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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 set "baseuri" "cic:/matita/LAMBDA-TYPES/Level-1/LambdaDelta/ty3/dec".
19 include "ty3/pr3_props.ma".
23 include "getl/flt.ma".
25 include "getl/dec.ma".
27 theorem ty3_inference:
28 \forall (g: G).(\forall (c: C).(\forall (t1: T).(or (ex T (\lambda (t2:
29 T).(ty3 g c t1 t2))) (\forall (t2: T).((ty3 g c t1 t2) \to (\forall (P:
32 \lambda (g: G).(\lambda (c: C).(\lambda (t1: T).(flt_wf_ind (\lambda (c0:
33 C).(\lambda (t: T).(or (ex T (\lambda (t2: T).(ty3 g c0 t t2))) (\forall (t2:
34 T).((ty3 g c0 t t2) \to (\forall (P: Prop).P)))))) (\lambda (c2: C).(\lambda
35 (t2: T).(match t2 in T return (\lambda (t: T).(((\forall (c1: C).(\forall
36 (t3: T).((flt c1 t3 c2 t) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4)))
37 (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or
38 (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2 t t3)
39 \to (\forall (P: Prop).P)))))) with [(TSort n) \Rightarrow (\lambda (_:
40 ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (TSort n)) \to (or (ex T
41 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
42 (\forall (P: Prop).P))))))))).(or_introl (ex T (\lambda (t3: T).(ty3 g c2
43 (TSort n) t3))) (\forall (t3: T).((ty3 g c2 (TSort n) t3) \to (\forall (P:
44 Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (TSort n) t3)) (TSort (next
45 g n)) (ty3_sort g c2 n)))) | (TLRef n) \Rightarrow (\lambda (H: ((\forall
46 (c1: C).(\forall (t3: T).((flt c1 t3 c2 (TLRef n)) \to (or (ex T (\lambda
47 (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall
48 (P: Prop).P))))))))).(let H_x \def (getl_dec c2 n) in (let H0 \def H_x in
49 (or_ind (ex_3 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n
50 c2 (CHead e (Bind b) v)))))) (\forall (d: C).((getl n c2 d) \to (\forall (P:
51 Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3:
52 T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))) (\lambda (H1: (ex_3
53 C B T (\lambda (e: C).(\lambda (b: B).(\lambda (v: T).(getl n c2 (CHead e
54 (Bind b) v))))))).(ex_3_ind C B T (\lambda (e: C).(\lambda (b: B).(\lambda
55 (v: T).(getl n c2 (CHead e (Bind b) v))))) (or (ex T (\lambda (t3: T).(ty3 g
56 c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P:
57 Prop).P)))) (\lambda (x0: C).(\lambda (x1: B).(\lambda (x2: T).(\lambda (H2:
58 (getl n c2 (CHead x0 (Bind x1) x2))).(let H3 \def (H x0 x2 (getl_flt x1 c2 x0
59 x2 n H2)) in (or_ind (ex T (\lambda (t3: T).(ty3 g x0 x2 t3))) (\forall (t3:
60 T).((ty3 g x0 x2 t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3:
61 T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to
62 (\forall (P: Prop).P)))) (\lambda (H4: (ex T (\lambda (t3: T).(ty3 g x0 x2
63 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g x0 x2 t3)) (or (ex T (\lambda (t3:
64 T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to
65 (\forall (P: Prop).P)))) (\lambda (x: T).(\lambda (H5: (ty3 g x0 x2
66 x)).((match x1 in B return (\lambda (b: B).((getl n c2 (CHead x0 (Bind b)
67 x2)) \to (or (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3:
68 T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))))) with [Abbr
69 \Rightarrow (\lambda (H6: (getl n c2 (CHead x0 (Bind Abbr) x2))).(or_introl
70 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
71 (TLRef n) t3) \to (\forall (P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g
72 c2 (TLRef n) t3)) (lift (S n) O x) (ty3_abbr g n c2 x0 x2 H6 x H5)))) | Abst
73 \Rightarrow (\lambda (H6: (getl n c2 (CHead x0 (Bind Abst) x2))).(or_introl
74 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
75 (TLRef n) t3) \to (\forall (P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g
76 c2 (TLRef n) t3)) (lift (S n) O x2) (ty3_abst g n c2 x0 x2 H6 x H5)))) | Void
77 \Rightarrow (\lambda (H6: (getl n c2 (CHead x0 (Bind Void) x2))).(or_intror
78 (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2
79 (TLRef n) t3) \to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H7: (ty3
