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_1A/pc3/dec.ma".
19 include "basic_1A/getl/flt.ma".
21 include "basic_1A/getl/dec.ma".
23 include "basic_1A/flt/fwd.ma".
26 \forall (g: G).(\forall (c: C).(\forall (t1: T).(or (ex T (\lambda (t2:
27 T).(ty3 g c t1 t2))) (\forall (t2: T).((ty3 g c t1 t2) \to False)))))
29 \lambda (g: G).(\lambda (c: C).(\lambda (t1: T).(flt_wf_ind (\lambda (c0:
30 C).(\lambda (t: T).(or (ex T (\lambda (t2: T).(ty3 g c0 t t2))) (\forall (t2:
31 T).((ty3 g c0 t t2) \to False))))) (\lambda (c2: C).(\lambda (t2: T).(T_ind
32 (\lambda (t: T).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 t) \to (or
33 (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4)
34 \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall
35 (t3: T).((ty3 g c2 t t3) \to False))))) (\lambda (n: nat).(\lambda (_:
36 ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (TSort n)) \to (or (ex T
37 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
38 False)))))))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TSort n) t3)))
39 (\forall (t3: T).((ty3 g c2 (TSort n) t3) \to False)) (ex_intro T (\lambda
40 (t3: T).(ty3 g c2 (TSort n) t3)) (TSort (next g n)) (ty3_sort g c2 n)))))
41 (\lambda (n: nat).(\lambda (H: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3
42 c2 (TLRef n)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
43 T).((ty3 g c1 t3 t4) \to False)))))))).(let H_x \def (getl_dec c2 n) in (let
44 H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda
45 (v: T).(getl n c2 (CHead e (Bind b) v)))))) (\forall (d: C).((getl n c2 d)
46 \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n)
47 t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (H1:
48 (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n c2 (CHead
49 e (Bind b) v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda
50 (v: T).(getl n c2 (CHead e (Bind b) v))))) (or (ex T (\lambda (t3: T).(ty3 g
51 c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False)))
52 (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl n c2
53 (CHead x0 (Bind x1) x2))).(let H3 \def (H x0 x2 (getl_flt x1 c2 x0 x2 n H2))
54 in (or_ind (ex T (\lambda (t3: T).(ty3 g x0 x2 t3))) (\forall (t3: T).((ty3 g
55 x0 x2 t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
56 (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (H4: (ex T
57 (\lambda (t3: T).(ty3 g x0 x2 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g x0 x2
58 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3:
59 T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (x: T).(\lambda (H5: (ty3 g
60 x0 x2 x)).(B_ind (\lambda (b: B).((getl n c2 (CHead x0 (Bind b) x2)) \to (or
61 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
62 (TLRef n) t3) \to False))))) (\lambda (H6: (getl n c2 (CHead x0 (Bind Abbr)
63 x2))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall
64 (t3: T).((ty3 g c2 (TLRef n) t3) \to False)) (ex_intro T (\lambda (t3:
65 T).(ty3 g c2 (TLRef n) t3)) (lift (S n) O x) (ty3_abbr g n c2 x0 x2 H6 x
66 H5)))) (\lambda (H6: (getl n c2 (CHead x0 (Bind Abst) x2))).(or_introl (ex T
67 (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef
68 n) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))
69 (lift (S n) O x2) (ty3_abst g n c2 x0 x2 H6 x H5)))) (\lambda (H6: (getl n c2
70 (CHead x0 (Bind Void) x2))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2
71 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))
72 (\lambda (t3: T).(\lambda (H7: (ty3 g c2 (TLRef n) t3)).(or_ind (ex3_3 C T T
73 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
74 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
75 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
76 t))))) (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2
77 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
78 n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
79 T).(ty3 g e u t))))) False (\lambda (H8: (ex3_3 C T T (\lambda (_:
80 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
81 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
82 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind
83 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O
84 t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
85 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
86 t)))) False (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_:
87 (pc3 c2 (lift (S n) O x5) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind
88 Abbr) x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0
89 (Bind Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abbr) x4)
90 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10))
91 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
92 ee with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k
93 with [(Bind b) \Rightarrow (match b with [Abbr \Rightarrow False | Abst
