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 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/ty3/tau0".
19 include "ty3/pr3_props.ma".
21 include "tau0/defs.ma".
24 \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t1: T).((ty3 g c u
25 t1) \to (\forall (t2: T).((tau0 g c u t2) \to (ty3 g c u t2)))))))
27 \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (t1: T).(\lambda (H:
28 (ty3 g c u t1)).(ty3_ind g (\lambda (c0: C).(\lambda (t: T).(\lambda (_:
29 T).(\forall (t2: T).((tau0 g c0 t t2) \to (ty3 g c0 t t2)))))) (\lambda (c0:
30 C).(\lambda (t2: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 t2 t)).(\lambda
31 (_: ((\forall (t3: T).((tau0 g c0 t2 t3) \to (ty3 g c0 t2 t3))))).(\lambda
32 (u0: T).(\lambda (t3: T).(\lambda (_: (ty3 g c0 u0 t3)).(\lambda (H3:
33 ((\forall (t4: T).((tau0 g c0 u0 t4) \to (ty3 g c0 u0 t4))))).(\lambda (_:
34 (pc3 c0 t3 t2)).(\lambda (t0: T).(\lambda (H5: (tau0 g c0 u0 t0)).(H3 t0
35 H5))))))))))))) (\lambda (c0: C).(\lambda (m: nat).(\lambda (t2: T).(\lambda
36 (H0: (tau0 g c0 (TSort m) t2)).(let H1 \def (match H0 in tau0 return (\lambda
37 (c1: C).(\lambda (t: T).(\lambda (t0: T).(\lambda (_: (tau0 ? c1 t t0)).((eq
38 C c1 c0) \to ((eq T t (TSort m)) \to ((eq T t0 t2) \to (ty3 g c0 (TSort m)
39 t2)))))))) with [(tau0_sort c1 n) \Rightarrow (\lambda (H1: (eq C c1
40 c0)).(\lambda (H2: (eq T (TSort n) (TSort m))).(\lambda (H3: (eq T (TSort
41 (next g n)) t2)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n) (TSort m)) \to
42 ((eq T (TSort (next g n)) t2) \to (ty3 g c0 (TSort m) t2)))) (\lambda (H4:
43 (eq T (TSort n) (TSort m))).(let H5 \def (f_equal T nat (\lambda (e:
44 T).(match e in T return (\lambda (_: T).nat) with [(TSort n0) \Rightarrow n0
45 | (TLRef _) \Rightarrow n | (THead _ _ _) \Rightarrow n])) (TSort n) (TSort
46 m) H4) in (eq_ind nat m (\lambda (n0: nat).((eq T (TSort (next g n0)) t2) \to
47 (ty3 g c0 (TSort m) t2))) (\lambda (H6: (eq T (TSort (next g m)) t2)).(eq_ind
48 T (TSort (next g m)) (\lambda (t: T).(ty3 g c0 (TSort m) t)) (ty3_sort g c0
49 m) t2 H6)) n (sym_eq nat n m H5)))) c1 (sym_eq C c1 c0 H1) H2 H3)))) |
50 (tau0_abbr c1 d v i H1 w H2) \Rightarrow (\lambda (H3: (eq C c1 c0)).(\lambda
51 (H4: (eq T (TLRef i) (TSort m))).(\lambda (H5: (eq T (lift (S i) O w)
52 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (TSort m)) \to ((eq T
53 (lift (S i) O w) t2) \to ((getl i c2 (CHead d (Bind Abbr) v)) \to ((tau0 g d
54 v w) \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6: (eq T (TLRef i) (TSort
55 m))).(let H7 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return
56 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
57 \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort m) H6) in
58 (False_ind ((eq T (lift (S i) O w) t2) \to ((getl i c0 (CHead d (Bind Abbr)
59 v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2)))) H7))) c1 (sym_eq C c1
60 c0 H3) H4 H5 H1 H2)))) | (tau0_abst c1 d v i H1 w H2) \Rightarrow (\lambda
61 (H3: (eq C c1 c0)).(\lambda (H4: (eq T (TLRef i) (TSort m))).(\lambda (H5:
62 (eq T (lift (S i) O v) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i)
63 (TSort m)) \to ((eq T (lift (S i) O v) t2) \to ((getl i c2 (CHead d (Bind
64 Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6:
65 (eq T (TLRef i) (TSort m))).(let H7 \def (eq_ind T (TLRef i) (\lambda (e:
66 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
67 False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I
68 (TSort m) H6) in (False_ind ((eq T (lift (S i) O v) t2) \to ((getl i c0
69 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2))))
70 H7))) c1 (sym_eq C c1 c0 H3) H4 H5 H1 H2)))) | (tau0_bind b c1 v t0 t3 H1)
71 \Rightarrow (\lambda (H2: (eq C c1 c0)).(\lambda (H3: (eq T (THead (Bind b) v
72 t0) (TSort m))).(\lambda (H4: (eq T (THead (Bind b) v t3) t2)).(eq_ind C c0
73 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TSort m)) \to ((eq T (THead
74 (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0 t3) \to (ty3 g c0
75 (TSort m) t2))))) (\lambda (H5: (eq T (THead (Bind b) v t0) (TSort m))).(let
76 H6 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e: T).(match e in T return
77 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
78 \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort m) H5) in
79 (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c0 (Bind b)
80 v) t0 t3) \to (ty3 g c0 (TSort m) t2))) H6))) c1 (sym_eq C c1 c0 H2) H3 H4
81 H1)))) | (tau0_appl c1 v t0 t3 H1) \Rightarrow (\lambda (H2: (eq C c1
82 c0)).(\lambda (H3: (eq T (THead (Flat Appl) v t0) (TSort m))).(\lambda (H4:
83 (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T
84 (THead (Flat Appl) v t0) (TSort m)) \to ((eq T (THead (Flat Appl) v t3) t2)
85 \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TSort m) t2))))) (\lambda (H5: (eq T
86 (THead (Flat Appl) v t0) (TSort m))).(let H6 \def (eq_ind T (THead (Flat
87 Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
88 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
89 \Rightarrow True])) I (TSort m) H5) in (False_ind ((eq T (THead (Flat Appl) v
90 t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TSort m) t2))) H6))) c1 (sym_eq
91 C c1 c0 H2) H3 H4 H1)))) | (tau0_cast c1 v1 v2 H1 t0 t3 H2) \Rightarrow
92 (\lambda (H3: (eq C c1 c0)).(\lambda (H4: (eq T (THead (Flat Cast) v1 t0)
93 (TSort m))).(\lambda (H5: (eq T (THead (Flat Cast) v2 t3) t2)).(eq_ind C c0
94 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TSort m)) \to ((eq T
95 (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to ((tau0 g c2 t0 t3)
96 \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6: (eq T (THead (Flat Cast) v1
97 t0) (TSort m))).(let H7 \def (eq_ind T (THead (Flat Cast) v1 t0) (\lambda (e:
98 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