80 g c2 (TLRef n) t3)).(\lambda (P: Prop).(or_ind (ex3_3 C T T (\lambda (_:
81 C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda
82 (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u)))))
83 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T
84 T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
85 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
86 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
87 t))))) P (\lambda (H8: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda
88 (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u:
89 T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
90 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
91 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
92 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
93 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
94 t)))) P (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3
95 c2 (lift (S n) O x5) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind Abbr)
96 x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0 (Bind
97 Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abbr) x4)
98 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10))
99 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
100 ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False |
101 (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
102 [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
103 \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]) | (Flat
104 _) \Rightarrow False])])) I (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0
105 (Bind Void) x2) n H6 (CHead x3 (Bind Abbr) x4) H10)) in (False_ind P
106 H13))))))))) H8)) (\lambda (H8: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
107 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
108 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
109 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
110 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
111 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
112 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
113 t)))) P (\lambda (x3: C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3
114 c2 (lift (S n) O x4) t3)).(\lambda (H10: (getl n c2 (CHead x3 (Bind Abst)
115 x4))).(\lambda (_: (ty3 g x3 x4 x5)).(let H12 \def (eq_ind C (CHead x0 (Bind
116 Void) x2) (\lambda (c0: C).(getl n c2 c0)) H6 (CHead x3 (Bind Abst) x4)
117 (getl_mono c2 (CHead x0 (Bind Void) x2) n H6 (CHead x3 (Bind Abst) x4) H10))
118 in (let H13 \def (eq_ind C (CHead x0 (Bind Void) x2) (\lambda (ee: C).(match
119 ee in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False |
120 (CHead _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
121 [(Bind b) \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr
122 \Rightarrow False | Abst \Rightarrow False | Void \Rightarrow True]) | (Flat
123 _) \Rightarrow False])])) I (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0
124 (Bind Void) x2) n H6 (CHead x3 (Bind Abst) x4) H10)) in (False_ind P
125 H13))))))))) H8)) (ty3_gen_lref g c2 t3 n H7)))))))]) H2))) H4)) (\lambda
126 (H4: ((\forall (t3: T).((ty3 g x0 x2 t3) \to (\forall (P:
127 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (TLRef n) t3)))
128 (\forall (t3: T).((ty3 g c2 (TLRef n) t3) \to (\forall (P: Prop).P)))
129 (\lambda (t3: T).(\lambda (H5: (ty3 g c2 (TLRef n) t3)).(\lambda (P:
130 Prop).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t:
131 T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda
132 (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u:
133 T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda (_: C).(\lambda
134 (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e:
135 C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u)))))
136 (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) P (\lambda
137 (H6: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2
138 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
