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/ty3/pr3_props.ma".
19 include "LambdaDelta-1/tau0/defs.ma".
22 \forall (g: G).(\forall (c: C).(\forall (u: T).(\forall (t1: T).((ty3 g c u
23 t1) \to (\forall (t2: T).((tau0 g c u t2) \to (ty3 g c u t2)))))))
25 \lambda (g: G).(\lambda (c: C).(\lambda (u: T).(\lambda (t1: T).(\lambda (H:
26 (ty3 g c u t1)).(ty3_ind g (\lambda (c0: C).(\lambda (t: T).(\lambda (_:
27 T).(\forall (t2: T).((tau0 g c0 t t2) \to (ty3 g c0 t t2)))))) (\lambda (c0:
28 C).(\lambda (t2: T).(\lambda (t: T).(\lambda (_: (ty3 g c0 t2 t)).(\lambda
29 (_: ((\forall (t3: T).((tau0 g c0 t2 t3) \to (ty3 g c0 t2 t3))))).(\lambda
30 (u0: T).(\lambda (t3: T).(\lambda (_: (ty3 g c0 u0 t3)).(\lambda (H3:
31 ((\forall (t4: T).((tau0 g c0 u0 t4) \to (ty3 g c0 u0 t4))))).(\lambda (_:
32 (pc3 c0 t3 t2)).(\lambda (t0: T).(\lambda (H5: (tau0 g c0 u0 t0)).(H3 t0
33 H5))))))))))))) (\lambda (c0: C).(\lambda (m: nat).(\lambda (t2: T).(\lambda
34 (H0: (tau0 g c0 (TSort m) t2)).(let H1 \def (match H0 in tau0 return (\lambda
35 (c1: C).(\lambda (t: T).(\lambda (t0: T).(\lambda (_: (tau0 ? c1 t t0)).((eq
36 C c1 c0) \to ((eq T t (TSort m)) \to ((eq T t0 t2) \to (ty3 g c0 (TSort m)
37 t2)))))))) with [(tau0_sort c1 n) \Rightarrow (\lambda (H1: (eq C c1
38 c0)).(\lambda (H2: (eq T (TSort n) (TSort m))).(\lambda (H3: (eq T (TSort
39 (next g n)) t2)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n) (TSort m)) \to
40 ((eq T (TSort (next g n)) t2) \to (ty3 g c0 (TSort m) t2)))) (\lambda (H4:
41 (eq T (TSort n) (TSort m))).(let H5 \def (f_equal T nat (\lambda (e:
42 T).(match e in T return (\lambda (_: T).nat) with [(TSort n0) \Rightarrow n0
43 | (TLRef _) \Rightarrow n | (THead _ _ _) \Rightarrow n])) (TSort n) (TSort
44 m) H4) in (eq_ind nat m (\lambda (n0: nat).((eq T (TSort (next g n0)) t2) \to
45 (ty3 g c0 (TSort m) t2))) (\lambda (H6: (eq T (TSort (next g m)) t2)).(eq_ind
46 T (TSort (next g m)) (\lambda (t: T).(ty3 g c0 (TSort m) t)) (ty3_sort g c0
47 m) t2 H6)) n (sym_eq nat n m H5)))) c1 (sym_eq C c1 c0 H1) H2 H3)))) |
48 (tau0_abbr c1 d v i H1 w H2) \Rightarrow (\lambda (H3: (eq C c1 c0)).(\lambda
49 (H4: (eq T (TLRef i) (TSort m))).(\lambda (H5: (eq T (lift (S i) O w)
50 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (TSort m)) \to ((eq T
51 (lift (S i) O w) t2) \to ((getl i c2 (CHead d (Bind Abbr) v)) \to ((tau0 g d
52 v w) \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6: (eq T (TLRef i) (TSort
53 m))).(let H7 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return
54 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
55 \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (TSort m) H6) in
56 (False_ind ((eq T (lift (S i) O w) t2) \to ((getl i c0 (CHead d (Bind Abbr)
57 v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2)))) H7))) c1 (sym_eq C c1
58 c0 H3) H4 H5 H1 H2)))) | (tau0_abst c1 d v i H1 w H2) \Rightarrow (\lambda
59 (H3: (eq C c1 c0)).(\lambda (H4: (eq T (TLRef i) (TSort m))).(\lambda (H5:
60 (eq T (lift (S i) O v) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i)
61 (TSort m)) \to ((eq T (lift (S i) O v) t2) \to ((getl i c2 (CHead d (Bind
62 Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6:
63 (eq T (TLRef i) (TSort m))).(let H7 \def (eq_ind T (TLRef i) (\lambda (e:
64 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
65 False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I
66 (TSort m) H6) in (False_ind ((eq T (lift (S i) O v) t2) \to ((getl i c0
67 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (TSort m) t2))))
68 H7))) c1 (sym_eq C c1 c0 H3) H4 H5 H1 H2)))) | (tau0_bind b c1 v t0 t3 H1)
69 \Rightarrow (\lambda (H2: (eq C c1 c0)).(\lambda (H3: (eq T (THead (Bind b) v
70 t0) (TSort m))).(\lambda (H4: (eq T (THead (Bind b) v t3) t2)).(eq_ind C c0
71 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TSort m)) \to ((eq T (THead
72 (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0 t3) \to (ty3 g c0
73 (TSort m) t2))))) (\lambda (H5: (eq T (THead (Bind b) v t0) (TSort m))).(let
74 H6 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e: T).(match e in T return
75 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
76 \Rightarrow False | (THead _ _ _) \Rightarrow True])) I (TSort m) H5) in
77 (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c0 (Bind b)
78 v) t0 t3) \to (ty3 g c0 (TSort m) t2))) H6))) c1 (sym_eq C c1 c0 H2) H3 H4
79 H1)))) | (tau0_appl c1 v t0 t3 H1) \Rightarrow (\lambda (H2: (eq C c1
80 c0)).(\lambda (H3: (eq T (THead (Flat Appl) v t0) (TSort m))).(\lambda (H4:
81 (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T
82 (THead (Flat Appl) v t0) (TSort m)) \to ((eq T (THead (Flat Appl) v t3) t2)
83 \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TSort m) t2))))) (\lambda (H5: (eq T
84 (THead (Flat Appl) v t0) (TSort m))).(let H6 \def (eq_ind T (THead (Flat
85 Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
86 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