94 \Rightarrow False | Void \Rightarrow True]) | (Flat _) \Rightarrow False])]))
95 I (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind Void) x2) n H6
96 (CHead x3 (Bind Abbr) x4) H10)) in (False_ind False H13))))))))) H8))
97 (\lambda (H8: (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_:
98 T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
99 (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u:
100 T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_:
101 C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda
102 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
103 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) False
104 (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift
105 (S n) O x4) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind Abst)
106 x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0 (Bind
107 Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abst) x4)
108 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abst) x4) H10))
109 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
110 ee with [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k
111 with [(Bind b) \Rightarrow (match b with [Abbr \Rightarrow False | Abst
112 \Rightarrow False | Void \Rightarrow True]) | (Flat _) \Rightarrow False])]))
113 I (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind Void) x2) n H6
114 (CHead x3 (Bind Abst) x4) H10)) in (False_ind False H13))))))))) H8))
115 (ty3_gen_lref g c2 t3 n H7)))))) x1 H2))) H4)) (\lambda (H4: ((\forall (t3:
116 T).((ty3 g x0 x2 t3) \to False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g
117 c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))
118 (\lambda (t3: T).(\lambda (H5: (ty3 g c2 (TLRef n) t3)).(or_ind (ex3_3 C T T
119 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
120 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
121 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
122 t))))) (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2
123 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
124 n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
125 T).(ty3 g e u t))))) False (\lambda (H6: (ex3_3 C T T (\lambda (_:
126 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
127 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
128 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind
129 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O
130 t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
131 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
132 t)))) False (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_:
133 (pc3 c2 (lift (S n) O x5) t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abbr)
134 x4))).(\lambda (H9: (ty3 g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind
135 x1) x2) (\lambda (c0: C).(getl n c2 c0)) H2 (CHead x3 (Bind Abbr) x4)
136 (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in
137 (let H11 \def (f_equal C C (\lambda (e: C).(match e with [(CSort _)
138 \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0])) (CHead x0 (Bind x1) x2)
139 (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead
140 x3 (Bind Abbr) x4) H8)) in ((let H12 \def (f_equal C B (\lambda (e: C).(match
141 e with [(CSort _) \Rightarrow x1 | (CHead _ k _) \Rightarrow (match k with
142 [(Bind b) \Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0 (Bind x1)
143 x2) (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2
144 (CHead x3 (Bind Abbr) x4) H8)) in ((let H13 \def (f_equal C T (\lambda (e:
145 C).(match e with [(CSort _) \Rightarrow x2 | (CHead _ _ t) \Rightarrow t]))
146 (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0
147 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in (\lambda (_: (eq B x1
148 Abbr)).(\lambda (H15: (eq C x0 x3)).(let H16 \def (eq_ind_r T x4 (\lambda (t:
149 T).(getl n c2 (CHead x3 (Bind Abbr) t))) H10 x2 H13) in (let H17 \def
150 (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2 H13) in (let H18 \def
151 (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead c0 (Bind Abbr) x2))) H16 x0
152 H15) in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(ty3 g c0 x2 x5)) H17
153 x0 H15) in (H4 x5 H19)))))))) H12)) H11))))))))) H6)) (\lambda (H6: (ex3_3 C
154 T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
155 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
156 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
157 t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3
158 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_:
159 T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u:
160 T).(\lambda (t: T).(ty3 g e u t)))) False (\lambda (x3: C).(\lambda (x4:
161 T).(\lambda (x5: T).(\lambda (H7: (pc3 c2 (lift (S n) O x4) t3)).(\lambda
162 (H8: (getl n c2 (CHead x3 (Bind Abst) x4))).(\lambda (H9: (ty3 g x3 x4
