP_223)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
1195 )))))))))))))))))))))) in (conj TMP_100 TMP_110 TMP_115
1196 TMP_224)))))))))))))))))) in (land_ind TMP_65 TMP_73 TMP_92 TMP_225
1197 H4)))))))))))))))))))))))))))))))) in (A_ind TMP_7 TMP_59 TMP_226 a2)))))).
projects / helm.git / blob