87 \Rightarrow True])) I (TSort m) H5) in (False_ind ((eq T (THead (Flat Appl) v
88 t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TSort m) t2))) H6))) c1 (sym_eq
89 C c1 c0 H2) H3 H4 H1)))) | (tau0_cast c1 v1 v2 H1 t0 t3 H2) \Rightarrow
90 (\lambda (H3: (eq C c1 c0)).(\lambda (H4: (eq T (THead (Flat Cast) v1 t0)
91 (TSort m))).(\lambda (H5: (eq T (THead (Flat Cast) v2 t3) t2)).(eq_ind C c0
92 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TSort m)) \to ((eq T
93 (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to ((tau0 g c2 t0 t3)
94 \to (ty3 g c0 (TSort m) t2)))))) (\lambda (H6: (eq T (THead (Flat Cast) v1
95 t0) (TSort m))).(let H7 \def (eq_ind T (THead (Flat Cast) v1 t0) (\lambda (e:
96 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
97 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
98 (TSort m) H6) in (False_ind ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g
99 c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TSort m) t2)))) H7))) c1
100 (sym_eq C c1 c0 H3) H4 H5 H1 H2))))]) in (H1 (refl_equal C c0) (refl_equal T
101 (TSort m)) (refl_equal T t2))))))) (\lambda (n: nat).(\lambda (c0:
102 C).(\lambda (d: C).(\lambda (u0: T).(\lambda (H0: (getl n c0 (CHead d (Bind
103 Abbr) u0))).(\lambda (t: T).(\lambda (_: (ty3 g d u0 t)).(\lambda (H2:
104 ((\forall (t2: T).((tau0 g d u0 t2) \to (ty3 g d u0 t2))))).(\lambda (t2:
105 T).(\lambda (H3: (tau0 g c0 (TLRef n) t2)).(let H4 \def (match H3 in tau0
106 return (\lambda (c1: C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (tau0
107 ? c1 t0 t3)).((eq C c1 c0) \to ((eq T t0 (TLRef n)) \to ((eq T t3 t2) \to
108 (ty3 g c0 (TLRef n) t2)))))))) with [(tau0_sort c1 n0) \Rightarrow (\lambda
109 (H4: (eq C c1 c0)).(\lambda (H5: (eq T (TSort n0) (TLRef n))).(\lambda (H6:
110 (eq T (TSort (next g n0)) t2)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n0)
111 (TLRef n)) \to ((eq T (TSort (next g n0)) t2) \to (ty3 g c0 (TLRef n) t2))))
112 (\lambda (H7: (eq T (TSort n0) (TLRef n))).(let H8 \def (eq_ind T (TSort n0)
113 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
114 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
115 False])) I (TLRef n) H7) in (False_ind ((eq T (TSort (next g n0)) t2) \to
116 (ty3 g c0 (TLRef n) t2)) H8))) c1 (sym_eq C c1 c0 H4) H5 H6)))) | (tau0_abbr
117 c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq
118 T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift (S i) O w) t2)).(eq_ind C
119 c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O w)
120 t2) \to ((getl i c2 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g
121 c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def
122 (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
123 [(TSort _) \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _)
124 \Rightarrow i])) (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0:
125 nat).((eq T (lift (S n0) O w) t2) \to ((getl n0 c0 (CHead d0 (Bind Abbr) v))
126 \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T
127 (lift (S n) O w) t2)).(eq_ind T (lift (S n) O w) (\lambda (t0: T).((getl n c0
128 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0))))
129 (\lambda (H12: (getl n c0 (CHead d0 (Bind Abbr) v))).(\lambda (H13: (tau0 g
130 d0 v w)).(let H14 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda (c2:
131 C).(getl n c0 c2)) H0 (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d (Bind
132 Abbr) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in (let H15 \def (f_equal C C
133 (\lambda (e: C).(match e in C return (\lambda (_: C).C) with [(CSort _)
134 \Rightarrow d | (CHead c2 _ _) \Rightarrow c2])) (CHead d (Bind Abbr) u0)
135 (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead
136 d0 (Bind Abbr) v) H12)) in ((let H16 \def (f_equal C T (\lambda (e: C).(match
137 e in C return (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _
138 t0) \Rightarrow t0])) (CHead d (Bind Abbr) u0) (CHead d0 (Bind Abbr) v)
139 (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in
140 (\lambda (H17: (eq C d d0)).(let H18 \def (eq_ind_r T v (\lambda (t0:
141 T).(getl n c0 (CHead d0 (Bind Abbr) t0))) H14 u0 H16) in (let H19 \def
142 (eq_ind_r T v (\lambda (t0: T).(tau0 g d0 t0 w)) H13 u0 H16) in (let H20 \def
143 (eq_ind_r C d0 (\lambda (c2: C).(getl n c0 (CHead c2 (Bind Abbr) u0))) H18 d
144 H17) in (let H21 \def (eq_ind_r C d0 (\lambda (c2: C).(tau0 g c2 u0 w)) H19 d
145 H17) in (ty3_abbr g n c0 d u0 H20 w (H2 w H21)))))))) H15))))) t2 H11)) i
146 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_abst
147 c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq
148 T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift (S i) O v) t2)).(eq_ind C
149 c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O v)
150 t2) \to ((getl i c2 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g
151 c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def