99 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
100 (TSort m) H6) in (False_ind ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g
101 c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TSort m) t2)))) H7))) c1
102 (sym_eq C c1 c0 H3) H4 H5 H1 H2))))]) in (H1 (refl_equal C c0) (refl_equal T
103 (TSort m)) (refl_equal T t2))))))) (\lambda (n: nat).(\lambda (c0:
104 C).(\lambda (d: C).(\lambda (u0: T).(\lambda (H0: (getl n c0 (CHead d (Bind
105 Abbr) u0))).(\lambda (t: T).(\lambda (_: (ty3 g d u0 t)).(\lambda (H2:
106 ((\forall (t2: T).((tau0 g d u0 t2) \to (ty3 g d u0 t2))))).(\lambda (t2:
107 T).(\lambda (H3: (tau0 g c0 (TLRef n) t2)).(let H4 \def (match H3 in tau0
108 return (\lambda (c1: C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (tau0
109 ? c1 t0 t3)).((eq C c1 c0) \to ((eq T t0 (TLRef n)) \to ((eq T t3 t2) \to
110 (ty3 g c0 (TLRef n) t2)))))))) with [(tau0_sort c1 n0) \Rightarrow (\lambda
111 (H4: (eq C c1 c0)).(\lambda (H5: (eq T (TSort n0) (TLRef n))).(\lambda (H6:
112 (eq T (TSort (next g n0)) t2)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n0)
113 (TLRef n)) \to ((eq T (TSort (next g n0)) t2) \to (ty3 g c0 (TLRef n) t2))))
114 (\lambda (H7: (eq T (TSort n0) (TLRef n))).(let H8 \def (eq_ind T (TSort n0)
115 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
116 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
117 False])) I (TLRef n) H7) in (False_ind ((eq T (TSort (next g n0)) t2) \to
118 (ty3 g c0 (TLRef n) t2)) H8))) c1 (sym_eq C c1 c0 H4) H5 H6)))) | (tau0_abbr
119 c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq
120 T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift (S i) O w) t2)).(eq_ind C
121 c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O w)
122 t2) \to ((getl i c2 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g
123 c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def
124 (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
125 [(TSort _) \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _)
126 \Rightarrow i])) (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0:
127 nat).((eq T (lift (S n0) O w) t2) \to ((getl n0 c0 (CHead d0 (Bind Abbr) v))
128 \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T
129 (lift (S n) O w) t2)).(eq_ind T (lift (S n) O w) (\lambda (t0: T).((getl n c0
130 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0))))
131 (\lambda (H12: (getl n c0 (CHead d0 (Bind Abbr) v))).(\lambda (H13: (tau0 g
132 d0 v w)).(let H14 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda (c2:
133 C).(getl n c0 c2)) H0 (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d (Bind
134 Abbr) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in (let H15 \def (f_equal C C
135 (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
136 \Rightarrow d | (CHead c2 _ _) \Rightarrow c2])) (CHead d (Bind Abbr) u0)
137 (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead
138 d0 (Bind Abbr) v) H12)) in ((let H16 \def (f_equal C T (\lambda (e: C).(match
139 e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _
140 t0) \Rightarrow t0])) (CHead d (Bind Abbr) u0) (CHead d0 (Bind Abbr) v)
141 (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in
142 (\lambda (H17: (eq C d d0)).(let H18 \def (eq_ind_r T v (\lambda (t0:
143 T).(getl n c0 (CHead d0 (Bind Abbr) t0))) H14 u0 H16) in (let H19 \def
144 (eq_ind_r T v (\lambda (t0: T).(tau0 g d0 t0 w)) H13 u0 H16) in (let H20 \def
145 (eq_ind_r C d0 (\lambda (c2: C).(getl n c0 (CHead c2 (Bind Abbr) u0))) H18 d
146 H17) in (let H21 \def (eq_ind_r C d0 (\lambda (c2: C).(tau0 g c2 u0 w)) H19 d
147 H17) in (ty3_abbr g n c0 d u0 H20 w (H2 w H21)))))))) H15))))) t2 H11)) i
148 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_abst
149 c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq
150 T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift (S i) O v) t2)).(eq_ind C
151 c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O v)
152 t2) \to ((getl i c2 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g
153 c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def
154 (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
155 [(TSort _) \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _)
156 \Rightarrow i])) (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0:
157 nat).((eq T (lift (S n0) O v) t2) \to ((getl n0 c0 (CHead d0 (Bind Abst) v))
158 \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T
159 (lift (S n) O v) t2)).(eq_ind T (lift (S n) O v) (\lambda (t0: T).((getl n c0
160 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0))))
161 (\lambda (H12: (getl n c0 (CHead d0 (Bind Abst) v))).(\lambda (_: (tau0 g d0
162 v w)).(let H14 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda (c2: C).(getl
163 n c0 c2)) H0 (CHead d0 (Bind Abst) v) (getl_mono c0 (CHead d (Bind Abbr) u0)
164 n H0 (CHead d0 (Bind Abst) v) H12)) in (let H15 \def (eq_ind C (CHead d (Bind
165 Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with
166 [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return
167 (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return
168 (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False |
169 Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d0 (Bind
170 Abst) v) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead d0 (Bind Abst) v)
171 H12)) in (False_ind (ty3 g c0 (TLRef n) (lift (S n) O v)) H15))))) t2 H11)) i
172 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_bind b
173 c1 v t0 t3 H4) \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T
174 (THead (Bind b) v t0) (TLRef n))).(\lambda (H7: (eq T (THead (Bind b) v t3)
175 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TLRef n))
176 \to ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0
177 t3) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H8: (eq T (THead (Bind b) v t0)