139 n c2 (CHead e (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
140 T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (_:
141 T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
142 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
143 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3:
144 C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (lift (S n) O x5)
145 t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abbr) x4))).(\lambda (H9: (ty3
146 g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind x1) x2) (\lambda (c0:
147 C).(getl n c2 c0)) H2 (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind
148 x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in (let H11 \def (f_equal C C
149 (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
150 \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0])) (CHead x0 (Bind x1) x2)
151 (CHead x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead
152 x3 (Bind Abbr) x4) H8)) in ((let H12 \def (f_equal C B (\lambda (e: C).(match
153 e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow x1 | (CHead _ k
154 _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b)
155 \Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0 (Bind x1) x2) (CHead
156 x3 (Bind Abbr) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind
157 Abbr) x4) H8)) in ((let H13 \def (f_equal C T (\lambda (e: C).(match e in C
158 return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2 | (CHead _ _ t)
159 \Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abbr) x4) (getl_mono
160 c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abbr) x4) H8)) in (\lambda
161 (_: (eq B x1 Abbr)).(\lambda (H15: (eq C x0 x3)).(let H16 \def (eq_ind_r T x4
162 (\lambda (t: T).(getl n c2 (CHead x3 (Bind Abbr) t))) H10 x2 H13) in (let H17
163 \def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2 H13) in (let H18
164 \def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead c0 (Bind Abbr) x2)))
165 H16 x0 H15) in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(ty3 g c0 x2
166 x5)) H17 x0 H15) in (H4 x5 H19 P)))))))) H12)) H11))))))))) H6)) (\lambda
167 (H6: (ex3_3 C T T (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2
168 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl
169 n c2 (CHead e (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t:
170 T).(ty3 g e u t)))))).(ex3_3_ind C T T (\lambda (_: C).(\lambda (u:
171 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
172 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
173 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))) P (\lambda (x3:
174 C).(\lambda (x4: T).(\lambda (x5: T).(\lambda (H7: (pc3 c2 (lift (S n) O x4)
175 t3)).(\lambda (H8: (getl n c2 (CHead x3 (Bind Abst) x4))).(\lambda (H9: (ty3
176 g x3 x4 x5)).(let H10 \def (eq_ind C (CHead x0 (Bind x1) x2) (\lambda (c0:
177 C).(getl n c2 c0)) H2 (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind
178 x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in (let H11 \def (f_equal C C
179 (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
180 \Rightarrow x0 | (CHead c0 _ _) \Rightarrow c0])) (CHead x0 (Bind x1) x2)
181 (CHead x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead
182 x3 (Bind Abst) x4) H8)) in ((let H12 \def (f_equal C B (\lambda (e: C).(match
183 e in C return (\lambda (_: C).B) with [(CSort _) \Rightarrow x1 | (CHead _ k
184 _) \Rightarrow (match k in K return (\lambda (_: K).B) with [(Bind b)
185 \Rightarrow b | (Flat _) \Rightarrow x1])])) (CHead x0 (Bind x1) x2) (CHead
186 x3 (Bind Abst) x4) (getl_mono c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind
187 Abst) x4) H8)) in ((let H13 \def (f_equal C T (\lambda (e: C).(match e in C
188 return (\lambda (_: C).T) with [(CSort _) \Rightarrow x2 | (CHead _ _ t)
189 \Rightarrow t])) (CHead x0 (Bind x1) x2) (CHead x3 (Bind Abst) x4) (getl_mono
190 c2 (CHead x0 (Bind x1) x2) n H2 (CHead x3 (Bind Abst) x4) H8)) in (\lambda
191 (_: (eq B x1 Abst)).(\lambda (H15: (eq C x0 x3)).(let H16 \def (eq_ind_r T x4
