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 "LambdaDelta-1/pc3/dec.ma".
19 include "LambdaDelta-1/getl/flt.ma".
21 include "LambdaDelta-1/getl/dec.ma".
23 theorem ty3_inference:
24 \forall (g: G).(\forall (c: C).(\forall (t1: T).(or (ex T (\lambda (t2:
25 T).(ty3 g c t1 t2))) (\forall (t2: T).((ty3 g c t1 t2) \to False)))))
27 \lambda (g: G).(\lambda (c: C).(\lambda (t1: T).(flt_wf_ind (\lambda (c0:
28 C).(\lambda (t: T).(or (ex T (\lambda (t2: T).(ty3 g c0 t t2))) (\forall (t2:
29 T).((ty3 g c0 t t2) \to False))))) (\lambda (c2: C).(\lambda (t2: T).(T_ind
30 (\lambda (t: T).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 t) \to (or
31 (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4)
32 \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall
33 (t3: T).((ty3 g c2 t t3) \to False))))) (\lambda (n: nat).(\lambda (_:
34 ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (TSort n)) \to (or (ex T
35 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
36 False)))))))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TSort n) t3)))
37 (\forall (t3: T).((ty3 g c2 (TSort n) t3) \to False)) (ex_intro T (\lambda
38 (t3: T).(ty3 g c2 (TSort n) t3)) (TSort (next g n)) (ty3_sort g c2 n)))))
39 (\lambda (n: nat).(\lambda (H: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3
40 c2 (TLRef n)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
41 T).((ty3 g c1 t3 t4) \to False)))))))).(let H_x \def (getl_dec c2 n) in (let
42 H0 \def H_x in (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda
43 (v: T).(getl n c2 (CHead e (Bind b) v)))))) (\forall (d: C).((getl n c2 d)
44 \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n)
45 t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (H1:
46 (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n c2 (CHead
47 e (Bind b) v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda
48 (v: T).(getl n c2 (CHead e (Bind b) v))))) (or (ex T (\lambda (t3: T).(ty3 g
49 c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False)))
50 (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2: (getl n c2
51 (CHead x0 (Bind x1) x2))).(let H3 \def (H x0 x2 (getl_flt x1 c2 x0 x2 n H2))
52 in (or_ind (ex T (\lambda (t3: T).(ty3 g x0 x2 t3))) (\forall (t3: T).((ty3 g
53 x0 x2 t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
54 (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (H4: (ex T
55 (\lambda (t3: T).(ty3 g x0 x2 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g x0 x2
56 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3:
57 T).((ty3 g c2 (TLRef n) t3) \to False))) (\lambda (x: T).(\lambda (H5: (ty3 g
58 x0 x2 x)).(B_ind (\lambda (b: B).((getl n c2 (CHead x0 (Bind b) x2)) \to (or
59 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
60 (TLRef n) t3) \to False))))) (\lambda (H6: (getl n c2 (CHead x0 (Bind Abbr)
61 x2))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall
62 (t3: T).((ty3 g c2 (TLRef n) t3) \to False)) (ex_intro T (\lambda (t3:
63 T).(ty3 g c2 (TLRef n) t3)) (lift (S n) O x) (ty3_abbr g n c2 x0 x2 H6 x
64 H5)))) (\lambda (H6: (getl n c2 (CHead x0 (Bind Abst) x2))).(or_introl (ex T
65 (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef
66 n) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))
67 (lift (S n) O x2) (ty3_abst g n c2 x0 x2 H6 x H5)))) (\lambda (H6: (getl n c2
68 (CHead x0 (Bind Void) x2))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2
69 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False))
70 (\lambda (t3: T).(\lambda (H7: (ty3 g c2 (TLRef n) t3)).(or_ind (ex3_3 C T T
71 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
72 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
73 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
74 t))))) (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2
75 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
76 n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
77 T).(ty3 g e u t))))) False (\lambda (H8: (ex3_3 C T T (\lambda (_:
78 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
79 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
80 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind
81 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O
82 t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
83 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
84 t)))) False (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_:
85 (pc3 c2 (lift (S n) O x5) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind
86 Abbr) x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0
87 (Bind Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abbr) x4)
88 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10))
89 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
90 ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False |
91 (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
92 [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