178 (TLRef n))).(let H9 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e:
179 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
180 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
181 (TLRef n) H8) in (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g
182 (CHead c0 (Bind b) v) t0 t3) \to (ty3 g c0 (TLRef n) t2))) H9))) c1 (sym_eq C
183 c1 c0 H5) H6 H7 H4)))) | (tau0_appl c1 v t0 t3 H4) \Rightarrow (\lambda (H5:
184 (eq C c1 c0)).(\lambda (H6: (eq T (THead (Flat Appl) v t0) (TLRef
185 n))).(\lambda (H7: (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda
186 (c2: C).((eq T (THead (Flat Appl) v t0) (TLRef n)) \to ((eq T (THead (Flat
187 Appl) v t3) t2) \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))
188 (\lambda (H8: (eq T (THead (Flat Appl) v t0) (TLRef n))).(let H9 \def (eq_ind
189 T (THead (Flat Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_:
190 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
191 (THead _ _ _) \Rightarrow True])) I (TLRef n) H8) in (False_ind ((eq T (THead
192 (Flat Appl) v t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef n) t2)))
193 H9))) c1 (sym_eq C c1 c0 H5) H6 H7 H4)))) | (tau0_cast c1 v1 v2 H4 t0 t3 H5)
194 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat
195 Cast) v1 t0) (TLRef n))).(\lambda (H8: (eq T (THead (Flat Cast) v2 t3)
196 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TLRef
197 n)) \to ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to
198 ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T
199 (THead (Flat Cast) v1 t0) (TLRef n))).(let H10 \def (eq_ind T (THead (Flat
200 Cast) v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
201 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
202 \Rightarrow True])) I (TLRef n) H9) in (False_ind ((eq T (THead (Flat Cast)
203 v2 t3) t2) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef
204 n) t2)))) H10))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5))))]) in (H4 (refl_equal
205 C c0) (refl_equal T (TLRef n)) (refl_equal T t2))))))))))))) (\lambda (n:
206 nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (H0: (getl n
207 c0 (CHead d (Bind Abst) u0))).(\lambda (t: T).(\lambda (H1: (ty3 g d u0
208 t)).(\lambda (_: ((\forall (t2: T).((tau0 g d u0 t2) \to (ty3 g d u0
209 t2))))).(\lambda (t2: T).(\lambda (H3: (tau0 g c0 (TLRef n) t2)).(let H4 \def
210 (match H3 in tau0 return (\lambda (c1: C).(\lambda (t0: T).(\lambda (t3:
211 T).(\lambda (_: (tau0 ? c1 t0 t3)).((eq C c1 c0) \to ((eq T t0 (TLRef n)) \to
212 ((eq T t3 t2) \to (ty3 g c0 (TLRef n) t2)))))))) with [(tau0_sort c1 n0)
213 \Rightarrow (\lambda (H4: (eq C c1 c0)).(\lambda (H5: (eq T (TSort n0) (TLRef
214 n))).(\lambda (H6: (eq T (TSort (next g n0)) t2)).(eq_ind C c0 (\lambda (_:
215 C).((eq T (TSort n0) (TLRef n)) \to ((eq T (TSort (next g n0)) t2) \to (ty3 g
216 c0 (TLRef n) t2)))) (\lambda (H7: (eq T (TSort n0) (TLRef n))).(let H8 \def
217 (eq_ind T (TSort n0) (\lambda (e: T).(match e in T return (\lambda (_:
218 T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
219 (THead _ _ _) \Rightarrow False])) I (TLRef n) H7) in (False_ind ((eq T
220 (TSort (next g n0)) t2) \to (ty3 g c0 (TLRef n) t2)) H8))) c1 (sym_eq C c1 c0
221 H4) H5 H6)))) | (tau0_abbr c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C
222 c1 c0)).(\lambda (H7: (eq T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift
223 (S i) O w) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to
224 ((eq T (lift (S i) O w) t2) \to ((getl i c2 (CHead d0 (Bind Abbr) v)) \to
225 ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef
226 i) (TLRef n))).(let H10 \def (f_equal T nat (\lambda (e: T).(match e in T
227 return (\lambda (_: T).nat) with [(TSort _) \Rightarrow i | (TLRef n0)
228 \Rightarrow n0 | (THead _ _ _) \Rightarrow i])) (TLRef i) (TLRef n) H9) in
229 (eq_ind nat n (\lambda (n0: nat).((eq T (lift (S n0) O w) t2) \to ((getl n0
230 c0 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n)
231 t2))))) (\lambda (H11: (eq T (lift (S n) O w) t2)).(eq_ind T (lift (S n) O w)
232 (\lambda (t0: T).((getl n c0 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w)
233 \to (ty3 g c0 (TLRef n) t0)))) (\lambda (H12: (getl n c0 (CHead d0 (Bind
234 Abbr) v))).(\lambda (_: (tau0 g d0 v w)).(let H14 \def (eq_ind C (CHead d
235 (Bind Abst) u0) (\lambda (c2: C).(getl n c0 c2)) H0 (CHead d0 (Bind Abbr) v)
236 (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in
237 (let H15 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda (ee: C).(match ee
238 in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead
239 _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
240 \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
241 False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _)
242 \Rightarrow False])])) I (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d
243 (Bind Abst) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in (False_ind (ty3 g c0
244 (TLRef n) (lift (S n) O w)) H15))))) t2 H11)) i (sym_eq nat i n H10)))) c1
245 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_abst c1 d0 v i H4 w H5)
246 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (TLRef i) (TLRef
247 n))).(\lambda (H8: (eq T (lift (S i) O v) t2)).(eq_ind C c0 (\lambda (c2:
248 C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O v) t2) \to ((getl i
249 c2 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n)
250 t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def (f_equal T
251 nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _)
252 \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _) \Rightarrow i]))
253 (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0: nat).((eq T (lift (S
254 n0) O v) t2) \to ((getl n0 c0 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w)
255 \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T (lift (S n) O v)