152 (f_equal T nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with
153 [(TSort _) \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _)
154 \Rightarrow i])) (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0:
155 nat).((eq T (lift (S n0) O v) t2) \to ((getl n0 c0 (CHead d0 (Bind Abst) v))
156 \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T
157 (lift (S n) O v) t2)).(eq_ind T (lift (S n) O v) (\lambda (t0: T).((getl n c0
158 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0))))
159 (\lambda (H12: (getl n c0 (CHead d0 (Bind Abst) v))).(\lambda (_: (tau0 g d0
160 v w)).(let H14 \def (eq_ind C (CHead d (Bind Abbr) u0) (\lambda (c2: C).(getl
161 n c0 c2)) H0 (CHead d0 (Bind Abst) v) (getl_mono c0 (CHead d (Bind Abbr) u0)
162 n H0 (CHead d0 (Bind Abst) v) H12)) in (let H15 \def (eq_ind C (CHead d (Bind
163 Abbr) u0) (\lambda (ee: C).(match ee in C return (\lambda (_: C).Prop) with
164 [(CSort _) \Rightarrow False | (CHead _ k _) \Rightarrow (match k in K return
165 (\lambda (_: K).Prop) with [(Bind b) \Rightarrow (match b in B return
166 (\lambda (_: B).Prop) with [Abbr \Rightarrow True | Abst \Rightarrow False |
167 Void \Rightarrow False]) | (Flat _) \Rightarrow False])])) I (CHead d0 (Bind
168 Abst) v) (getl_mono c0 (CHead d (Bind Abbr) u0) n H0 (CHead d0 (Bind Abst) v)
169 H12)) in (False_ind (ty3 g c0 (TLRef n) (lift (S n) O v)) H15))))) t2 H11)) i
170 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_bind b
171 c1 v t0 t3 H4) \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T
172 (THead (Bind b) v t0) (TLRef n))).(\lambda (H7: (eq T (THead (Bind b) v t3)
173 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TLRef n))
174 \to ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0
175 t3) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H8: (eq T (THead (Bind b) v t0)
176 (TLRef n))).(let H9 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e:
177 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
178 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
179 (TLRef n) H8) in (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g
180 (CHead c0 (Bind b) v) t0 t3) \to (ty3 g c0 (TLRef n) t2))) H9))) c1 (sym_eq C
181 c1 c0 H5) H6 H7 H4)))) | (tau0_appl c1 v t0 t3 H4) \Rightarrow (\lambda (H5:
182 (eq C c1 c0)).(\lambda (H6: (eq T (THead (Flat Appl) v t0) (TLRef
183 n))).(\lambda (H7: (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda
184 (c2: C).((eq T (THead (Flat Appl) v t0) (TLRef n)) \to ((eq T (THead (Flat
185 Appl) v t3) t2) \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))
186 (\lambda (H8: (eq T (THead (Flat Appl) v t0) (TLRef n))).(let H9 \def (eq_ind
187 T (THead (Flat Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_:
188 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
189 (THead _ _ _) \Rightarrow True])) I (TLRef n) H8) in (False_ind ((eq T (THead
190 (Flat Appl) v t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef n) t2)))
191 H9))) c1 (sym_eq C c1 c0 H5) H6 H7 H4)))) | (tau0_cast c1 v1 v2 H4 t0 t3 H5)
192 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat
193 Cast) v1 t0) (TLRef n))).(\lambda (H8: (eq T (THead (Flat Cast) v2 t3)
194 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TLRef
195 n)) \to ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to
196 ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T
197 (THead (Flat Cast) v1 t0) (TLRef n))).(let H10 \def (eq_ind T (THead (Flat
198 Cast) v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
199 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
200 \Rightarrow True])) I (TLRef n) H9) in (False_ind ((eq T (THead (Flat Cast)
201 v2 t3) t2) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef
202 n) t2)))) H10))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5))))]) in (H4 (refl_equal
203 C c0) (refl_equal T (TLRef n)) (refl_equal T t2))))))))))))) (\lambda (n:
204 nat).(\lambda (c0: C).(\lambda (d: C).(\lambda (u0: T).(\lambda (H0: (getl n
205 c0 (CHead d (Bind Abst) u0))).(\lambda (t: T).(\lambda (H1: (ty3 g d u0
206 t)).(\lambda (_: ((\forall (t2: T).((tau0 g d u0 t2) \to (ty3 g d u0
207 t2))))).(\lambda (t2: T).(\lambda (H3: (tau0 g c0 (TLRef n) t2)).(let H4 \def
208 (match H3 in tau0 return (\lambda (c1: C).(\lambda (t0: T).(\lambda (t3:
209 T).(\lambda (_: (tau0 ? c1 t0 t3)).((eq C c1 c0) \to ((eq T t0 (TLRef n)) \to
210 ((eq T t3 t2) \to (ty3 g c0 (TLRef n) t2)))))))) with [(tau0_sort c1 n0)
211 \Rightarrow (\lambda (H4: (eq C c1 c0)).(\lambda (H5: (eq T (TSort n0) (TLRef
212 n))).(\lambda (H6: (eq T (TSort (next g n0)) t2)).(eq_ind C c0 (\lambda (_:
213 C).((eq T (TSort n0) (TLRef n)) \to ((eq T (TSort (next g n0)) t2) \to (ty3 g
214 c0 (TLRef n) t2)))) (\lambda (H7: (eq T (TSort n0) (TLRef n))).(let H8 \def
215 (eq_ind T (TSort n0) (\lambda (e: T).(match e in T return (\lambda (_:
216 T).Prop) with [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False |