192 (\lambda (t: T).(getl n c2 (CHead x3 (Bind Abst) t))) H10 x2 H13) in (let H17
193 \def (eq_ind_r T x4 (\lambda (t: T).(ty3 g x3 t x5)) H9 x2 H13) in (let H18
194 \def (eq_ind_r T x4 (\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)) H7 x2 H13)
195 in (let H19 \def (eq_ind_r C x3 (\lambda (c0: C).(getl n c2 (CHead c0 (Bind
196 Abst) x2))) H16 x0 H15) in (let H20 \def (eq_ind_r C x3 (\lambda (c0: C).(ty3
197 g c0 x2 x5)) H17 x0 H15) in (H4 x5 H20 P))))))))) H12)) H11))))))))) H6))
198 (ty3_gen_lref g c2 t3 n H5))))))) H3)))))) H1)) (\lambda (H1: ((\forall (d:
199 C).((getl n c2 d) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda
200 (t3: T).(ty3 g c2 (TLRef n) t3))) (\forall (t3: T).((ty3 g c2 (TLRef n) t3)
201 \to (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H2: (ty3 g c2 (TLRef
202 n) t3)).(\lambda (P: Prop).(or_ind (ex3_3 C T T (\lambda (_: C).(\lambda (_:
203 T).(\lambda (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda
204 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
205 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t))))) (ex3_3 C T T (\lambda
206 (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3))))
207 (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind
208 Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
209 t))))) P (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (_: T).(\lambda
210 (t: T).(pc3 c2 (lift (S n) O t) t3)))) (\lambda (e: C).(\lambda (u:
211 T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abbr) u))))) (\lambda (e:
212 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
213 (\lambda (_: C).(\lambda (_: T).(\lambda (t: T).(pc3 c2 (lift (S n) O t)
214 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
215 (Bind Abbr) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
216 t)))) P (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3
217 c2 (lift (S n) O x2) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abbr)
218 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abbr) x1) H5
219 P))))))) H3)) (\lambda (H3: (ex3_3 C T T (\lambda (_: C).(\lambda (u:
220 T).(\lambda (_: T).(pc3 c2 (lift (S n) O u) t3)))) (\lambda (e: C).(\lambda
221 (u: T).(\lambda (_: T).(getl n c2 (CHead e (Bind Abst) u))))) (\lambda (e:
222 C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u t)))))).(ex3_3_ind C T T
223 (\lambda (_: C).(\lambda (u: T).(\lambda (_: T).(pc3 c2 (lift (S n) O u)
224 t3)))) (\lambda (e: C).(\lambda (u: T).(\lambda (_: T).(getl n c2 (CHead e
225 (Bind Abst) u))))) (\lambda (e: C).(\lambda (u: T).(\lambda (t: T).(ty3 g e u
226 t)))) P (\lambda (x0: C).(\lambda (x1: T).(\lambda (x2: T).(\lambda (_: (pc3
227 c2 (lift (S n) O x1) t3)).(\lambda (H5: (getl n c2 (CHead x0 (Bind Abst)
228 x1))).(\lambda (_: (ty3 g x0 x1 x2)).(H1 (CHead x0 (Bind Abst) x1) H5
229 P))))))) H3)) (ty3_gen_lref g c2 t3 n H2))))))) H0)))) | (THead k t t0)
230 \Rightarrow (\lambda (H: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2
231 (THead k t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall
232 (t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P))))))))).((match k in K
233 return (\lambda (k0: K).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2
234 (THead k0 t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall
235 (t4: T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or (ex T
236 (\lambda (t3: T).(ty3 g c2 (THead k0 t t0) t3))) (\forall (t3: T).((ty3 g c2
237 (THead k0 t t0) t3) \to (\forall (P: Prop).P)))))) with [(Bind b) \Rightarrow
238 (\lambda (H0: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Bind
239 b) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4:
240 T).((ty3 g c1 t3 t4) \to (\forall (P: Prop).P))))))))).(let H1 \def (H0 c2 t
241 (flt_thead_sx (Bind b) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g c2
242 t t3))) (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P: Prop).P))) (or (ex
243 T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3:
244 T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda
245 (H2: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda (t3:
246 T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
247 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
248 (P: Prop).P)))) (\lambda (x: T).(\lambda (H3: (ty3 g c2 t x)).(let H4 \def
249 (H0 (CHead c2 (Bind b) t) t0 (flt_shift (Bind b) c2 t t0)) in (or_ind (ex T
250 (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3))) (\forall (t3: T).((ty3
251 g (CHead c2 (Bind b) t) t0 t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda
252 (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2
253 (THead (Bind b) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H5: (ex T
254 (\lambda (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3)))).(ex_ind T (\lambda
255 (t3: T).(ty3 g (CHead c2 (Bind b) t) t0 t3)) (or (ex T (\lambda (t3: T).(ty3
256 g c2 (THead (Bind b) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b)
257 t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x0: T).(\lambda (H6: (ty3 g
258 (CHead c2 (Bind b) t) t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g (CHead c2
259 (Bind b) t) x0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
260 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
261 (P: Prop).P)))) (\lambda (x1: T).(\lambda (H7: (ty3 g (CHead c2 (Bind b) t)
262 x0 x1)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0)
263 t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall (P:
264 Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t t0) t3))
265 (THead (Bind b) t x0) (ty3_bind g c2 t x H3 b t0 x0 H6 x1 H7)))))
266 (ty3_correct g (CHead c2 (Bind b) t) t0 x0 H6)))) H5)) (\lambda (H5:
267 ((\forall (t3: T).((ty3 g (CHead c2 (Bind b) t) t0 t3) \to (\forall (P:
268 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
269 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
270 (P: Prop).P))) (\lambda (t3: T).(\lambda (H6: (ty3 g c2 (THead (Bind b) t t0)
271 t3)).(\lambda (P: Prop).(ex4_3_ind T T T (\lambda (t4: T).(\lambda (_:
272 T).(\lambda (_: T).(pc3 c2 (THead (Bind b) t t4) t3)))) (\lambda (_:
273 T).(\lambda (t5: T).(\lambda (_: T).(ty3 g c2 t t5)))) (\lambda (t4:
274 T).(\lambda (_: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0 t4))))
275 (\lambda (t4: T).(\lambda (_: T).(\lambda (t6: T).(ty3 g (CHead c2 (Bind b)
276 t) t4 t6)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (x2: T).(\lambda
277 (_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda (_: (ty3 g c2 t x1)).(\lambda
278 (H9: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(\lambda (_: (ty3 g (CHead c2 (Bind
279 b) t) x0 x2)).(H5 x0 H9 P)))))))) (ty3_gen_bind g b c2 t t0 t3 H6)))))))
280 H4)))) H2)) (\lambda (H2: ((\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P:
281 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Bind b) t
282 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Bind b) t t0) t3) \to (\forall
283 (P: Prop).P))) (\lambda (t3: T).(\lambda (H3: (ty3 g c2 (THead (Bind b) t t0)
284 t3)).(\lambda (P: Prop).(ex4_3_ind T T T (\lambda (t4: T).(\lambda (_:
285 T).(\lambda (_: T).(pc3 c2 (THead (Bind b) t t4) t3)))) (\lambda (_:
286 T).(\lambda (t5: T).(\lambda (_: T).(ty3 g c2 t t5)))) (\lambda (t4:
287 T).(\lambda (_: T).(\lambda (_: T).(ty3 g (CHead c2 (Bind b) t) t0 t4))))
288 (\lambda (t4: T).(\lambda (_: T).(\lambda (t6: T).(ty3 g (CHead c2 (Bind b)
289 t) t4 t6)))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (x2: T).(\lambda
290 (_: (pc3 c2 (THead (Bind b) t x0) t3)).(\lambda (H5: (ty3 g c2 t
291 x1)).(\lambda (_: (ty3 g (CHead c2 (Bind b) t) t0 x0)).(\lambda (_: (ty3 g
292 (CHead c2 (Bind b) t) x0 x2)).(H2 x1 H5 P)))))))) (ty3_gen_bind g b c2 t t0
293 t3 H3))))))) H1))) | (Flat f) \Rightarrow (\lambda (H0: ((\forall (c1:
294 C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat f) t t0)) \to (or (ex T
295 (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to
296 (\forall (P: Prop).P))))))))).((match f in F return (\lambda (f0:
297 F).(((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat f0) t t0))
298 \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1
299 t3 t4) \to (\forall (P: Prop).P)))))))) \to (or (ex T (\lambda (t3: T).(ty3 g
300 c2 (THead (Flat f0) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat f0)
301 t t0) t3) \to (\forall (P: Prop).P)))))) with [Appl \Rightarrow (\lambda (H1:
302 ((\forall (c1: C).(\forall (t3: T).((flt c1 t3 c2 (THead (Flat Appl) t t0))
303 \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3 t4))) (\forall (t4: T).((ty3 g c1
304 t3 t4) \to (\forall (P: Prop).P))))))))).(let H2 \def (H1 c2 t (flt_thead_sx
305 (Flat Appl) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t t3)))
306 (\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P: Prop).P))) (or (ex T
307 (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
308 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P))))
309 (\lambda (H3: (ex T (\lambda (t3: T).(ty3 g c2 t t3)))).(ex_ind T (\lambda
310 (t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat
311 Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3)
312 \to (\forall (P: Prop).P)))) (\lambda (x: T).(\lambda (H4: (ty3 g c2 t
313 x)).(let H5 \def (H1 c2 t0 (flt_thead_dx (Flat Appl) c2 t t0)) in (or_ind (ex
314 T (\lambda (t3: T).(ty3 g c2 t0 t3))) (\forall (t3: T).((ty3 g c2 t0 t3) \to
315 (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat
316 Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3)
317 \to (\forall (P: Prop).P)))) (\lambda (H6: (ex T (\lambda (t3: T).(ty3 g c2
318 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0 t3)) (or (ex T (\lambda
319 (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
320 (THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x0:
321 T).(\lambda (H7: (ty3 g c2 t0 x0)).(ex_ind T (\lambda (t3: T).(ty3 g c2 x0
322 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3)))
323 (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall (P:
324 Prop).P)))) (\lambda (x1: T).(\lambda (H8: (ty3 g c2 x0 x1)).(ex_ind T
325 (\lambda (t3: T).(ty3 g c2 x t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead
326 (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0)
327 t3) \to (\forall (P: Prop).P)))) (\lambda (x2: T).(\lambda (H9: (ty3 g c2 x
328 x2)).(let H10 \def (ty3_sn3 g c2 x x2 H9) in (let H_x \def (nf2_sn3 c2 x H10)
329 in (let H11 \def H_x in (ex2_ind T (\lambda (u: T).(pr3 c2 x u)) (\lambda (u:
330 T).(nf2 c2 u)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0)
331 t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall
332 (P: Prop).P)))) (\lambda (x3: T).(\lambda (H12: (pr3 c2 x x3)).(\lambda (H13:
333 (nf2 c2 x3)).(let H14 \def (ty3_sred_pr3 c2 x x3 H12 g x2 H9) in (let H_x0
334 \def (pc3_abst_dec g c2 x0 x1 H8 x3 x2 H14) in (let H15 \def H_x0 in (or_ind
335 (ex4_2 T T (\lambda (u: T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3
336 u)))) (\lambda (u: T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u)
337 x1))) (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_:
338 T).(\lambda (v2: T).(nf2 c2 v2)))) (\forall (u: T).((pc3 c2 x0 (THead (Bind
339 Abst) x3 u)) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2
340 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl)
341 t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H16: (ex4_2 T T (\lambda (u:
342 T).(\lambda (_: T).(pc3 c2 x0 (THead (Bind Abst) x3 u)))) (\lambda (u:
343 T).(\lambda (v2: T).(ty3 g c2 (THead (Bind Abst) v2 u) x1))) (\lambda (_:
344 T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda (_: T).(\lambda (v2: T).(nf2 c2
345 v2))))).(ex4_2_ind T T (\lambda (u: T).(\lambda (_: T).(pc3 c2 x0 (THead
346 (Bind Abst) x3 u)))) (\lambda (u: T).(\lambda (v2: T).(ty3 g c2 (THead (Bind
347 Abst) v2 u) x1))) (\lambda (_: T).(\lambda (v2: T).(pr3 c2 x3 v2))) (\lambda
348 (_: T).(\lambda (v2: T).(nf2 c2 v2))) (or (ex T (\lambda (t3: T).(ty3 g c2
349 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl)