93 \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]) | (Flat
94 _) \Rightarrow False])])) I (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0
95 (Bind Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10)) in (False_ind False
96 H13))))))))) H8)) (\lambda (H8: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
97 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
98 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
99 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
100 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
101 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
102 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
103 t)))) False (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_:
104 (pc3 c2 (lift (S n) O x4) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind
105 Abst) x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0
106 (Bind Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abst) x4)
107 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abst) x4) H10))
108 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
109 ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False |
110 (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
111 [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
112 \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]) | (Flat
113 _) \Rightarrow False])])) I (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0
114 (Bind Void) x2) n H6 (CHead x3 (Bind Abst) x4) H10)) in (False_ind False
115 H13))))))))) H8)) (ty3_gen_lref g c2 t3 n H7)))))) x1 H2))) H4)) (\lambda
116 (H4: ((\forall (t3: T).((ty3 g x0 x2 t3) \to False)))).(or_intror (ex T
117 (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef
118 n) t3) \to False)) (\lambda (t3: T).(\lambda (H5: (ty3 g c2 (TLRef n)
119 t3)).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
120 T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
121 (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
122 T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda (_: C).(\lambda
123 (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e:
124 C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
125 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) False
126 (\lambda (H6: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
127 T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
128 (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
129 T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_:
130 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
131 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
132 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) False
133 (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift
134 (S n) O x5) t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abbr)
135 x4))).(\lambda (H9: (ty3 g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind
136 x1) x2) (\lambda (c0: C).(getl n c2 c0)) H2 (CHead x3 (Bind Abbr) x4)
137 (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in
138 (let H11 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda (_:
139 C).C) with [(CSort _) \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0]))
140 (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0
141 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in ((let H12 \def (f_equal
142 C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
143 \Rightarrow x1 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_:
144 K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0
145 (Bind x1) x2) (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2)
146 n H2 (CHead x3 (Bind Abbr) x4) H8)) in ((let H13 \def (f_equal C T (\lambda
147 (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2
148 | (CHead _ _ t) \Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind
149 Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr)
150 x4) H8)) in (\lambda (_: (eq B x1 Abbr)).(\lambda (H15: (eq C x0 x3)).(let
151 H16 \def (eq_ind_r T x4 (\lambda (t: T).(getl n c2 (CHead x3 (Bind Abbr) t)))
152 H10 x2 H13) in (let H17 \def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5))
153 H9 x2 H13) in (let H18 \def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead
154 c0 (Bind Abbr) x2))) H16 x0 H15) in (let H19 \def (eq_ind_r C x3 (\lambda
155 (c0: C).(ty3 g c0 x2 x5)) H17 x0 H15) in (H4 x5 H19)))))))) H12))
156 H11))))))))) H6)) (\lambda (H6: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
157 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
158 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
159 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
160 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
161 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
162 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
163 t)))) False (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (H7:
164 (pc3 c2 (lift (S n) O x4) t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abst)