217 (THead _ _ _) \Rightarrow False])) I (TLRef n) H7) in (False_ind ((eq T
218 (TSort (next g n0)) t2) \to (ty3 g c0 (TLRef n) t2)) H8))) c1 (sym_eq C c1 c0
219 H4) H5 H6)))) | (tau0_abbr c1 d0 v i H4 w H5) \Rightarrow (\lambda (H6: (eq C
220 c1 c0)).(\lambda (H7: (eq T (TLRef i) (TLRef n))).(\lambda (H8: (eq T (lift
221 (S i) O w) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (TLRef n)) \to
222 ((eq T (lift (S i) O w) t2) \to ((getl i c2 (CHead d0 (Bind Abbr) v)) \to
223 ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T (TLRef
224 i) (TLRef n))).(let H10 \def (f_equal T nat (\lambda (e: T).(match e in T
225 return (\lambda (_: T).nat) with [(TSort _) \Rightarrow i | (TLRef n0)
226 \Rightarrow n0 | (THead _ _ _) \Rightarrow i])) (TLRef i) (TLRef n) H9) in
227 (eq_ind nat n (\lambda (n0: nat).((eq T (lift (S n0) O w) t2) \to ((getl n0
228 c0 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n)
229 t2))))) (\lambda (H11: (eq T (lift (S n) O w) t2)).(eq_ind T (lift (S n) O w)
230 (\lambda (t0: T).((getl n c0 (CHead d0 (Bind Abbr) v)) \to ((tau0 g d0 v w)
231 \to (ty3 g c0 (TLRef n) t0)))) (\lambda (H12: (getl n c0 (CHead d0 (Bind
232 Abbr) v))).(\lambda (_: (tau0 g d0 v w)).(let H14 \def (eq_ind C (CHead d
233 (Bind Abst) u0) (\lambda (c2: C).(getl n c0 c2)) H0 (CHead d0 (Bind Abbr) v)
234 (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in
235 (let H15 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda (ee: C).(match ee
236 in C return (\lambda (_: C).Prop) with [(CSort _) \Rightarrow False | (CHead
237 _ k _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind b)
238 \Rightarrow (match b in B return (\lambda (_: B).Prop) with [Abbr \Rightarrow
239 False | Abst \Rightarrow True | Void \Rightarrow False]) | (Flat _)
240 \Rightarrow False])])) I (CHead d0 (Bind Abbr) v) (getl_mono c0 (CHead d
241 (Bind Abst) u0) n H0 (CHead d0 (Bind Abbr) v) H12)) in (False_ind (ty3 g c0
242 (TLRef n) (lift (S n) O w)) H15))))) t2 H11)) i (sym_eq nat i n H10)))) c1
243 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_abst c1 d0 v i H4 w H5)
244 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (TLRef i) (TLRef
245 n))).(\lambda (H8: (eq T (lift (S i) O v) t2)).(eq_ind C c0 (\lambda (c2:
246 C).((eq T (TLRef i) (TLRef n)) \to ((eq T (lift (S i) O v) t2) \to ((getl i
247 c2 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n)
248 t2)))))) (\lambda (H9: (eq T (TLRef i) (TLRef n))).(let H10 \def (f_equal T
249 nat (\lambda (e: T).(match e in T return (\lambda (_: T).nat) with [(TSort _)
250 \Rightarrow i | (TLRef n0) \Rightarrow n0 | (THead _ _ _) \Rightarrow i]))
251 (TLRef i) (TLRef n) H9) in (eq_ind nat n (\lambda (n0: nat).((eq T (lift (S
252 n0) O v) t2) \to ((getl n0 c0 (CHead d0 (Bind Abst) v)) \to ((tau0 g d0 v w)
253 \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H11: (eq T (lift (S n) O v)
254 t2)).(eq_ind T (lift (S n) O v) (\lambda (t0: T).((getl n c0 (CHead d0 (Bind
255 Abst) v)) \to ((tau0 g d0 v w) \to (ty3 g c0 (TLRef n) t0)))) (\lambda (H12:
256 (getl n c0 (CHead d0 (Bind Abst) v))).(\lambda (H13: (tau0 g d0 v w)).(let
257 H14 \def (eq_ind C (CHead d (Bind Abst) u0) (\lambda (c2: C).(getl n c0 c2))
258 H0 (CHead d0 (Bind Abst) v) (getl_mono c0 (CHead d (Bind Abst) u0) n H0
259 (CHead d0 (Bind Abst) v) H12)) in (let H15 \def (f_equal C C (\lambda (e:
260 C).(match e in C return (\lambda (_: C).C) with [(CSort _) \Rightarrow d |
261 (CHead c2 _ _) \Rightarrow c2])) (CHead d (Bind Abst) u0) (CHead d0 (Bind
262 Abst) v) (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abst) v)
263 H12)) in ((let H16 \def (f_equal C T (\lambda (e: C).(match e in C return
264 (\lambda (_: C).T) with [(CSort _) \Rightarrow u0 | (CHead _ _ t0)
265 \Rightarrow t0])) (CHead d (Bind Abst) u0) (CHead d0 (Bind Abst) v)
266 (getl_mono c0 (CHead d (Bind Abst) u0) n H0 (CHead d0 (Bind Abst) v) H12)) in
267 (\lambda (H17: (eq C d d0)).(let H18 \def (eq_ind_r T v (\lambda (t0:
268 T).(getl n c0 (CHead d0 (Bind Abst) t0))) H14 u0 H16) in (let H19 \def
269 (eq_ind_r T v (\lambda (t0: T).(tau0 g d0 t0 w)) H13 u0 H16) in (eq_ind T u0
270 (\lambda (t0: T).(ty3 g c0 (TLRef n) (lift (S n) O t0))) (let H20 \def
271 (eq_ind_r C d0 (\lambda (c2: C).(getl n c0 (CHead c2 (Bind Abst) u0))) H18 d
272 H17) in (let H21 \def (eq_ind_r C d0 (\lambda (c2: C).(tau0 g c2 u0 w)) H19 d
273 H17) in (ty3_abst g n c0 d u0 H20 t H1))) v H16))))) H15))))) t2 H11)) i
274 (sym_eq nat i n H10)))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5)))) | (tau0_bind b
275 c1 v t0 t3 H4) \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T
276 (THead (Bind b) v t0) (TLRef n))).(\lambda (H7: (eq T (THead (Bind b) v t3)
277 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Bind b) v t0) (TLRef n))
278 \to ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g (CHead c2 (Bind b) v) t0
279 t3) \to (ty3 g c0 (TLRef n) t2))))) (\lambda (H8: (eq T (THead (Bind b) v t0)
280 (TLRef n))).(let H9 \def (eq_ind T (THead (Bind b) v t0) (\lambda (e:
281 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
282 False | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow True])) I
283 (TLRef n) H8) in (False_ind ((eq T (THead (Bind b) v t3) t2) \to ((tau0 g
284 (CHead c0 (Bind b) v) t0 t3) \to (ty3 g c0 (TLRef n) t2))) H9))) c1 (sym_eq C
285 c1 c0 H5) H6 H7 H4)))) | (tau0_appl c1 v t0 t3 H4) \Rightarrow (\lambda (H5:
286 (eq C c1 c0)).(\lambda (H6: (eq T (THead (Flat Appl) v t0) (TLRef
287 n))).(\lambda (H7: (eq T (THead (Flat Appl) v t3) t2)).(eq_ind C c0 (\lambda
288 (c2: C).((eq T (THead (Flat Appl) v t0) (TLRef n)) \to ((eq T (THead (Flat
289 Appl) v t3) t2) \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))
290 (\lambda (H8: (eq T (THead (Flat Appl) v t0) (TLRef n))).(let H9 \def (eq_ind
291 T (THead (Flat Appl) v t0) (\lambda (e: T).(match e in T return (\lambda (_:
292 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
293 (THead _ _ _) \Rightarrow True])) I (TLRef n) H8) in (False_ind ((eq T (THead
294 (Flat Appl) v t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef n) t2)))
295 H9))) c1 (sym_eq C c1 c0 H5) H6 H7 H4)))) | (tau0_cast c1 v1 v2 H4 t0 t3 H5)
296 \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat
297 Cast) v1 t0) (TLRef n))).(\lambda (H8: (eq T (THead (Flat Cast) v2 t3)
298 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0) (TLRef
299 n)) \to ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c2 v1 v2) \to
300 ((tau0 g c2 t0 t3) \to (ty3 g c0 (TLRef n) t2)))))) (\lambda (H9: (eq T
301 (THead (Flat Cast) v1 t0) (TLRef n))).(let H10 \def (eq_ind T (THead (Flat
302 Cast) v1 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
303 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead _ _ _)
304 \Rightarrow True])) I (TLRef n) H9) in (False_ind ((eq T (THead (Flat Cast)
305 v2 t3) t2) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (TLRef
306 n) t2)))) H10))) c1 (sym_eq C c1 c0 H6) H7 H8 H4 H5))))]) in (H4 (refl_equal
307 C c0) (refl_equal T (TLRef n)) (refl_equal T t2))))))))))))) (\lambda (c0:
308 C).(\lambda (u0: T).(\lambda (t: T).(\lambda (H0: (ty3 g c0 u0 t)).(\lambda
309 (_: ((\forall (t2: T).((tau0 g c0 u0 t2) \to (ty3 g c0 u0 t2))))).(\lambda
310 (b: B).(\lambda (t2: T).(\lambda (t3: T).(\lambda (_: (ty3 g (CHead c0 (Bind
311 b) u0) t2 t3)).(\lambda (H3: ((\forall (t4: T).((tau0 g (CHead c0 (Bind b)
312 u0) t2 t4) \to (ty3 g (CHead c0 (Bind b) u0) t2 t4))))).(\lambda (t0:
313 T).(\lambda (H4: (tau0 g c0 (THead (Bind b) u0 t2) t0)).(let H5 \def (match
314 H4 in tau0 return (\lambda (c1: C).(\lambda (t4: T).(\lambda (t5: T).(\lambda
315 (_: (tau0 ? c1 t4 t5)).((eq C c1 c0) \to ((eq T t4 (THead (Bind b) u0 t2))
316 \to ((eq T t5 t0) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)))))))) with
317 [(tau0_sort c1 n) \Rightarrow (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T
318 (TSort n) (THead (Bind b) u0 t2))).(\lambda (H7: (eq T (TSort (next g n))
319 t0)).(eq_ind C c0 (\lambda (_: C).((eq T (TSort n) (THead (Bind b) u0 t2))
320 \to ((eq T (TSort (next g n)) t0) \to (ty3 g c0 (THead (Bind b) u0 t2) t0))))
321 (\lambda (H8: (eq T (TSort n) (THead (Bind b) u0 t2))).(let H9 \def (eq_ind T
322 (TSort n) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
323 [(TSort _) \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _)
324 \Rightarrow False])) I (THead (Bind b) u0 t2) H8) in (False_ind ((eq T (TSort
325 (next g n)) t0) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)) H9))) c1 (sym_eq C
326 c1 c0 H5) H6 H7)))) | (tau0_abbr c1 d v i H5 w H6) \Rightarrow (\lambda (H7:
327 (eq C c1 c0)).(\lambda (H8: (eq T (TLRef i) (THead (Bind b) u0 t2))).(\lambda
328 (H9: (eq T (lift (S i) O w) t0)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef
329 i) (THead (Bind b) u0 t2)) \to ((eq T (lift (S i) O w) t0) \to ((getl i c2
330 (CHead d (Bind Abbr) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Bind b) u0
331 t2) t0)))))) (\lambda (H10: (eq T (TLRef i) (THead (Bind b) u0 t2))).(let H11
332 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return (\lambda (_:
333 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True |
334 (THead _ _ _) \Rightarrow False])) I (THead (Bind b) u0 t2) H10) in
335 (False_ind ((eq T (lift (S i) O w) t0) \to ((getl i c0 (CHead d (Bind Abbr)
336 v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)))) H11))) c1
337 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) | (tau0_abst c1 d v i H5 w H6)
338 \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T (TLRef i) (THead
339 (Bind b) u0 t2))).(\lambda (H9: (eq T (lift (S i) O v) t0)).(eq_ind C c0
340 (\lambda (c2: C).((eq T (TLRef i) (THead (Bind b) u0 t2)) \to ((eq T (lift (S
341 i) O v) t0) \to ((getl i c2 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to
342 (ty3 g c0 (THead (Bind b) u0 t2) t0)))))) (\lambda (H10: (eq T (TLRef i)
343 (THead (Bind b) u0 t2))).(let H11 \def (eq_ind T (TLRef i) (\lambda (e:
344 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
345 False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow False])) I
346 (THead (Bind b) u0 t2) H10) in (False_ind ((eq T (lift (S i) O v) t0) \to
347 ((getl i c0 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead
348 (Bind b) u0 t2) t0)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) |
349 (tau0_bind b0 c1 v t4 t5 H5) \Rightarrow (\lambda (H6: (eq C c1 c0)).(\lambda
350 (H7: (eq T (THead (Bind b0) v t4) (THead (Bind b) u0 t2))).(\lambda (H8: (eq
351 T (THead (Bind b0) v t5) t0)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead
352 (Bind b0) v t4) (THead (Bind b) u0 t2)) \to ((eq T (THead (Bind b0) v t5) t0)
353 \to ((tau0 g (CHead c2 (Bind b0) v) t4 t5) \to (ty3 g c0 (THead (Bind b) u0
354 t2) t0))))) (\lambda (H9: (eq T (THead (Bind b0) v t4) (THead (Bind b) u0
355 t2))).(let H10 \def (f_equal T T (\lambda (e: T).(match e in T return
356 (\lambda (_: T).T) with [(TSort _) \Rightarrow t4 | (TLRef _) \Rightarrow t4
357 | (THead _ _ t6) \Rightarrow t6])) (THead (Bind b0) v t4) (THead (Bind b) u0
358 t2) H9) in ((let H11 \def (f_equal T T (\lambda (e: T).(match e in T return
359 (\lambda (_: T).T) with [(TSort _) \Rightarrow v | (TLRef _) \Rightarrow v |
360 (THead _ t6 _) \Rightarrow t6])) (THead (Bind b0) v t4) (THead (Bind b) u0
361 t2) H9) in ((let H12 \def (f_equal T B (\lambda (e: T).(match e in T return
362 (\lambda (_: T).B) with [(TSort _) \Rightarrow b0 | (TLRef _) \Rightarrow b0
363 | (THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).B) with
364 [(Bind b1) \Rightarrow b1 | (Flat _) \Rightarrow b0])])) (THead (Bind b0) v
365 t4) (THead (Bind b) u0 t2) H9) in (eq_ind B b (\lambda (b1: B).((eq T v u0)
366 \to ((eq T t4 t2) \to ((eq T (THead (Bind b1) v t5) t0) \to ((tau0 g (CHead
367 c0 (Bind b1) v) t4 t5) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)))))) (\lambda
368 (H13: (eq T v u0)).(eq_ind T u0 (\lambda (t6: T).((eq T t4 t2) \to ((eq T
369 (THead (Bind b) t6 t5) t0) \to ((tau0 g (CHead c0 (Bind b) t6) t4 t5) \to
370 (ty3 g c0 (THead (Bind b) u0 t2) t0))))) (\lambda (H14: (eq T t4 t2)).(eq_ind
371 T t2 (\lambda (t6: T).((eq T (THead (Bind b) u0 t5) t0) \to ((tau0 g (CHead
372 c0 (Bind b) u0) t6 t5) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)))) (\lambda
373 (H15: (eq T (THead (Bind b) u0 t5) t0)).(eq_ind T (THead (Bind b) u0 t5)
374 (\lambda (t6: T).((tau0 g (CHead c0 (Bind b) u0) t2 t5) \to (ty3 g c0 (THead
375 (Bind b) u0 t2) t6))) (\lambda (H16: (tau0 g (CHead c0 (Bind b) u0) t2
376 t5)).(ty3_bind g c0 u0 t H0 b t2 t5 (H3 t5 H16))) t0 H15)) t4 (sym_eq T t4 t2
377 H14))) v (sym_eq T v u0 H13))) b0 (sym_eq B b0 b H12))) H11)) H10))) c1
378 (sym_eq C c1 c0 H6) H7 H8 H5)))) | (tau0_appl c1 v t4 t5 H5) \Rightarrow
379 (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat Appl) v t4)
380 (THead (Bind b) u0 t2))).(\lambda (H8: (eq T (THead (Flat Appl) v t5)
381 t0)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Appl) v t4) (THead
382 (Bind b) u0 t2)) \to ((eq T (THead (Flat Appl) v t5) t0) \to ((tau0 g c2 t4
383 t5) \to (ty3 g c0 (THead (Bind b) u0 t2) t0))))) (\lambda (H9: (eq T (THead
384 (Flat Appl) v t4) (THead (Bind b) u0 t2))).(let H10 \def (eq_ind T (THead
385 (Flat Appl) v t4) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
386 with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _
387 _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
388 \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind b) u0 t2)
389 H9) in (False_ind ((eq T (THead (Flat Appl) v t5) t0) \to ((tau0 g c0 t4 t5)
390 \to (ty3 g c0 (THead (Bind b) u0 t2) t0))) H10))) c1 (sym_eq C c1 c0 H6) H7
391 H8 H5)))) | (tau0_cast c1 v1 v2 H5 t4 t5 H6) \Rightarrow (\lambda (H7: (eq C
392 c1 c0)).(\lambda (H8: (eq T (THead (Flat Cast) v1 t4) (THead (Bind b) u0
393 t2))).(\lambda (H9: (eq T (THead (Flat Cast) v2 t5) t0)).(eq_ind C c0
394 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t4) (THead (Bind b) u0 t2)) \to
395 ((eq T (THead (Flat Cast) v2 t5) t0) \to ((tau0 g c2 v1 v2) \to ((tau0 g c2
396 t4 t5) \to (ty3 g c0 (THead (Bind b) u0 t2) t0)))))) (\lambda (H10: (eq T
397 (THead (Flat Cast) v1 t4) (THead (Bind b) u0 t2))).(let H11 \def (eq_ind T
398 (THead (Flat Cast) v1 t4) (\lambda (e: T).(match e in T return (\lambda (_:
399 T).Prop) with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False |
400 (THead k _ _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with
401 [(Bind _) \Rightarrow False | (Flat _) \Rightarrow True])])) I (THead (Bind
402 b) u0 t2) H10) in (False_ind ((eq T (THead (Flat Cast) v2 t5) t0) \to ((tau0
403 g c0 v1 v2) \to ((tau0 g c0 t4 t5) \to (ty3 g c0 (THead (Bind b) u0 t2)
404 t0)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6))))]) in (H5 (refl_equal C
405 c0) (refl_equal T (THead (Bind b) u0 t2)) (refl_equal T t0)))))))))))))))
406 (\lambda (c0: C).(\lambda (w: T).(\lambda (u0: T).(\lambda (H0: (ty3 g c0 w