350 t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x4: T).(\lambda (x5:
351 T).(\lambda (H17: (pc3 c2 x0 (THead (Bind Abst) x3 x4))).(\lambda (H18: (ty3
352 g c2 (THead (Bind Abst) x5 x4) x1)).(\lambda (H19: (pr3 c2 x3 x5)).(\lambda
353 (_: (nf2 c2 x5)).(let H_y \def (nf2_pr3_unfold c2 x3 x5 H19 H13) in (let H21
354 \def (eq_ind_r T x5 (\lambda (t3: T).(pr3 c2 x3 t3)) H19 x3 H_y) in (let H22
355 \def (eq_ind_r T x5 (\lambda (t3: T).(ty3 g c2 (THead (Bind Abst) t3 x4) x1))
356 H18 x3 H_y) in (or_introl (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl)
357 t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
358 (\forall (P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2 (THead (Flat
359 Appl) t t0) t3)) (THead (Flat Appl) t (THead (Bind Abst) x3 x4)) (ty3_appl g
360 c2 t x3 (ty3_tred g c2 t x H4 x3 H12) t0 x4 (ty3_conv g c2 (THead (Bind Abst)
361 x3 x4) x1 H22 t0 x0 H7 H17))))))))))))) H16)) (\lambda (H16: ((\forall (u:
362 T).((pc3 c2 x0 (THead (Bind Abst) x3 u)) \to (\forall (P:
363 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t
364 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to
365 (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H17: (ty3 g c2 (THead
366 (Flat Appl) t t0) t3)).(\lambda (P: Prop).(ex3_2_ind T T (\lambda (u:
367 T).(\lambda (t4: T).(pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4))
368 t3))) (\lambda (u: T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u
369 t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2 t u))) P (\lambda (x4:
370 T).(\lambda (x5: T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind
371 Abst) x4 x5)) t3)).(\lambda (H19: (ty3 g c2 t0 (THead (Bind Abst) x4
372 x5))).(\lambda (H20: (ty3 g c2 t x4)).(let H_y \def (ty3_unique g c2 t x4 H20
373 x H4) in (let H_y0 \def (ty3_unique g c2 t0 (THead (Bind Abst) x4 x5) H19 x0
374 H7) in (H16 x5 (pc3_t (THead (Bind Abst) x4 x5) c2 x0 (pc3_s c2 x0 (THead
375 (Bind Abst) x4 x5) H_y0) (THead (Bind Abst) x3 x5) (pc3_head_1 c2 x4 x3
376 (pc3_t x c2 x4 H_y x3 (pc3_pr3_r c2 x x3 H12)) (Bind Abst) x5)) P))))))))
377 (ty3_gen_appl g c2 t t0 t3 H17))))))) H15))))))) H11)))))) (ty3_correct g c2
378 t x H4)))) (ty3_correct g c2 t0 x0 H7)))) H6)) (\lambda (H6: ((\forall (t3:
379 T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda
380 (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3: T).((ty3 g c2
381 (THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P))) (\lambda (t3:
382 T).(\lambda (H7: (ty3 g c2 (THead (Flat Appl) t t0) t3)).(\lambda (P:
383 Prop).(ex3_2_ind T T (\lambda (u: T).(\lambda (t4: T).(pc3 c2 (THead (Flat
384 Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda (u: T).(\lambda (t4: T).(ty3
385 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u: T).(\lambda (_: T).(ty3 g c2
386 t u))) P (\lambda (x0: T).(\lambda (x1: T).(\lambda (_: (pc3 c2 (THead (Flat
387 Appl) t (THead (Bind Abst) x0 x1)) t3)).(\lambda (H9: (ty3 g c2 t0 (THead
388 (Bind Abst) x0 x1))).(\lambda (_: (ty3 g c2 t x0)).(H6 (THead (Bind Abst) x0
389 x1) H9 P)))))) (ty3_gen_appl g c2 t t0 t3 H7))))))) H5)))) H3)) (\lambda (H3:
390 ((\forall (t3: T).((ty3 g c2 t t3) \to (\forall (P: Prop).P))))).(or_intror
391 (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Appl) t t0) t3))) (\forall (t3:
392 T).((ty3 g c2 (THead (Flat Appl) t t0) t3) \to (\forall (P: Prop).P)))
393 (\lambda (t3: T).(\lambda (H4: (ty3 g c2 (THead (Flat Appl) t t0)
394 t3)).(\lambda (P: Prop).(ex3_2_ind T T (\lambda (u: T).(\lambda (t4: T).(pc3
395 c2 (THead (Flat Appl) t (THead (Bind Abst) u t4)) t3))) (\lambda (u:
396 T).(\lambda (t4: T).(ty3 g c2 t0 (THead (Bind Abst) u t4)))) (\lambda (u:
397 T).(\lambda (_: T).(ty3 g c2 t u))) P (\lambda (x0: T).(\lambda (x1:
398 T).(\lambda (_: (pc3 c2 (THead (Flat Appl) t (THead (Bind Abst) x0 x1))
399 t3)).(\lambda (_: (ty3 g c2 t0 (THead (Bind Abst) x0 x1))).(\lambda (H7: (ty3
400 g c2 t x0)).(H3 x0 H7 P)))))) (ty3_gen_appl g c2 t t0 t3 H4))))))) H2))) |
401 Cast \Rightarrow (\lambda (H1: ((\forall (c1: C).(\forall (t3: T).((flt c1 t3