163 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind x1) x2) (\lambda (c0: C).(getl n
164 c2 c0)) H2 (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n
165 H2 (CHead x3 (Bind Abst) x4) H8)) in (let H11 \def (f_equal C C (\lambda (e:
166 C).(match e with [(CSort _) \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0]))
167 (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0
168 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in ((let H12 \def (f_equal
169 C B (\lambda (e: C).(match e with [(CSort _) \Rightarrow x1 | (CHead _ k _)
170 \Rightarrow (match k with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow
171 x1])])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono c2
172 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in ((let H13 \def
173 (f_equal C T (\lambda (e: C).(match e with [(CSort _) \Rightarrow x2 | (CHead
174 _ _ t) \Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4)
175 (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in
176 (\lambda (_: (eq B x1 Abst)).(\lambda (H15: (eq C x0 x3)).(let H16 \def
177 (eq_ind_r T x4 (\lambda (t: T).(getl n c2 (CHead x3 (Bind Abst) t))) H10 x2
178 H13) in (let H17 \def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2
179 H13) in (let H18 \def (eq_ind_r T x4 (\lambda (t: T).(pc3 c2 (lift (S n) O t)
180 t3)) H7 x2 H13) in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2
181 (CHead c0 (Bind Abst) x2))) H16 x0 H15) in (let H20 \def (eq_ind_r C x3
182 (\lambda (c0: C).(ty3 g c0 x2 x5)) H17 x0 H15) in (H4 x5 H20))))))))) H12))
183 H11))))))))) H6)) (ty3_gen_lref g c2 t3 n H5)))))) H3)))))) H1)) (\lambda
184 (H1: ((\forall (d: C).((getl n c2 d) \to (\forall (P: Prop).P))))).(or_intror
185 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
186 (TLRef n) t3) \to False)) (\lambda (t3: T).(\lambda (H2: (ty3 g c2 (TLRef n)
187 t3)).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
188 T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
189 (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
190 T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda (_: C).(\lambda
191 (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e:
192 C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
193 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) False
194 (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
195 T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
196 (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
197 T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_:
198 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
199 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
200 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) False
201 (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3 c2 (lift
202 (S n) O x2) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abbr)
203 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abbr) x1) H5
204 False))))))) H3)) (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
205 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
206 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
207 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
208 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
209 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
210 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
211 t)))) False (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_:
212 (pc3 c2 (lift (S n) O x1) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abst)
213 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abst) x1) H5
214 False))))))) H3)) (ty3_gen_lref g c2 t3 n H2)))))) H0))))) (\lambda (k:
215 K).(\lambda (t: T).(\lambda (_: ((((\forall (c1: C).(\forall (t3: T).((flt c1
216 t3 c2 t) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
217 T).((ty3 g c1 t3 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g
218 c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)))))).(\lambda (t0:
219 T).(\lambda (_: ((((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 t0) \to
220 (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3
221 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 t0 t3)))
222 (\forall (t3: T).((ty3 g c2 t0 t3) \to False)))))).(\lambda (H1: ((\forall
223 (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead k t t0)) \to (or (ex T
224 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
225 False)))))))).(K_ind (\lambda (k0: K).(((\forall (c1: C).(\forall (t3:
226 T).((flt c1 t3 c2 (THead k0 t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1
227 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False))))))) \to (or (ex T
228 (\lambda (t3: T).(ty3 g c2 (THead k0 t t0) t3))) (\forall (t3: T).((ty3 g c2
229 (THead k0 t t0) t3) \to False))))) (\lambda (b: B).(\lambda (H2: ((\forall
230 (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Bind b) t t0)) \to (or (ex T