256 t2)).(eq_ind T (lift (S n) O v) (\lambda (t0: T).((getl n c0 (CHead d0 (Bind
257 Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0)))) (\lambda (H12:
258 (getl n c0 (CHead d0 (Bind Abst) v))).(\lambda (H13: (tau0 g d0 v w)).(let
259 H14 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda (c2: C).(getl n c0 c2))
260 H0 (CHead d0 (Bind Abst) v) (getl_mono c0 (CHead d (Bind Abst) u0) n H0
261 (CHead d0 (Bind Abst) v) H12)) in (let H15 \def (f_equal C C (\lambda (e:
262 C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d |
263 (CHead c2 _ _) \Rightarrow c2])) (CHead d (Bind Abst) u0) (CHead d0 (Bind
264 Abst) v) (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abst) v)
265 H12)) in ((let H16 \def (f_equal C T (\lambda (e: C).(match e in C return
266 (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t0)
267 \Rightarrow t0])) (CHead d (Bind Abst) u0) (CHead d0 (Bind Abst) v)
268 (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abst) v) H12)) in
269 (\lambda (H17: (eq C d d0)).(let H18 \def (eq_ind_r T v (\lambda (t0:
270 T).(getl n c0 (CHead d0 (Bind Abst) t0))) H14 u0 H16) in (let H19 \def
271 (eq_ind_r T v (\lambda (t0: T).(tau0 g d0 t0 w)) H13 u0 H16) in (eq_ind T u0
272 (\lambda (t0: T).(ty3 g c0 (TLRef n) (lift (S n) O t0))) (let H20 \def
273 (eq_ind_r C d0 (\lambda (c2: C).(getl n c0 (CHead c2 (Bind Abst) u0))) H18 d
274 H17) in (let H21 \def (eq_ind_r C d0 (\lambda (c2: C).(tau0 g c2 u0 w)) H19 d
275 H17) in (ty3_abst g n c0 d u0 H20 t H1))) v H16))))) H15))))) t2 H11)) i
276 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_bind b
277 c1 v t0 t3 H4) \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T
278 (THead (Bind b) v t0) (TLRef n))).(\lambda (H7: (eq T (THead (Bind b) v t3)
279 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TLRef n))
280 \to ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0
281 t3) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H8: (eq T (THead (Bind b) v t0)
282 (TLRef n))).(let H9 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e:
283 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
284 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
285 (TLRef n) H8) in (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g
286 (CHead c0 (Bind b) v) t0 t3) \to (ty3 g c0 (TLRef n) t2))) H9))) c1 (sym_eq C
287 c1 c0 H5) H6 H7 H4)))) | (tau0_appl c1 v t0 t3 H4) \Rightarrow (\lambda (H5:
288 (eq C c1 c0)).(\lambda (H6: (eq T (THead (Flat Appl) v t0) (TLRef
289 n))).(\lambda (H7: (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda
290 (c2: C).((eq T (THead (Flat Appl) v t0) (TLRef n)) \to ((eq T (THead (Flat
291 Appl) v t3) t2) \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))
292 (\lambda (H8: (eq T (THead (Flat Appl) v t0) (TLRef n))).(let H9 \def (eq_ind
293 T (THead (Flat Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_:
294 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
295 (THead _ _ _) \Rightarrow True])) I (TLRef n) H8) in (False_ind ((eq T (THead
296 (Flat Appl) v t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef n) t2)))
297 H9))) c1 (sym_eq C c1 c0 H5) H6 H7 H4)))) | (tau0_cast c1 v1 v2 H4 t0 t3 H5)
298 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat
299 Cast) v1 t0) (TLRef n))).(\lambda (H8: (eq T (THead (Flat Cast) v2 t3)
300 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TLRef
301 n)) \to ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to
302 ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T
303 (THead (Flat Cast) v1 t0) (TLRef n))).(let H10 \def (eq_ind T (THead (Flat
304 Cast) v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
305 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
306 \Rightarrow True])) I (TLRef n) H9) in (False_ind ((eq T (THead (Flat Cast)
307 v2 t3) t2) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef
308 n) t2)))) H10))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5))))]) in (H4 (refl_equal
309 C c0) (refl_equal T (TLRef n)) (refl_equal T t2))))))))))))) (\lambda (c0:
310 C).(\lambda (u0: T).(\lambda (t: T).(\lambda (H0: (ty3 g c0 u0 t)).(\lambda
311 (_: ((\forall (t2: T).((tau0 g c0 u0 t2) \to (ty3 g c0 u0 t2))))).(\lambda
312 (b: B).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (ty3 g (CHead c0 (Bind
313 b) u0) t2 t3)).(\lambda (H3: ((\forall (t4: T).((tau0 g (CHead c0 (Bind b)
314 u0) t2 t4) \to (ty3 g (CHead c0 (Bind b) u0) t2 t4))))).(\lambda (t0:
315 T).(\lambda (_: (ty3 g (CHead c0 (Bind b) u0) t3 t0)).(\lambda (_: ((\forall
316 (t4: T).((tau0 g (CHead c0 (Bind b) u0) t3 t4) \to (ty3 g (CHead c0 (Bind b)
317 u0) t3 t4))))).(\lambda (t4: T).(\lambda (H6: (tau0 g c0 (THead (Bind b) u0
318 t2) t4)).(let H7 \def (match H6 in tau0 return (\lambda (c1: C).(\lambda (t5:
319 T).(\lambda (t6: T).(\lambda (_: (tau0 ? c1 t5 t6)).((eq C c1 c0) \to ((eq T
320 t5 (THead (Bind b) u0 t2)) \to ((eq T t6 t4) \to (ty3 g c0 (THead (Bind b) u0
321 t2) t4)))))))) with [(tau0_sort c1 n) \Rightarrow (\lambda (H7: (eq C c1
322 c0)).(\lambda (H8: (eq T (TSort n) (THead (Bind b) u0 t2))).(\lambda (H9: (eq
323 T (TSort (next g n)) t4)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n)
324 (THead (Bind b) u0 t2)) \to ((eq T (TSort (next g n)) t4) \to (ty3 g c0
325 (THead (Bind b) u0 t2) t4)))) (\lambda (H10: (eq T (TSort n) (THead (Bind b)
326 u0 t2))).(let H11 \def (eq_ind T (TSort n) (\lambda (e: T).(match e in T
327 return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _)
328 \Rightarrow False | (THead _ _ _) \Rightarrow False])) I (THead (Bind b) u0
329 t2) H10) in (False_ind ((eq T (TSort (next g n)) t4) \to (ty3 g c0 (THead
330 (Bind b) u0 t2) t4)) H11))) c1 (sym_eq C c1 c0 H7) H8 H9)))) | (tau0_abbr c1
331 d v i H7 w H8) \Rightarrow (\lambda (H9: (eq C c1 c0)).(\lambda (H10: (eq T