165 x4))).(\lambda (H9: (ty3 g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind
166 x1) x2) (\lambda (c0: C).(getl n c2 c0)) H2 (CHead x3 (Bind Abst) x4)
167 (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in
168 (let H11 \def (f_equal C C (\lambda (e: C).(match e in C return (\lambda (_:
169 C).C) with [(CSort _) \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0]))
170 (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0
171 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in ((let H12 \def (f_equal
172 C B (\lambda (e: C).(match e in C return (\lambda (_: C).B) with [(CSort _)
173 \Rightarrow x1 | (CHead _ k _) \Rightarrow (match k in K return (\lambda (_:
174 K).B) with [(Bind b) \Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0
175 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2)
176 n H2 (CHead x3 (Bind Abst) x4) H8)) in ((let H13 \def (f_equal C T (\lambda
177 (e: C).(match e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2
178 | (CHead _ _ t) \Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind
179 Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst)
180 x4) H8)) in (\lambda (_: (eq B x1 Abst)).(\lambda (H15: (eq C x0 x3)).(let
181 H16 \def (eq_ind_r T x4 (\lambda (t: T).(getl n c2 (CHead x3 (Bind Abst) t)))
182 H10 x2 H13) in (let H17 \def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5))
183 H9 x2 H13) in (let H18 \def (eq_ind_r T x4 (\lambda (t: T).(pc3 c2 (lift (S
184 n) O t) t3)) H7 x2 H13) in (let H19 \def (eq_ind_r C x3 (\lambda (c0:
185 C).(getl n c2 (CHead c0 (Bind Abst) x2))) H16 x0 H15) in (let H20 \def
186 (eq_ind_r C x3 (\lambda (c0: C).(ty3 g c0 x2 x5)) H17 x0 H15) in (H4 x5
187 H20))))))))) H12)) H11))))))))) H6)) (ty3_gen_lref g c2 t3 n H5))))))
188 H3)))))) H1)) (\lambda (H1: ((\forall (d: C).((getl n c2 d) \to (\forall (P:
189 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
190 (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to False)) (\lambda (t3:
191 T).(\lambda (H2: (ty3 g c2 (TLRef n) t3)).(or_ind (ex3_3 C T T (\lambda (_:
192 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
193 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
194 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T
195 T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
196 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
197 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
198 t))))) False (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (_:
199 T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
200 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
201 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
202 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
203 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
204 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
205 t)))) False (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_:
206 (pc3 c2 (lift (S n) O x2) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abbr)
207 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abbr) x1) H5
208 False))))))) H3)) (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
209 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
210 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
211 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
212 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
213 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
214 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
215 t)))) False (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_:
216 (pc3 c2 (lift (S n) O x1) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abst)
217 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abst) x1) H5
218 False))))))) H3)) (ty3_gen_lref g c2 t3 n H2)))))) H0))))) (\lambda (k:
219 K).(\lambda (t: T).(\lambda (_: ((((\forall (c1: C).(\forall (t3: T).((flt c1
220 t3 c2 t) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
221 T).((ty3 g c1 t3 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g
222 c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)))))).(\lambda (t0:
223 T).(\lambda (_: ((((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 t0) \to
224 (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3
225 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 t0 t3)))
226 (\forall (t3: T).((ty3 g c2 t0 t3) \to False)))))).(\lambda (H1: ((\forall
227 (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead k t t0)) \to (or (ex T
228 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
229 False)))))))).(K_ind (\lambda (k0: K).(((\forall (c1: C).(\forall (t3:
230 T).((flt c1 t3 c2 (THead k0 t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1
231 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False))))))) \to (or (ex T
232 (\lambda (t3: T).(ty3 g c2 (THead k0 t t0) t3))) (\forall (t3: T).((ty3 g c2
233 (THead k0 t t0) t3) \to False))))) (\lambda (b: B).(\lambda (H2: ((\forall