231 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
232 False)))))))).(let H3 \def (H2 c2 t (flt_thead_sx (Bind b) c2 t t0)) in
233 (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2
234 t t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0)
235 t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to False)))
236 (\lambda (H4: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda
237 (t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b)
238 t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to
239 False))) (\lambda (x: T).(\lambda (H5: (ty3 g c2 t x)).(let H6 \def (H2
240 (CHead c2 (Bind b) t) t0 (flt_shift (Bind b) c2 t t0)) in (or_ind (ex T
241 (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3))) (\forall (t3: T).((ty3
242 g (CHead c2 (Bind b) t) t0 t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g
243 c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t
244 t0) t3) \to False))) (\lambda (H7: (ex T (\lambda (t3: T).(ty3 g (CHead c2
245 (Bind b) t) t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t)
246 t0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3)))
247 (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to False))) (\lambda
248 (x0: T).(\lambda (H8: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(or_introl (ex T
249 (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3
250 g c2 (THead (Bind b) t t0) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3
251 g c2 (THead (Bind b) t t0) t3)) (THead (Bind b) t x0) (ty3_bind g c2 t x H5 b
252 t0 x0 H8))))) H7)) (\lambda (H7: ((\forall (t3: T).((ty3 g (CHead c2 (Bind b)
253 t) t0 t3) \to False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead
254 (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3)
255 \to False)) (\lambda (t3: T).(\lambda (H8: (ty3 g c2 (THead (Bind b) t t0)
256 t3)).(ex3_2_ind T T (\lambda (t4: T).(\lambda (_: T).(pc3 c2 (THead (Bind b)
257 t t4) t3))) (\lambda (_: T).(\lambda (t5: T).(ty3 g c2 t t5))) (\lambda (t4:
258 T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0 t4))) False (\lambda (x0:
259 T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda
260 (_: (ty3 g c2 t x1)).(\lambda (H11: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(H7
261 x0 H11)))))) (ty3_gen_bind g b c2 t t0 t3 H8)))))) H6)))) H4)) (\lambda (H4:
262 ((\forall (t3: T).((ty3 g c2 t t3) \to False)))).(or_intror (ex T (\lambda
263 (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2
264 (THead (Bind b) t t0) t3) \to False)) (\lambda (t3: T).(\lambda (H5: (ty3 g
265 c2 (THead (Bind b) t t0) t3)).(ex3_2_ind T T (\lambda (t4: T).(\lambda (_:
266 T).(pc3 c2 (THead (Bind b) t t4) t3))) (\lambda (_: T).(\lambda (t5: T).(ty3
267 g c2 t t5))) (\lambda (t4: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0
268 t4))) False (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead
269 (Bind b) t x0) t3)).(\lambda (H7: (ty3 g c2 t x1)).(\lambda (_: (ty3 g (CHead
270 c2 (Bind b) t) t0 x0)).(H4 x1 H7)))))) (ty3_gen_bind g b c2 t t0 t3 H5))))))
271 H3)))) (\lambda (f: F).(\lambda (H2: ((\forall (c1: C).(\forall (t3: T).((flt
272 c1 t3 c2 (THead (Flat f) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
273 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(F_ind (\lambda
274 (f0: F).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat f0) t
275 t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3
276 g c1 t3 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 (THead
277 (Flat f0) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat f0) t t0) t3)
278 \to False))))) (\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3
279 c2 (THead (Flat Appl) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
280 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(let H4 \def (H3
281 c2 t (flt_thead_sx (Flat Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3:
282 T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)) (or (ex T
283 (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
284 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H5: (ex T
285 (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t
286 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
287 (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)))
288 (\lambda (x: T).(\lambda (H6: (ty3 g c2 t x)).(let H7 \def (H3 c2 t0
289 (flt_thead_dx (Flat Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g
290 c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to False)) (or (ex T (\lambda
291 (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
292 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H8: (ex T (\lambda (t3:
293 T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T
294 (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
295 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x0:
296 T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
297 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