407 u0)).(\lambda (_: ((\forall (t2: T).((tau0 g c0 w t2) \to (ty3 g c0 w
408 t2))))).(\lambda (v: T).(\lambda (t: T).(\lambda (H2: (ty3 g c0 v (THead
409 (Bind Abst) u0 t))).(\lambda (H3: ((\forall (t2: T).((tau0 g c0 v t2) \to
410 (ty3 g c0 v t2))))).(\lambda (t2: T).(\lambda (H4: (tau0 g c0 (THead (Flat
411 Appl) w v) t2)).(let H5 \def (match H4 in tau0 return (\lambda (c1:
412 C).(\lambda (t0: T).(\lambda (t3: T).(\lambda (_: (tau0 ? c1 t0 t3)).((eq C
413 c1 c0) \to ((eq T t0 (THead (Flat Appl) w v)) \to ((eq T t3 t2) \to (ty3 g c0
414 (THead (Flat Appl) w v) t2)))))))) with [(tau0_sort c1 n) \Rightarrow
415 (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T (TSort n) (THead (Flat Appl)
416 w v))).(\lambda (H7: (eq T (TSort (next g n)) t2)).(eq_ind C c0 (\lambda (_:
417 C).((eq T (TSort n) (THead (Flat Appl) w v)) \to ((eq T (TSort (next g n))
418 t2) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))) (\lambda (H8: (eq T (TSort
419 n) (THead (Flat Appl) w v))).(let H9 \def (eq_ind T (TSort n) (\lambda (e:
420 T).(match e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow
421 True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow False])) I
422 (THead (Flat Appl) w v) H8) in (False_ind ((eq T (TSort (next g n)) t2) \to
423 (ty3 g c0 (THead (Flat Appl) w v) t2)) H9))) c1 (sym_eq C c1 c0 H5) H6 H7))))
424 | (tau0_abbr c1 d v0 i H5 w0 H6) \Rightarrow (\lambda (H7: (eq C c1
425 c0)).(\lambda (H8: (eq T (TLRef i) (THead (Flat Appl) w v))).(\lambda (H9:
426 (eq T (lift (S i) O w0) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i)
427 (THead (Flat Appl) w v)) \to ((eq T (lift (S i) O w0) t2) \to ((getl i c2
428 (CHead d (Bind Abbr) v0)) \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat
429 Appl) w v) t2)))))) (\lambda (H10: (eq T (TLRef i) (THead (Flat Appl) w
430 v))).(let H11 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return
431 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
432 \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Appl) w
433 v) H10) in (False_ind ((eq T (lift (S i) O w0) t2) \to ((getl i c0 (CHead d
434 (Bind Abbr) v0)) \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v)
435 t2)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) | (tau0_abst c1 d v0 i
436 H5 w0 H6) \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T (TLRef
437 i) (THead (Flat Appl) w v))).(\lambda (H9: (eq T (lift (S i) O v0)
438 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef i) (THead (Flat Appl) w v))
439 \to ((eq T (lift (S i) O v0) t2) \to ((getl i c2 (CHead d (Bind Abst) v0))
440 \to ((tau0 g d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))) (\lambda
441 (H10: (eq T (TLRef i) (THead (Flat Appl) w v))).(let H11 \def (eq_ind T
442 (TLRef i) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with
443 [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _)
444 \Rightarrow False])) I (THead (Flat Appl) w v) H10) in (False_ind ((eq T
445 (lift (S i) O v0) t2) \to ((getl i c0 (CHead d (Bind Abst) v0)) \to ((tau0 g
446 d v0 w0) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))) H11))) c1 (sym_eq C c1
447 c0 H7) H8 H9 H5 H6)))) | (tau0_bind b c1 v0 t0 t3 H5) \Rightarrow (\lambda
448 (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Bind b) v0 t0) (THead (Flat
449 Appl) w v))).(\lambda (H8: (eq T (THead (Bind b) v0 t3) t2)).(eq_ind C c0
450 (\lambda (c2: C).((eq T (THead (Bind b) v0 t0) (THead (Flat Appl) w v)) \to
451 ((eq T (THead (Bind b) v0 t3) t2) \to ((tau0 g (CHead c2 (Bind b) v0) t0 t3)
452 \to (ty3 g c0 (THead (Flat Appl) w v) t2))))) (\lambda (H9: (eq T (THead
453 (Bind b) v0 t0) (THead (Flat Appl) w v))).(let H10 \def (eq_ind T (THead
454 (Bind b) v0 t0) (\lambda (e: T).(match e in T return (\lambda (_: T).Prop)
455 with [(TSort _) \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _
456 _) \Rightarrow (match k in K return (\lambda (_: K).Prop) with [(Bind _)
457 \Rightarrow True | (Flat _) \Rightarrow False])])) I (THead (Flat Appl) w v)
458 H9) in (False_ind ((eq T (THead (Bind b) v0 t3) t2) \to ((tau0 g (CHead c0
459 (Bind b) v0) t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2))) H10))) c1
460 (sym_eq C c1 c0 H6) H7 H8 H5)))) | (tau0_appl c1 v0 t0 t3 H5) \Rightarrow
461 (\lambda (H6: (eq C c1 c0)).(\lambda (H7: (eq T (THead (Flat Appl) v0 t0)
462 (THead (Flat Appl) w v))).(\lambda (H8: (eq T (THead (Flat Appl) v0 t3)
463 t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Appl) v0 t0) (THead
464 (Flat Appl) w v)) \to ((eq T (THead (Flat Appl) v0 t3) t2) \to ((tau0 g c2 t0
465 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2))))) (\lambda (H9: (eq T (THead
466 (Flat Appl) v0 t0) (THead (Flat Appl) w v))).(let H10 \def (f_equal T T
467 (\lambda (e: T).(match e in T return (\lambda (_: T).T) with [(TSort _)
468 \Rightarrow t0 | (TLRef _) \Rightarrow t0 | (THead _ _ t4) \Rightarrow t4]))
469 (THead (Flat Appl) v0 t0) (THead (Flat Appl) w v) H9) in ((let H11 \def