332 (TLRef i) (THead (Bind b) u0 t2))).(\lambda (H11: (eq T (lift (S i) O w)
333 t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (THead (Bind b) u0 t2))
334 \to ((eq T (lift (S i) O w) t4) \to ((getl i c2 (CHead d (Bind Abbr) v)) \to
335 ((tau0 g d v w) \to (ty3 g c0 (THead (Bind b) u0 t2) t4)))))) (\lambda (H12:
336 (eq T (TLRef i) (THead (Bind b) u0 t2))).(let H13 \def (eq_ind T (TLRef i)
337 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
338 \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
339 False])) I (THead (Bind b) u0 t2) H12) in (False_ind ((eq T (lift (S i) O w)
340 t4) \to ((getl i c0 (CHead d (Bind Abbr) v)) \to ((tau0 g d v w) \to (ty3 g
341 c0 (THead (Bind b) u0 t2) t4)))) H13))) c1 (sym_eq C c1 c0 H9) H10 H11 H7
342 H8)))) | (tau0_abst c1 d v i H7 w H8) \Rightarrow (\lambda (H9: (eq C c1
343 c0)).(\lambda (H10: (eq T (TLRef i) (THead (Bind b) u0 t2))).(\lambda (H11:
344 (eq T (lift (S i) O v) t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i)
345 (THead (Bind b) u0 t2)) \to ((eq T (lift (S i) O v) t4) \to ((getl i c2
346 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Bind b) u0
347 t2) t4)))))) (\lambda (H12: (eq T (TLRef i) (THead (Bind b) u0 t2))).(let H13
348 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return (\lambda (_:
349 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
350 (THead _ _ _) \Rightarrow False])) I (THead (Bind b) u0 t2) H12) in
351 (False_ind ((eq T (lift (S i) O v) t4) \to ((getl i c0 (CHead d (Bind Abst)
352 v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Bind b) u0 t2) t4)))) H13))) c1
353 (sym_eq C c1 c0 H9) H10 H11 H7 H8)))) | (tau0_bind b0 c1 v t5 t6 H7)
354 \Rightarrow (\lambda (H8: (eq C c1 c0)).(\lambda (H9: (eq T (THead (Bind b0)
355 v t5) (THead (Bind b) u0 t2))).(\lambda (H10: (eq T (THead (Bind b0) v t6)
356 t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Bind b0) v t5) (THead (Bind
357 b) u0 t2)) \to ((eq T (THead (Bind b0) v t6) t4) \to ((tau0 g (CHead c2 (Bind
358 b0) v) t5 t6) \to (ty3 g c0 (THead (Bind b) u0 t2) t4))))) (\lambda (H11: (eq
359 T (THead (Bind b0) v t5) (THead (Bind b) u0 t2))).(let H12 \def (f_equal T T
360 (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
361 \Rightarrow t5 | (TLRef _) \Rightarrow t5 | (THead _ _ t7) \Rightarrow t7]))
362 (THead (Bind b0) v t5) (THead (Bind b) u0 t2) H11) in ((let H13 \def (f_equal
363 T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
364 \Rightarrow v | (TLRef _) \Rightarrow v | (THead _ t7 _) \Rightarrow t7]))
365 (THead (Bind b0) v t5) (THead (Bind b) u0 t2) H11) in ((let H14 \def (f_equal
366 T B (\lambda (e: T).(match e in T return (\lambda (_: T).B) with [(TSort _)
367 \Rightarrow b0 | (TLRef _) \Rightarrow b0 | (THead k _ _) \Rightarrow (match
368 k in K return (\lambda (_: K).B) with [(Bind b1) \Rightarrow b1 | (Flat _)
369 \Rightarrow b0])])) (THead (Bind b0) v t5) (THead (Bind b) u0 t2) H11) in
370 (eq_ind B b (\lambda (b1: B).((eq T v u0) \to ((eq T t5 t2) \to ((eq T (THead
371 (Bind b1) v t6) t4) \to ((tau0 g (CHead c0 (Bind b1) v) t5 t6) \to (ty3 g c0
372 (THead (Bind b) u0 t2) t4)))))) (\lambda (H15: (eq T v u0)).(eq_ind T u0
373 (\lambda (t7: T).((eq T t5 t2) \to ((eq T (THead (Bind b) t7 t6) t4) \to
374 ((tau0 g (CHead c0 (Bind b) t7) t5 t6) \to (ty3 g c0 (THead (Bind b) u0 t2)
375 t4))))) (\lambda (H16: (eq T t5 t2)).(eq_ind T t2 (\lambda (t7: T).((eq T
376 (THead (Bind b) u0 t6) t4) \to ((tau0 g (CHead c0 (Bind b) u0) t7 t6) \to
377 (ty3 g c0 (THead (Bind b) u0 t2) t4)))) (\lambda (H17: (eq T (THead (Bind b)
378 u0 t6) t4)).(eq_ind T (THead (Bind b) u0 t6) (\lambda (t7: T).((tau0 g (CHead
379 c0 (Bind b) u0) t2 t6) \to (ty3 g c0 (THead (Bind b) u0 t2) t7))) (\lambda
380 (H18: (tau0 g (CHead c0 (Bind b) u0) t2 t6)).(let H_y \def (H3 t6 H18) in
381 (ex_ind T (\lambda (t7: T).(ty3 g (CHead c0 (Bind b) u0) t6 t7)) (ty3 g c0
382 (THead (Bind b) u0 t2) (THead (Bind b) u0 t6)) (\lambda (x: T).(\lambda (H19:
383 (ty3 g (CHead c0 (Bind b) u0) t6 x)).(ty3_bind g c0 u0 t H0 b t2 t6 H_y x
384 H19))) (ty3_correct g (CHead c0 (Bind b) u0) t2 t6 H_y)))) t4 H17)) t5
385 (sym_eq T t5 t2 H16))) v (sym_eq T v u0 H15))) b0 (sym_eq B b0 b H14))) H13))
386 H12))) c1 (sym_eq C c1 c0 H8) H9 H10 H7)))) | (tau0_appl c1 v t5 t6 H7)
387 \Rightarrow (\lambda (H8: (eq C c1 c0)).(\lambda (H9: (eq T (THead (Flat
388 Appl) v t5) (THead (Bind b) u0 t2))).(\lambda (H10: (eq T (THead (Flat Appl)
389 v t6) t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Appl) v t5)
390 (THead (Bind b) u0 t2)) \to ((eq T (THead (Flat Appl) v t6) t4) \to ((tau0 g
391 c2 t5 t6) \to (ty3 g c0 (THead (Bind b) u0 t2) t4))))) (\lambda (H11: (eq T
392 (THead (Flat Appl) v t5) (THead (Bind b) u0 t2))).(let H12 \def (eq_ind T
393 (THead (Flat Appl) v t5) (\lambda (e: T).(match e in T return (\lambda (_:
394 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
395 (THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
396 [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
397 b) u0 t2) H11) in (False_ind ((eq T (THead (Flat Appl) v t6) t4) \to ((tau0 g
398 c0 t5 t6) \to (ty3 g c0 (THead (Bind b) u0 t2) t4))) H12))) c1 (sym_eq C c1
399 c0 H8) H9 H10 H7)))) | (tau0_cast c1 v1 v2 H7 t5 t6 H8) \Rightarrow (\lambda
400 (H9: (eq C c1 c0)).(\lambda (H10: (eq T (THead (Flat Cast) v1 t5) (THead
401 (Bind b) u0 t2))).(\lambda (H11: (eq T (THead (Flat Cast) v2 t6) t4)).(eq_ind
402 C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t5) (THead (Bind b) u0
403 t2)) \to ((eq T (THead (Flat Cast) v2 t6) t4) \to ((tau0 g c2 v1 v2) \to
404 ((tau0 g c2 t5 t6) \to (ty3 g c0 (THead (Bind b) u0 t2) t4)))))) (\lambda
405 (H12: (eq T (THead (Flat Cast) v1 t5) (THead (Bind b) u0 t2))).(let H13 \def
406 (eq_ind T (THead (Flat Cast) v1 t5) (\lambda (e: T).(match e in T return
407 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