298 (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)))
299 (\lambda (x1: T).(\lambda (H10: (ty3 g c2 x0 x1)).(ex_ind T (\lambda (t3:
300 T).(ty3 g c2 x t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
301 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
302 False))) (\lambda (x2: T).(\lambda (H11: (ty3 g c2 x x2)).(let H12 \def
303 (ty3_sn3 g c2 x x2 H11) in (let H_x \def (nf2_sn3 c2 x H12) in (let H13 \def
304 H_x in (ex2_ind T (\lambda (u: T).(pr3 c2 x u)) (\lambda (u: T).(nf2 c2 u))
305 (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall
306 (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x3:
307 T).(\lambda (H14: (pr3 c2 x x3)).(\lambda (H15: (nf2 c2 x3)).(let H16 \def
308 (ty3_sred_pr3 c2 x x3 H14 g x2 H11) in (let H_x0 \def (pc3_abst_dec g c2 x0
309 x1 H10 x3 x2 H16) in (let H17 \def H_x0 in (or_ind (ex4_2 T T (\lambda (u:
310 T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u:
311 T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1))) (\lambda (_:
312 T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2
313 v2)))) (\forall (u: T).((pc3 c2 x0 (THead (Bind Abst) x3 u)) \to False)) (or
314 (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
315 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H18: (ex4_2
316 T T (\lambda (u: T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u))))
317 (\lambda (u: T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1)))
318 (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda
319 (v2: T).(nf2 c2 v2))))).(ex4_2_ind T T (\lambda (u: T).(\lambda (_: T).(pc3
320 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u: T).(\lambda (v2: T).(ty3 g c2
321 (THead (Bind Abst) v2 u) x1))) (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3
322 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2 v2))) (or (ex T (\lambda (t3:
323 T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
324 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x4: T).(\lambda (x5:
325 T).(\lambda (H19: (pc3 c2 x0 (THead (Bind Abst) x3 x4))).(\lambda (H20: (ty3
326 g c2 (THead (Bind Abst) x5 x4) x1)).(\lambda (H21: (pr3 c2 x3 x5)).(\lambda
327 (_: (nf2 c2 x5)).(let H_y \def (nf2_pr3_unfold c2 x3 x5 H21 H15) in (let H23
328 \def (eq_ind_r T x5 (\lambda (t3: T).(pr3 c2 x3 t3)) H21 x3 H_y) in (let H24
329 \def (eq_ind_r T x5 (\lambda (t3: T).(ty3 g c2 (THead (Bind Abst) t3 x4) x1))
330 H20 x3 H_y) in (or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl)
331 t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
332 False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))
333 (THead (Flat Appl) t (THead (Bind Abst) x3 x4)) (ty3_appl g c2 t x3 (ty3_tred
334 g c2 t x H6 x3 H14) t0 x4 (ty3_conv g c2 (THead (Bind Abst) x3 x4) x1 H24 t0
335 x0 H9 H19))))))))))))) H18)) (\lambda (H18: ((\forall (u: T).((pc3 c2 x0
336 (THead (Bind Abst) x3 u)) \to False)))).(or_intror (ex T (\lambda (t3:
337 T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
338 (THead (Flat Appl) t t0) t3) \to False)) (\lambda (t3: T).(\lambda (H19: (ty3
339 g c2 (THead (Flat Appl) t t0) t3)).(ex3_2_ind T T (\lambda (u: T).(\lambda
340 (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda
341 (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u:
342 T).(\lambda (_: T).(ty3 g c2 t u))) False (\lambda (x4: T).(\lambda (x5:
343 T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) x4 x5))
344 t3)).(\lambda (H21: (ty3 g c2 t0 (THead (Bind Abst) x4 x5))).(\lambda (H22:
345 (ty3 g c2 t x4)).(let H_y \def (ty3_unique g c2 t x4 H22 x H6) in (let H_y0
346 \def (ty3_unique g c2 t0 (THead (Bind Abst) x4 x5) H21 x0 H9) in (H18 x5
347 (pc3_t (THead (Bind Abst) x4 x5) c2 x0 (pc3_s c2 x0 (THead (Bind Abst) x4 x5)
348 H_y0) (THead (Bind Abst) x3 x5) (pc3_head_1 c2 x4 x3 (pc3_t x c2 x4 H_y x3
349 (pc3_pr3_r c2 x x3 H14)) (Bind Abst) x5)))))))))) (ty3_gen_appl g c2 t t0 t3
350 H19)))))) H17))))))) H13)))))) (ty3_correct g c2 t x H6)))) (ty3_correct g c2
351 t0 x0 H9)))) H8)) (\lambda (H8: ((\forall (t3: T).((ty3 g c2 t0 t3) \to
352 False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
353 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
354 False)) (\lambda (t3: T).(\lambda (H9: (ty3 g c2 (THead (Flat Appl) t t0)
355 t3)).(ex3_2_ind T T (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat
356 Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3
357 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2
358 t u))) False (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead
359 (Flat Appl) t (THead (Bind Abst) x0 x1)) t3)).(\lambda (H11: (ty3 g c2 t0
360 (THead (Bind Abst) x0 x1))).(\lambda (_: (ty3 g c2 t x0)).(H8 (THead (Bind
361 Abst) x0 x1) H11)))))) (ty3_gen_appl g c2 t t0 t3 H9)))))) H7)))) H5))
362 (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t t3) \to False)))).(or_intror (ex