402 c2 (THead (Flat Cast) t t0)) \to (or (ex T (\lambda (t4: T).(ty3 g c1 t3
403 t4))) (\forall (t4: T).((ty3 g c1 t3 t4) \to (\forall (P:
404 Prop).P))))))))).(let H2 \def (H1 c2 t (flt_thead_sx (Flat Cast) c2 t t0)) in
405 (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t t3))) (\forall (t3: T).((ty3 g c2
406 t t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead
407 (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0)
408 t3) \to (\forall (P: Prop).P)))) (\lambda (H3: (ex T (\lambda (t3: T).(ty3 g
409 c2 t t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t t3)) (or (ex T (\lambda
410 (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
411 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x:
412 T).(\lambda (H4: (ty3 g c2 t x)).(let H5 \def (H1 c2 t0 (flt_thead_dx (Flat
413 Cast) c2 t t0)) in (or_ind (ex T (\lambda (t3: T).(ty3 g c2 t0 t3))) (\forall
414 (t3: T).((ty3 g c2 t0 t3) \to (\forall (P: Prop).P))) (or (ex T (\lambda (t3:
415 T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
416 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (H6: (ex T
417 (\lambda (t3: T).(ty3 g c2 t0 t3)))).(ex_ind T (\lambda (t3: T).(ty3 g c2 t0
418 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3)))
419 (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P:
420 Prop).P)))) (\lambda (x0: T).(\lambda (H7: (ty3 g c2 t0 x0)).(ex_ind T
421 (\lambda (t3: T).(ty3 g c2 x0 t3)) (or (ex T (\lambda (t3: T).(ty3 g c2
422 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
423 t t0) t3) \to (\forall (P: Prop).P)))) (\lambda (x1: T).(\lambda (H8: (ty3 g
424 c2 x0 x1)).(let H_x \def (pc3_dec g c2 x0 x1 H8 t x H4) in (let H9 \def H_x
425 in (or_ind (pc3 c2 x0 t) ((pc3 c2 x0 t) \to (\forall (P: Prop).P)) (or (ex T
426 (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3:
427 T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P))))
428 (\lambda (H10: (pc3 c2 x0 t)).(or_introl (ex T (\lambda (t3: T).(ty3 g c2
429 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast)
430 t t0) t3) \to (\forall (P: Prop).P))) (ex_intro T (\lambda (t3: T).(ty3 g c2
431 (THead (Flat Cast) t t0) t3)) t (ty3_cast g c2 t0 t (ty3_conv g c2 t x H4 t0
432 x0 H7 H10) x H4)))) (\lambda (H10: (((pc3 c2 x0 t) \to (\forall (P:
433 Prop).P)))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
434 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
435 (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H11: (ty3 g c2 (THead
436 (Flat Cast) t t0) t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0
437 t) P (\lambda (_: (pc3 c2 t t3)).(\lambda (H13: (ty3 g c2 t0 t)).(let H_y
438 \def (ty3_unique g c2 t0 t H13 x0 H7) in (H10 (pc3_s c2 x0 t H_y) P))))
439 (ty3_gen_cast g c2 t0 t t3 H11))))))) H9))))) (ty3_correct g c2 t0 x0 H7))))
440 H6)) (\lambda (H6: ((\forall (t3: T).((ty3 g c2 t0 t3) \to (\forall (P:
441 Prop).P))))).(or_intror (ex T (\lambda (t3: T).(ty3 g c2 (THead (Flat Cast) t
442 t0) t3))) (\forall (t3: T).((ty3 g c2 (THead (Flat Cast) t t0) t3) \to
443 (\forall (P: Prop).P))) (\lambda (t3: T).(\lambda (H7: (ty3 g c2 (THead (Flat
444 Cast) t t0) t3)).(\lambda (P: Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P
445 (\lambda (_: (pc3 c2 t t3)).(\lambda (H9: (ty3 g c2 t0 t)).(H6 t H9 P)))
446 (ty3_gen_cast g c2 t0 t t3 H7))))))) H5)))) H3)) (\lambda (H3: ((\forall (t3:
447 T).((ty3 g c2 t t3) \to (\forall (P: Prop).P))))).(or_intror (ex T (\lambda
448 (t3: T).(ty3 g c2 (THead (Flat Cast) t t0) t3))) (\forall (t3: T).((ty3 g c2
449 (THead (Flat Cast) t t0) t3) \to (\forall (P: Prop).P))) (\lambda (t3:
450 T).(\lambda (H4: (ty3 g c2 (THead (Flat Cast) t t0) t3)).(\lambda (P:
451 Prop).(and_ind (pc3 c2 t t3) (ty3 g c2 t0 t) P (\lambda (_: (pc3 c2 t
452 t3)).(\lambda (H6: (ty3 g c2 t0 t)).(ex_ind T (\lambda (t4: T).(ty3 g c2 t
453 t4)) P (\lambda (x: T).(\lambda (H7: (ty3 g c2 t x)).(H3 x H7 P)))
454 (ty3_correct g c2 t0 t H6)))) (ty3_gen_cast g c2 t0 t t3 H4))))))) H2)))])
455 H0))]) H))]))) c t1))).
projects / helm.git / blob