234 (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Bind b) t t0)) \to (or (ex T
235 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
236 False)))))))).(let H3 \def (H2 c2 t (flt_thead_sx (Bind b) c2 t t0)) in
237 (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2
238 t t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0)
239 t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to False)))
240 (\lambda (H4: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda
241 (t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b)
242 t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to
243 False))) (\lambda (x: T).(\lambda (H5: (ty3 g c2 t x)).(let H6 \def (H2
244 (CHead c2 (Bind b) t) t0 (flt_shift (Bind b) c2 t t0)) in (or_ind (ex T
245 (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3))) (\forall (t3: T).((ty3
246 g (CHead c2 (Bind b) t) t0 t3) \to False)) (or (ex T (\lambda (t3: T).(ty3 g
247 c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t
248 t0) t3) \to False))) (\lambda (H7: (ex T (\lambda (t3: T).(ty3 g (CHead c2
249 (Bind b) t) t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t)
250 t0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3)))
251 (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to False))) (\lambda
252 (x0: T).(\lambda (H8: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(or_introl (ex T
253 (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3
254 g c2 (THead (Bind b) t t0) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3
255 g c2 (THead (Bind b) t t0) t3)) (THead (Bind b) t x0) (ty3_bind g c2 t x H5 b
256 t0 x0 H8))))) H7)) (\lambda (H7: ((\forall (t3: T).((ty3 g (CHead c2 (Bind b)
257 t) t0 t3) \to False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead
258 (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3)
259 \to False)) (\lambda (t3: T).(\lambda (H8: (ty3 g c2 (THead (Bind b) t t0)
260 t3)).(ex3_2_ind T T (\lambda (t4: T).(\lambda (_: T).(pc3 c2 (THead (Bind b)
261 t t4) t3))) (\lambda (_: T).(\lambda (t5: T).(ty3 g c2 t t5))) (\lambda (t4:
262 T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0 t4))) False (\lambda (x0:
263 T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda
264 (_: (ty3 g c2 t x1)).(\lambda (H11: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(H7
265 x0 H11)))))) (ty3_gen_bind g b c2 t t0 t3 H8)))))) H6)))) H4)) (\lambda (H4:
266 ((\forall (t3: T).((ty3 g c2 t t3) \to False)))).(or_intror (ex T (\lambda
267 (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2
268 (THead (Bind b) t t0) t3) \to False)) (\lambda (t3: T).(\lambda (H5: (ty3 g
269 c2 (THead (Bind b) t t0) t3)).(ex3_2_ind T T (\lambda (t4: T).(\lambda (_:
270 T).(pc3 c2 (THead (Bind b) t t4) t3))) (\lambda (_: T).(\lambda (t5: T).(ty3
271 g c2 t t5))) (\lambda (t4: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0
272 t4))) False (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead
273 (Bind b) t x0) t3)).(\lambda (H7: (ty3 g c2 t x1)).(\lambda (_: (ty3 g (CHead
274 c2 (Bind b) t) t0 x0)).(H4 x1 H7)))))) (ty3_gen_bind g b c2 t t0 t3 H5))))))
275 H3)))) (\lambda (f: F).(\lambda (H2: ((\forall (c1: C).(\forall (t3: T).((flt
276 c1 t3 c2 (THead (Flat f) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
277 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(F_ind (\lambda
278 (f0: F).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat f0) t
279 t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3
280 g c1 t3 t4) \to False))))))) \to (or (ex T (\lambda (t3: T).(ty3 g c2 (THead
281 (Flat f0) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat f0) t t0) t3)
282 \to False))))) (\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3
283 c2 (THead (Flat Appl) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
284 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(let H4 \def (H3
285 c2 t (flt_thead_sx (Flat Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3:
286 T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)) (or (ex T
287 (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
288 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H5: (ex T
289 (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t
290 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
291 (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)))
292 (\lambda (x: T).(\lambda (H6: (ty3 g c2 t x)).(let H7 \def (H3 c2 t0
293 (flt_thead_dx (Flat Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g
294 c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to False)) (or (ex T (\lambda
295 (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
296 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H8: (ex T (\lambda (t3:
297 T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T
298 (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
299 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x0:
300 T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