363 T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
364 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)) (\lambda (t3:
365 T).(\lambda (H6: (ty3 g c2 (THead (Flat Appl) t t0) t3)).(ex3_2_ind T T
366 (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind
367 Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind
368 Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2 t u))) False
369 (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t
370 (THead (Bind Abst) x0 x1)) t3)).(\lambda (_: (ty3 g c2 t0 (THead (Bind Abst)
371 x0 x1))).(\lambda (H9: (ty3 g c2 t x0)).(H5 x0 H9)))))) (ty3_gen_appl g c2 t
372 t0 t3 H6)))))) H4))) (\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt
373 c1 t3 c2 (THead (Flat Cast) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1
374 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(let H4 \def
375 (H3 c2 t (flt_thead_sx (Flat Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3:
376 T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)) (or (ex T
377 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
378 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (H5: (ex T
379 (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t
380 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
381 (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
382 (\lambda (x: T).(\lambda (H6: (ty3 g c2 t x)).(let H7 \def (H3 c2 t0
383 (flt_thead_dx (Flat Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g
384 c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to False)) (or (ex T (\lambda
385 (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
386 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (H8: (ex T (\lambda (t3:
387 T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T
388 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
389 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (x0:
390 T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
391 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
392 (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
393 (\lambda (x1: T).(\lambda (H10: (ty3 g c2 x0 x1)).(let H_x \def (pc3_dec g c2
394 x0 x1 H10 t x H6) in (let H11 \def H_x in (or_ind (pc3 c2 x0 t) ((pc3 c2 x0
395 t) \to False) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
396 t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
397 (\lambda (H12: (pc3 c2 x0 t)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2
398 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
399 t t0) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat
400 Cast) t t0) t3)) (THead (Flat Cast) x t) (ty3_cast g c2 t0 t (ty3_conv g c2 t
401 x H6 t0 x0 H9 H12) x H6)))) (\lambda (H12: (((pc3 c2 x0 t) \to
402 False))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
403 t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))
404 (\lambda (t3: T).(\lambda (H13: (ty3 g c2 (THead (Flat Cast) t t0)
405 t3)).(ex3_ind T (\lambda (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3))
406 (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False
407 (\lambda (x2: T).(\lambda (_: (pc3 c2 (THead (Flat Cast) x2 t) t3)).(\lambda
408 (H15: (ty3 g c2 t0 t)).(\lambda (H16: (ty3 g c2 t x2)).(let H_y \def
409 (ty3_unique g c2 t x2 H16 x H6) in (let H_y0 \def (ty3_unique g c2 t0 t H15
410 x0 H9) in (H12 (ex2_sym T (pr3 c2 t) (pr3 c2 x0) H_y0)))))))) (ty3_gen_cast g
411 c2 t0 t t3 H13)))))) H11))))) (ty3_correct g c2 t0 x0 H9)))) H8)) (\lambda
412 (H8: ((\forall (t3: T).((ty3 g c2 t0 t3) \to False)))).(or_intror (ex T
413 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
414 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)) (\lambda (t3:
415 T).(\lambda (H9: (ty3 g c2 (THead (Flat Cast) t t0) t3)).(ex3_ind T (\lambda
416 (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3)) (\lambda (_: T).(ty3 g c2 t0
417 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False (\lambda (x0: T).(\lambda (_:
418 (pc3 c2 (THead (Flat Cast) x0 t) t3)).(\lambda (H11: (ty3 g c2 t0
419 t)).(\lambda (_: (ty3 g c2 t x0)).(H8 t H11))))) (ty3_gen_cast g c2 t0 t t3
420 H9)))))) H7)))) H5)) (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t t3) \to
421 False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
422 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
423 False)) (\lambda (t3: T).(\lambda (H6: (ty3 g c2 (THead (Flat Cast) t t0)
424 t3)).(ex3_ind T (\lambda (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3))
425 (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False
426 (\lambda (x0: T).(\lambda (_: (pc3 c2 (THead (Flat Cast) x0 t) t3)).(\lambda
427 (_: (ty3 g c2 t0 t)).(\lambda (H9: (ty3 g c2 t x0)).(ex_ind T (\lambda (t4:
428 T).(ty3 g c2 x0 t4)) False (\lambda (x: T).(\lambda (_: (ty3 g c2 x0 x)).(H5
429 x0 H9))) (ty3_correct g c2 t x0 H9)))))) (ty3_gen_cast g c2 t0 t t3 H6))))))
430 H4))) f H2))) k H1))))))) t2))) c t1))).