408 \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return (\lambda
409 (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat _) \Rightarrow
410 True])])) I (THead (Bind b) u0 t2) H12) in (False_ind ((eq T (THead (Flat
411 Cast) v2 t6) t4) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0 t5 t6) \to (ty3 g c0
412 (THead (Bind b) u0 t2) t4)))) H13))) c1 (sym_eq C c1 c0 H9) H10 H11 H7
413 H8))))]) in (H7 (refl_equal C c0) (refl_equal T (THead (Bind b) u0 t2))
414 (refl_equal T t4)))))))))))))))))) (\lambda (c0: C).(\lambda (w: T).(\lambda
415 (u0: T).(\lambda (H0: (ty3 g c0 w u0)).(\lambda (_: ((\forall (t2: T).((tau0
416 g c0 w t2) \to (ty3 g c0 w t2))))).(\lambda (v: T).(\lambda (t: T).(\lambda
417 (H2: (ty3 g c0 v (THead (Bind Abst) u0 t))).(\lambda (H3: ((\forall (t2:
418 T).((tau0 g c0 v t2) \to (ty3 g c0 v t2))))).(\lambda (t2: T).(\lambda (H4:
419 (tau0 g c0 (THead (Flat Appl) w v) t2)).(let H5 \def (match H4 in tau0 return
420 (\lambda (c1: C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (tau0 ? c1 t0
421 t3)).((eq C c1 c0) \to ((eq T t0 (THead (Flat Appl) w v)) \to ((eq T t3 t2)
422 \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))))) with [(tau0_sort c1 n)
423 \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T (TSort n) (THead
424 (Flat Appl) w v))).(\lambda (H7: (eq T (TSort (next g n)) t2)).(eq_ind C c0
425 (\lambda (_: C).((eq T (TSort n) (THead (Flat Appl) w v)) \to ((eq T (TSort
426 (next g n)) t2) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))) (\lambda (H8:
427 (eq T (TSort n) (THead (Flat Appl) w v))).(let H9 \def (eq_ind T (TSort n)
428 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
429 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
430 False])) I (THead (Flat Appl) w v) H8) in (False_ind ((eq T (TSort (next g
431 n)) t2) \to (ty3 g c0 (THead (Flat Appl) w v) t2)) H9))) c1 (sym_eq C c1 c0
432 H5) H6 H7)))) | (tau0_abbr c1 d v0 i H5 w0 H6) \Rightarrow (\lambda (H7: (eq
433 C c1 c0)).(\lambda (H8: (eq T (TLRef i) (THead (Flat Appl) w v))).(\lambda
434 (H9: (eq T (lift (S i) O w0) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef
435 i) (THead (Flat Appl) w v)) \to ((eq T (lift (S i) O w0) t2) \to ((getl i c2
436 (CHead d (Bind Abbr) v0)) \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat
437 Appl) w v) t2)))))) (\lambda (H10: (eq T (TLRef i) (THead (Flat Appl) w
438 v))).(let H11 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return
439 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
440 \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) w
441 v) H10) in (False_ind ((eq T (lift (S i) O w0) t2) \to ((getl i c0 (CHead d
442 (Bind Abbr) v0)) \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v)
443 t2)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) | (tau0_abst c1 d v0 i
444 H5 w0 H6) \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T (TLRef
445 i) (THead (Flat Appl) w v))).(\lambda (H9: (eq T (lift (S i) O v0)
446 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (THead (Flat Appl) w v))
447 \to ((eq T (lift (S i) O v0) t2) \to ((getl i c2 (CHead d (Bind Abst) v0))
448 \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))) (\lambda
449 (H10: (eq T (TLRef i) (THead (Flat Appl) w v))).(let H11 \def (eq_ind T
450 (TLRef i) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
451 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _)
452 \Rightarrow False])) I (THead (Flat Appl) w v) H10) in (False_ind ((eq T
453 (lift (S i) O v0) t2) \to ((getl i c0 (CHead d (Bind Abst) v0)) \to ((tau0 g
454 d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))) H11))) c1 (sym_eq C c1
455 c0 H7) H8 H9 H5 H6)))) | (tau0_bind b c1 v0 t0 t3 H5) \Rightarrow (\lambda
456 (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Bind b) v0 t0) (THead (Flat
457 Appl) w v))).(\lambda (H8: (eq T (THead (Bind b) v0 t3) t2)).(eq_ind C c0
458 (\lambda (c2: C).((eq T (THead (Bind b) v0 t0) (THead (Flat Appl) w v)) \to
459 ((eq T (THead (Bind b) v0 t3) t2) \to ((tau0 g (CHead c2 (Bind b) v0) t0 t3)
460 \to (ty3 g c0 (THead (Flat Appl) w v) t2))))) (\lambda (H9: (eq T (THead
461 (Bind b) v0 t0) (THead (Flat Appl) w v))).(let H10 \def (eq_ind T (THead
462 (Bind b) v0 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
463 with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _
464 _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
465 \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat Appl) w v)
466 H9) in (False_ind ((eq T (THead (Bind b) v0 t3) t2) \to ((tau0 g (CHead c0
467 (Bind b) v0) t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2))) H10))) c1
468 (sym_eq C c1 c0 H6) H7 H8 H5)))) | (tau0_appl c1 v0 t0 t3 H5) \Rightarrow
469 (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat Appl) v0 t0)
470 (THead (Flat Appl) w v))).(\lambda (H8: (eq T (THead (Flat Appl) v0 t3)
471 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Appl) v0 t0) (THead
472 (Flat Appl) w v)) \to ((eq T (THead (Flat Appl) v0 t3) t2) \to ((tau0 g c2 t0
473 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2))))) (\lambda (H9: (eq T (THead
474 (Flat Appl) v0 t0) (THead (Flat Appl) w v))).(let H10 \def (f_equal T T
475 (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
476 \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t4) \Rightarrow t4]))
477 (THead (Flat Appl) v0 t0) (THead (Flat Appl) w v) H9) in ((let H11 \def
478 (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
479 [(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t4 _)
480 \Rightarrow t4])) (THead (Flat Appl) v0 t0) (THead (Flat Appl) w v) H9) in
481 (eq_ind T w (\lambda (t4: T).((eq T t0 v) \to ((eq T (THead (Flat Appl) t4
482 t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))
483 (\lambda (H12: (eq T t0 v)).(eq_ind T v (\lambda (t4: T).((eq T (THead (Flat