301 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
302 (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)))
303 (\lambda (x1: T).(\lambda (H10: (ty3 g c2 x0 x1)).(ex_ind T (\lambda (t3:
304 T).(ty3 g c2 x t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
305 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
306 False))) (\lambda (x2: T).(\lambda (H11: (ty3 g c2 x x2)).(let H12 \def
307 (ty3_sn3 g c2 x x2 H11) in (let H_x \def (nf2_sn3 c2 x H12) in (let H13 \def
308 H_x in (ex2_ind T (\lambda (u: T).(pr3 c2 x u)) (\lambda (u: T).(nf2 c2 u))
309 (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall
310 (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x3:
311 T).(\lambda (H14: (pr3 c2 x x3)).(\lambda (H15: (nf2 c2 x3)).(let H16 \def
312 (ty3_sred_pr3 c2 x x3 H14 g x2 H11) in (let H_x0 \def (pc3_abst_dec g c2 x0
313 x1 H10 x3 x2 H16) in (let H17 \def H_x0 in (or_ind (ex4_2 T T (\lambda (u:
314 T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u:
315 T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1))) (\lambda (_:
316 T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2
317 v2)))) (\forall (u: T).((pc3 c2 x0 (THead (Bind Abst) x3 u)) \to False)) (or
318 (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
319 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (H18: (ex4_2
320 T T (\lambda (u: T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u))))
321 (\lambda (u: T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1)))
322 (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda
323 (v2: T).(nf2 c2 v2))))).(ex4_2_ind T T (\lambda (u: T).(\lambda (_: T).(pc3
324 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u: T).(\lambda (v2: T).(ty3 g c2
325 (THead (Bind Abst) v2 u) x1))) (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3
326 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2 v2))) (or (ex T (\lambda (t3:
327 T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
328 (THead (Flat Appl) t t0) t3) \to False))) (\lambda (x4: T).(\lambda (x5:
329 T).(\lambda (H19: (pc3 c2 x0 (THead (Bind Abst) x3 x4))).(\lambda (H20: (ty3
330 g c2 (THead (Bind Abst) x5 x4) x1)).(\lambda (H21: (pr3 c2 x3 x5)).(\lambda
331 (_: (nf2 c2 x5)).(let H_y \def (nf2_pr3_unfold c2 x3 x5 H21 H15) in (let H23
332 \def (eq_ind_r T x5 (\lambda (t3: T).(pr3 c2 x3 t3)) H21 x3 H_y) in (let H24
333 \def (eq_ind_r T x5 (\lambda (t3: T).(ty3 g c2 (THead (Bind Abst) t3 x4) x1))
334 H20 x3 H_y) in (or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl)
335 t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
336 False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))
337 (THead (Flat Appl) t (THead (Bind Abst) x3 x4)) (ty3_appl g c2 t x3 (ty3_tred
338 g c2 t x H6 x3 H14) t0 x4 (ty3_conv g c2 (THead (Bind Abst) x3 x4) x1 H24 t0
339 x0 H9 H19))))))))))))) H18)) (\lambda (H18: ((\forall (u: T).((pc3 c2 x0
340 (THead (Bind Abst) x3 u)) \to False)))).(or_intror (ex T (\lambda (t3:
341 T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
342 (THead (Flat Appl) t t0) t3) \to False)) (\lambda (t3: T).(\lambda (H19: (ty3
343 g c2 (THead (Flat Appl) t t0) t3)).(ex3_2_ind T T (\lambda (u: T).(\lambda
344 (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda
345 (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u:
346 T).(\lambda (_: T).(ty3 g c2 t u))) False (\lambda (x4: T).(\lambda (x5:
347 T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) x4 x5))
348 t3)).(\lambda (H21: (ty3 g c2 t0 (THead (Bind Abst) x4 x5))).(\lambda (H22:
349 (ty3 g c2 t x4)).(let H_y \def (ty3_unique g c2 t x4 H22 x H6) in (let H_y0
350 \def (ty3_unique g c2 t0 (THead (Bind Abst) x4 x5) H21 x0 H9) in (H18 x5
351 (pc3_t (THead (Bind Abst) x4 x5) c2 x0 (pc3_s c2 x0 (THead (Bind Abst) x4 x5)
352 H_y0) (THead (Bind Abst) x3 x5) (pc3_head_1 c2 x4 x3 (pc3_t x c2 x4 H_y x3
353 (pc3_pr3_r c2 x x3 H14)) (Bind Abst) x5)))))))))) (ty3_gen_appl g c2 t t0 t3
354 H19)))))) H17))))))) H13)))))) (ty3_correct g c2 t x H6)))) (ty3_correct g c2
355 t0 x0 H9)))) H8)) (\lambda (H8: ((\forall (t3: T).((ty3 g c2 t0 t3) \to
356 False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
357 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
358 False)) (\lambda (t3: T).(\lambda (H9: (ty3 g c2 (THead (Flat Appl) t t0)
359 t3)).(ex3_2_ind T T (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat
360 Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3
361 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2
362 t u))) False (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead
363 (Flat Appl) t (THead (Bind Abst) x0 x1)) t3)).(\lambda (H11: (ty3 g c2 t0
364 (THead (Bind Abst) x0 x1))).(\lambda (_: (ty3 g c2 t x0)).(H8 (THead (Bind
365 Abst) x0 x1) H11)))))) (ty3_gen_appl g c2 t t0 t3 H9)))))) H7)))) H5))
366 (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t t3) \to False)))).(or_intror (ex
367 T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