484 Appl) w t3) t2) \to ((tau0 g c0 t4 t3) \to (ty3 g c0 (THead (Flat Appl) w v)
485 t2)))) (\lambda (H13: (eq T (THead (Flat Appl) w t3) t2)).(eq_ind T (THead
486 (Flat Appl) w t3) (\lambda (t4: T).((tau0 g c0 v t3) \to (ty3 g c0 (THead
487 (Flat Appl) w v) t4))) (\lambda (H14: (tau0 g c0 v t3)).(let H_y \def (H3 t3
488 H14) in (let H15 \def (ty3_unique g c0 v t3 H_y (THead (Bind Abst) u0 t) H2)
489 in (ex_ind T (\lambda (t4: T).(ty3 g c0 t3 t4)) (ty3 g c0 (THead (Flat Appl)
490 w v) (THead (Flat Appl) w t3)) (\lambda (x: T).(\lambda (H16: (ty3 g c0 t3
491 x)).(ex_ind T (\lambda (t4: T).(ty3 g c0 u0 t4)) (ty3 g c0 (THead (Flat Appl)
492 w v) (THead (Flat Appl) w t3)) (\lambda (x0: T).(\lambda (_: (ty3 g c0 u0
493 x0)).(ex_ind T (\lambda (t4: T).(ty3 g c0 (THead (Bind Abst) u0 t) t4)) (ty3
494 g c0 (THead (Flat Appl) w v) (THead (Flat Appl) w t3)) (\lambda (x1:
495 T).(\lambda (H18: (ty3 g c0 (THead (Bind Abst) u0 t) x1)).(ex4_3_ind T T T
496 (\lambda (t4: T).(\lambda (_: T).(\lambda (_: T).(pc3 c0 (THead (Bind Abst)
497 u0 t4) x1)))) (\lambda (_: T).(\lambda (t5: T).(\lambda (_: T).(ty3 g c0 u0
498 t5)))) (\lambda (t4: T).(\lambda (_: T).(\lambda (_: T).(ty3 g (CHead c0
499 (Bind Abst) u0) t t4)))) (\lambda (t4: T).(\lambda (_: T).(\lambda (t6:
500 T).(ty3 g (CHead c0 (Bind Abst) u0) t4 t6)))) (ty3 g c0 (THead (Flat Appl) w
501 v) (THead (Flat Appl) w t3)) (\lambda (x2: T).(\lambda (x3: T).(\lambda (x4:
502 T).(\lambda (_: (pc3 c0 (THead (Bind Abst) u0 x2) x1)).(\lambda (H20: (ty3 g
503 c0 u0 x3)).(\lambda (H21: (ty3 g (CHead c0 (Bind Abst) u0) t x2)).(\lambda
504 (H22: (ty3 g (CHead c0 (Bind Abst) u0) x2 x4)).(ty3_conv g c0 (THead (Flat
505 Appl) w t3) (THead (Flat Appl) w (THead (Bind Abst) u0 x2)) (ty3_appl g c0 w
506 u0 H0 t3 x2 (ty3_sconv g c0 t3 x H16 (THead (Bind Abst) u0 t) (THead (Bind
507 Abst) u0 x2) (ty3_bind g c0 u0 x3 H20 Abst t x2 H21 x4 H22) H15)) (THead
508 (Flat Appl) w v) (THead (Flat Appl) w (THead (Bind Abst) u0 t)) (ty3_appl g
509 c0 w u0 H0 v t H2) (pc3_thin_dx c0 (THead (Bind Abst) u0 t) t3 (ty3_unique g
510 c0 v (THead (Bind Abst) u0 t) H2 t3 H_y) w Appl))))))))) (ty3_gen_bind g Abst
511 c0 u0 t x1 H18)))) (ty3_correct g c0 v (THead (Bind Abst) u0 t) H2))))
512 (ty3_correct g c0 w u0 H0)))) (ty3_correct g c0 v t3 H_y))))) t2 H13)) t0
513 (sym_eq T t0 v H12))) v0 (sym_eq T v0 w H11))) H10))) c1 (sym_eq C c1 c0 H6)
514 H7 H8 H5)))) | (tau0_cast c1 v1 v2 H5 t0 t3 H6) \Rightarrow (\lambda (H7: (eq
515 C c1 c0)).(\lambda (H8: (eq T (THead (Flat Cast) v1 t0) (THead (Flat Appl) w
516 v))).(\lambda (H9: (eq T (THead (Flat Cast) v2 t3) t2)).(eq_ind C c0 (\lambda
517 (c2: C).((eq T (THead (Flat Cast) v1 t0) (THead (Flat Appl) w v)) \to ((eq T
518 (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to ((tau0 g c2 t0 t3)
519 \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))) (\lambda (H10: (eq T (THead
520 (Flat Cast) v1 t0) (THead (Flat Appl) w v))).(let H11 \def (eq_ind T (THead
521 (Flat Cast) v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
522 with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _
523 _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
524 \Rightarrow False | (Flat f) \Rightarrow (match f in F return (\lambda (_:
525 F).Prop) with [Appl \Rightarrow False | Cast \Rightarrow True])])])) I (THead
526 (Flat Appl) w v) H10) in (False_ind ((eq T (THead (Flat Cast) v2 t3) t2) \to
527 ((tau0 g c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (THead (Flat Appl) w
528 v) t2)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6))))]) in (H5 (refl_equal
529 C c0) (refl_equal T (THead (Flat Appl) w v)) (refl_equal T t2))))))))))))))
530 (\lambda (c0: C).(\lambda (t2: T).(\lambda (t3: T).(\lambda (H0: (ty3 g c0 t2
531 t3)).(\lambda (H1: ((\forall (t4: T).((tau0 g c0 t2 t4) \to (ty3 g c0 t2
532 t4))))).(\lambda (t0: T).(\lambda (_: (ty3 g c0 t3 t0)).(\lambda (H3:
533 ((\forall (t4: T).((tau0 g c0 t3 t4) \to (ty3 g c0 t3 t4))))).(\lambda (t4:
534 T).(\lambda (H4: (tau0 g c0 (THead (Flat Cast) t3 t2) t4)).(let H5 \def
535 (match H4 in tau0 return (\lambda (c1: C).(\lambda (t: T).(\lambda (t5:
536 T).(\lambda (_: (tau0 ? c1 t t5)).((eq C c1 c0) \to ((eq T t (THead (Flat
537 Cast) t3 t2)) \to ((eq T t5 t4) \to (ty3 g c0 (THead (Flat Cast) t3 t2)
538 t4)))))))) with [(tau0_sort c1 n) \Rightarrow (\lambda (H5: (eq C c1
539 c0)).(\lambda (H6: (eq T (TSort n) (THead (Flat Cast) t3 t2))).(\lambda (H7:
540 (eq T (TSort (next g n)) t4)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n)
541 (THead (Flat Cast) t3 t2)) \to ((eq T (TSort (next g n)) t4) \to (ty3 g c0
542 (THead (Flat Cast) t3 t2) t4)))) (\lambda (H8: (eq T (TSort n) (THead (Flat
543 Cast) t3 t2))).(let H9 \def (eq_ind T (TSort n) (\lambda (e: T).(match e in T
544 return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow True | (TLRef _)
545 \Rightarrow False | (THead _ _ _) \Rightarrow False])) I (THead (Flat Cast)
546 t3 t2) H8) in (False_ind ((eq T (TSort (next g n)) t4) \to (ty3 g c0 (THead
547 (Flat Cast) t3 t2) t4)) H9))) c1 (sym_eq C c1 c0 H5) H6 H7)))) | (tau0_abbr
548 c1 d v i H5 w H6) \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T
549 (TLRef i) (THead (Flat Cast) t3 t2))).(\lambda (H9: (eq T (lift (S i) O w)
550 t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (THead (Flat Cast) t3
551 t2)) \to ((eq T (lift (S i) O w) t4) \to ((getl i c2 (CHead d (Bind Abbr) v))
552 \to ((tau0 g d v w) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))) (\lambda
553 (H10: (eq T (TLRef i) (THead (Flat Cast) t3 t2))).(let H11 \def (eq_ind T
554 (TLRef i) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
555 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _)
556 \Rightarrow False])) I (THead (Flat Cast) t3 t2) H10) in (False_ind ((eq T
557 (lift (S i) O w) t4) \to ((getl i c0 (CHead d (Bind Abbr) v)) \to ((tau0 g d