368 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to False)) (\lambda (t3:
369 T).(\lambda (H6: (ty3 g c2 (THead (Flat Appl) t t0) t3)).(ex3_2_ind T T
370 (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind
371 Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind
372 Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2 t u))) False
373 (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t
374 (THead (Bind Abst) x0 x1)) t3)).(\lambda (_: (ty3 g c2 t0 (THead (Bind Abst)
375 x0 x1))).(\lambda (H9: (ty3 g c2 t x0)).(H5 x0 H9)))))) (ty3_gen_appl g c2 t
376 t0 t3 H6)))))) H4))) (\lambda (H3: ((\forall (c1: C).(\forall (t3: T).((flt
377 c1 t3 c2 (THead (Flat Cast) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1
378 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to False)))))))).(let H4 \def
379 (H3 c2 t (flt_thead_sx (Flat Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3:
380 T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to False)) (or (ex T
381 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
382 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (H5: (ex T
383 (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t
384 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
385 (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
386 (\lambda (x: T).(\lambda (H6: (ty3 g c2 t x)).(let H7 \def (H3 c2 t0
387 (flt_thead_dx (Flat Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g
388 c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to False)) (or (ex T (\lambda
389 (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
390 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (H8: (ex T (\lambda (t3:
391 T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T
392 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
393 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))) (\lambda (x0:
394 T).(\lambda (H9: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
395 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
396 (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
397 (\lambda (x1: T).(\lambda (H10: (ty3 g c2 x0 x1)).(let H_x \def (pc3_dec g c2
398 x0 x1 H10 t x H6) in (let H11 \def H_x in (or_ind (pc3 c2 x0 t) ((pc3 c2 x0
399 t) \to False) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
400 t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)))
401 (\lambda (H12: (pc3 c2 x0 t)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2
402 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
403 t t0) t3) \to False)) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat
404 Cast) t t0) t3)) (THead (Flat Cast) x t) (ty3_cast g c2 t0 t (ty3_conv g c2 t
405 x H6 t0 x0 H9 H12) x H6)))) (\lambda (H12: (((pc3 c2 x0 t) \to
406 False))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0)
407 t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False))
408 (\lambda (t3: T).(\lambda (H13: (ty3 g c2 (THead (Flat Cast) t t0)
409 t3)).(ex3_ind T (\lambda (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3))
410 (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False
411 (\lambda (x2: T).(\lambda (_: (pc3 c2 (THead (Flat Cast) x2 t) t3)).(\lambda
412 (H15: (ty3 g c2 t0 t)).(\lambda (H16: (ty3 g c2 t x2)).(let H_y \def
413 (ty3_unique g c2 t x2 H16 x H6) in (let H_y0 \def (ty3_unique g c2 t0 t H15
414 x0 H9) in (H12 (ex2_sym T (pr3 c2 t) (pr3 c2 x0) H_y0)))))))) (ty3_gen_cast g
415 c2 t0 t t3 H13)))))) H11))))) (ty3_correct g c2 t0 x0 H9)))) H8)) (\lambda
416 (H8: ((\forall (t3: T).((ty3 g c2 t0 t3) \to False)))).(or_intror (ex T
417 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
418 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to False)) (\lambda (t3:
419 T).(\lambda (H9: (ty3 g c2 (THead (Flat Cast) t t0) t3)).(ex3_ind T (\lambda
420 (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3)) (\lambda (_: T).(ty3 g c2 t0
421 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False (\lambda (x0: T).(\lambda (_:
422 (pc3 c2 (THead (Flat Cast) x0 t) t3)).(\lambda (H11: (ty3 g c2 t0
423 t)).(\lambda (_: (ty3 g c2 t x0)).(H8 t H11))))) (ty3_gen_cast g c2 t0 t t3
424 H9)))))) H7)))) H5)) (\lambda (H5: ((\forall (t3: T).((ty3 g c2 t t3) \to
425 False)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
426 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
427 False)) (\lambda (t3: T).(\lambda (H6: (ty3 g c2 (THead (Flat Cast) t t0)
428 t3)).(ex3_ind T (\lambda (t4: T).(pc3 c2 (THead (Flat Cast) t4 t) t3))
429 (\lambda (_: T).(ty3 g c2 t0 t)) (\lambda (t4: T).(ty3 g c2 t t4)) False
430 (\lambda (x0: T).(\lambda (_: (pc3 c2 (THead (Flat Cast) x0 t) t3)).(\lambda
431 (_: (ty3 g c2 t0 t)).(\lambda (H9: (ty3 g c2 t x0)).(ex_ind T (\lambda (t4:
432 T).(ty3 g c2 x0 t4)) False (\lambda (x: T).(\lambda (_: (ty3 g c2 x0 x)).(H5
433 x0 H9))) (ty3_correct g c2 t x0 H9)))))) (ty3_gen_cast g c2 t0 t t3 H6))))))
434 H4))) f H2))) k H1))))))) t2))) c t1))).