558 v w) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))) H11))) c1 (sym_eq C c1 c0
559 H7) H8 H9 H5 H6)))) | (tau0_abst c1 d v i H5 w H6) \Rightarrow (\lambda (H7:
560 (eq C c1 c0)).(\lambda (H8: (eq T (TLRef i) (THead (Flat Cast) t3
561 t2))).(\lambda (H9: (eq T (lift (S i) O v) t4)).(eq_ind C c0 (\lambda (c2:
562 C).((eq T (TLRef i) (THead (Flat Cast) t3 t2)) \to ((eq T (lift (S i) O v)
563 t4) \to ((getl i c2 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g
564 c0 (THead (Flat Cast) t3 t2) t4)))))) (\lambda (H10: (eq T (TLRef i) (THead
565 (Flat Cast) t3 t2))).(let H11 \def (eq_ind T (TLRef i) (\lambda (e: T).(match
566 e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
567 (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead
568 (Flat Cast) t3 t2) H10) in (False_ind ((eq T (lift (S i) O v) t4) \to ((getl
569 i c0 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Flat
570 Cast) t3 t2) t4)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) |
571 (tau0_bind b c1 v t5 t6 H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda
572 (H7: (eq T (THead (Bind b) v t5) (THead (Flat Cast) t3 t2))).(\lambda (H8:
573 (eq T (THead (Bind b) v t6) t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead
574 (Bind b) v t5) (THead (Flat Cast) t3 t2)) \to ((eq T (THead (Bind b) v t6)
575 t4) \to ((tau0 g (CHead c2 (Bind b) v) t5 t6) \to (ty3 g c0 (THead (Flat
576 Cast) t3 t2) t4))))) (\lambda (H9: (eq T (THead (Bind b) v t5) (THead (Flat
577 Cast) t3 t2))).(let H10 \def (eq_ind T (THead (Bind b) v t5) (\lambda (e:
578 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
579 False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K
580 return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True | (Flat _)
581 \Rightarrow False])])) I (THead (Flat Cast) t3 t2) H9) in (False_ind ((eq T
582 (THead (Bind b) v t6) t4) \to ((tau0 g (CHead c0 (Bind b) v) t5 t6) \to (ty3
583 g c0 (THead (Flat Cast) t3 t2) t4))) H10))) c1 (sym_eq C c1 c0 H6) H7 H8
584 H5)))) | (tau0_appl c1 v t5 t6 H5) \Rightarrow (\lambda (H6: (eq C c1
585 c0)).(\lambda (H7: (eq T (THead (Flat Appl) v t5) (THead (Flat Cast) t3
586 t2))).(\lambda (H8: (eq T (THead (Flat Appl) v t6) t4)).(eq_ind C c0 (\lambda
587 (c2: C).((eq T (THead (Flat Appl) v t5) (THead (Flat Cast) t3 t2)) \to ((eq T
588 (THead (Flat Appl) v t6) t4) \to ((tau0 g c2 t5 t6) \to (ty3 g c0 (THead
589 (Flat Cast) t3 t2) t4))))) (\lambda (H9: (eq T (THead (Flat Appl) v t5)
590 (THead (Flat Cast) t3 t2))).(let H10 \def (eq_ind T (THead (Flat Appl) v t5)
591 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
592 \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
593 (match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False |
594 (Flat f) \Rightarrow (match f in F return (\lambda (_: F).Prop) with [Appl
595 \Rightarrow True | Cast \Rightarrow False])])])) I (THead (Flat Cast) t3 t2)
596 H9) in (False_ind ((eq T (THead (Flat Appl) v t6) t4) \to ((tau0 g c0 t5 t6)
597 \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4))) H10))) c1 (sym_eq C c1 c0 H6)
598 H7 H8 H5)))) | (tau0_cast c1 v1 v2 H5 t5 t6 H6) \Rightarrow (\lambda (H7: (eq
599 C c1 c0)).(\lambda (H8: (eq T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3
600 t2))).(\lambda (H9: (eq T (THead (Flat Cast) v2 t6) t4)).(eq_ind C c0
601 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2))
602 \to ((eq T (THead (Flat Cast) v2 t6) t4) \to ((tau0 g c2 v1 v2) \to ((tau0 g
603 c2 t5 t6) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))) (\lambda (H10: (eq
604 T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2))).(let H11 \def
605 (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
606 [(TSort _) \Rightarrow t5 | (TLRef _) \Rightarrow t5 | (THead _ _ t)
607 \Rightarrow t])) (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2) H10) in
608 ((let H12 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_:
609 T).T) with [(TSort _) \Rightarrow v1 | (TLRef _) \Rightarrow v1 | (THead _ t
610 _) \Rightarrow t])) (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2) H10)
611 in (eq_ind T t3 (\lambda (t: T).((eq T t5 t2) \to ((eq T (THead (Flat Cast)
612 v2 t6) t4) \to ((tau0 g c0 t v2) \to ((tau0 g c0 t5 t6) \to (ty3 g c0 (THead
613 (Flat Cast) t3 t2) t4)))))) (\lambda (H13: (eq T t5 t2)).(eq_ind T t2
614 (\lambda (t: T).((eq T (THead (Flat Cast) v2 t6) t4) \to ((tau0 g c0 t3 v2)
615 \to ((tau0 g c0 t t6) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))
616 (\lambda (H14: (eq T (THead (Flat Cast) v2 t6) t4)).(eq_ind T (THead (Flat
617 Cast) v2 t6) (\lambda (t: T).((tau0 g c0 t3 v2) \to ((tau0 g c0 t2 t6) \to
618 (ty3 g c0 (THead (Flat Cast) t3 t2) t)))) (\lambda (H15: (tau0 g c0 t3
619 v2)).(\lambda (H16: (tau0 g c0 t2 t6)).(let H_y \def (H1 t6 H16) in (let H_y0
620 \def (H3 v2 H15) in (let H17 \def (ty3_unique g c0 t2 t6 H_y t3 H0) in
621 (ex_ind T (\lambda (t: T).(ty3 g c0 v2 t)) (ty3 g c0 (THead (Flat Cast) t3
622 t2) (THead (Flat Cast) v2 t6)) (\lambda (x: T).(\lambda (H18: (ty3 g c0 v2
623 x)).(ex_ind T (\lambda (t: T).(ty3 g c0 t6 t)) (ty3 g c0 (THead (Flat Cast)
624 t3 t2) (THead (Flat Cast) v2 t6)) (\lambda (x0: T).(\lambda (H19: (ty3 g c0
625 t6 x0)).(ty3_conv g c0 (THead (Flat Cast) v2 t6) (THead (Flat Cast) x v2)
626 (ty3_cast g c0 t6 v2 (ty3_sconv g c0 t6 x0 H19 t3 v2 H_y0 H17) x H18) (THead
627 (Flat Cast) t3 t2) (THead (Flat Cast) v2 t3) (ty3_cast g c0 t2 t3 H0 v2 H_y0)
628 (pc3_thin_dx c0 t3 t6 (ty3_unique g c0 t2 t3 H0 t6 H_y) v2 Cast))))
629 (ty3_correct g c0 t2 t6 H_y)))) (ty3_correct g c0 t3 v2 H_y0))))))) t4 H14))
630 t5 (sym_eq T t5 t2 H13))) v1 (sym_eq T v1 t3 H12))) H11))) c1 (sym_eq C c1 c0
631 H7) H8 H9 H5 H6))))]) in (H5 (refl_equal C c0) (refl_equal T (THead (Flat
632 Cast) t3 t2)) (refl_equal T t4))))))))))))) c u t1 H))))).
projects / helm.git / blob