470 (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
471 [(TSort _) \Rightarrow v0 | (TLRef _) \Rightarrow v0 | (THead _ t4 _)
472 \Rightarrow t4])) (THead (Flat Appl) v0 t0) (THead (Flat Appl) w v) H9) in
473 (eq_ind T w (\lambda (t4: T).((eq T t0 v) \to ((eq T (THead (Flat Appl) t4
474 t3) t2) \to ((tau0 g c0 t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))))
475 (\lambda (H12: (eq T t0 v)).(eq_ind T v (\lambda (t4: T).((eq T (THead (Flat
476 Appl) w t3) t2) \to ((tau0 g c0 t4 t3) \to (ty3 g c0 (THead (Flat Appl) w v)
477 t2)))) (\lambda (H13: (eq T (THead (Flat Appl) w t3) t2)).(eq_ind T (THead
478 (Flat Appl) w t3) (\lambda (t4: T).((tau0 g c0 v t3) \to (ty3 g c0 (THead
479 (Flat Appl) w v) t4))) (\lambda (H14: (tau0 g c0 v t3)).(let H_y \def (H3 t3
480 H14) in (let H15 \def (ty3_unique g c0 v t3 H_y (THead (Bind Abst) u0 t) H2)
481 in (ex_ind T (\lambda (t4: T).(ty3 g c0 t3 t4)) (ty3 g c0 (THead (Flat Appl)
482 w v) (THead (Flat Appl) w t3)) (\lambda (x: T).(\lambda (H16: (ty3 g c0 t3
483 x)).(ex_ind T (\lambda (t4: T).(ty3 g c0 u0 t4)) (ty3 g c0 (THead (Flat Appl)
484 w v) (THead (Flat Appl) w t3)) (\lambda (x0: T).(\lambda (_: (ty3 g c0 u0
485 x0)).(ex_ind T (\lambda (t4: T).(ty3 g c0 (THead (Bind Abst) u0 t) t4)) (ty3
486 g c0 (THead (Flat Appl) w v) (THead (Flat Appl) w t3)) (\lambda (x1:
487 T).(\lambda (H18: (ty3 g c0 (THead (Bind Abst) u0 t) x1)).(ex3_2_ind T T
488 (\lambda (t4: T).(\lambda (_: T).(pc3 c0 (THead (Bind Abst) u0 t4) x1)))
489 (\lambda (_: T).(\lambda (t5: T).(ty3 g c0 u0 t5))) (\lambda (t4: T).(\lambda
490 (_: T).(ty3 g (CHead c0 (Bind Abst) u0) t t4))) (ty3 g c0 (THead (Flat Appl)
491 w v) (THead (Flat Appl) w t3)) (\lambda (x2: T).(\lambda (x3: T).(\lambda (_:
492 (pc3 c0 (THead (Bind Abst) u0 x2) x1)).(\lambda (H20: (ty3 g c0 u0
493 x3)).(\lambda (H21: (ty3 g (CHead c0 (Bind Abst) u0) t x2)).(ty3_conv g c0
494 (THead (Flat Appl) w t3) (THead (Flat Appl) w (THead (Bind Abst) u0 x2))
495 (ty3_appl g c0 w u0 H0 t3 x2 (ty3_sconv g c0 t3 x H16 (THead (Bind Abst) u0
496 t) (THead (Bind Abst) u0 x2) (ty3_bind g c0 u0 x3 H20 Abst t x2 H21) H15))
497 (THead (Flat Appl) w v) (THead (Flat Appl) w (THead (Bind Abst) u0 t))
498 (ty3_appl g c0 w u0 H0 v t H2) (pc3_thin_dx c0 (THead (Bind Abst) u0 t) t3
499 (ty3_unique g c0 v (THead (Bind Abst) u0 t) H2 t3 H_y) w Appl)))))))
500 (ty3_gen_bind g Abst c0 u0 t x1 H18)))) (ty3_correct g c0 v (THead (Bind
501 Abst) u0 t) H2)))) (ty3_correct g c0 w u0 H0)))) (ty3_correct g c0 v t3
502 H_y))))) t2 H13)) t0 (sym_eq T t0 v H12))) v0 (sym_eq T v0 w H11))) H10))) c1
503 (sym_eq C c1 c0 H6) H7 H8 H5)))) | (tau0_cast c1 v1 v2 H5 t0 t3 H6)
504 \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T (THead (Flat
505 Cast) v1 t0) (THead (Flat Appl) w v))).(\lambda (H9: (eq T (THead (Flat Cast)
506 v2 t3) t2)).(eq_ind C c0 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t0)
507 (THead (Flat Appl) w v)) \to ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0
508 g c2 v1 v2) \to ((tau0 g c2 t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v)
509 t2)))))) (\lambda (H10: (eq T (THead (Flat Cast) v1 t0) (THead (Flat Appl) w
510 v))).(let H11 \def (eq_ind T (THead (Flat Cast) v1 t0) (\lambda (e: T).(match
511 e in T return (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False |
512 (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow (match k in K return
513 (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False | (Flat f) \Rightarrow
514 (match f in F return (\lambda (_: F).Prop) with [Appl \Rightarrow False |
515 Cast \Rightarrow True])])])) I (THead (Flat Appl) w v) H10) in (False_ind
516 ((eq T (THead (Flat Cast) v2 t3) t2) \to ((tau0 g c0 v1 v2) \to ((tau0 g c0
517 t0 t3) \to (ty3 g c0 (THead (Flat Appl) w v) t2)))) H11))) c1 (sym_eq C c1 c0
518 H7) H8 H9 H5 H6))))]) in (H5 (refl_equal C c0) (refl_equal T (THead (Flat
519 Appl) w v)) (refl_equal T t2)))))))))))))) (\lambda (c0: C).(\lambda (t2:
520 T).(\lambda (t3: T).(\lambda (H0: (ty3 g c0 t2 t3)).(\lambda (H1: ((\forall
521 (t4: T).((tau0 g c0 t2 t4) \to (ty3 g c0 t2 t4))))).(\lambda (t0: T).(\lambda
522 (_: (ty3 g c0 t3 t0)).(\lambda (H3: ((\forall (t4: T).((tau0 g c0 t3 t4) \to
523 (ty3 g c0 t3 t4))))).(\lambda (t4: T).(\lambda (H4: (tau0 g c0 (THead (Flat
524 Cast) t3 t2) t4)).(let H5 \def (match H4 in tau0 return (\lambda (c1:
525 C).(\lambda (t: T).(\lambda (t5: T).(\lambda (_: (tau0 ? c1 t t5)).((eq C c1
526 c0) \to ((eq T t (THead (Flat Cast) t3 t2)) \to ((eq T t5 t4) \to (ty3 g c0
527 (THead (Flat Cast) t3 t2) t4)))))))) with [(tau0_sort c1 n) \Rightarrow
528 (\lambda (H5: (eq C c1 c0)).(\lambda (H6: (eq T (TSort n) (THead (Flat Cast)
529 t3 t2))).(\lambda (H7: (eq T (TSort (next g n)) t4)).(eq_ind C c0 (\lambda
530 (_: C).((eq T (TSort n) (THead (Flat Cast) t3 t2)) \to ((eq T (TSort (next g
531 n)) t4) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))) (\lambda (H8: (eq T
532 (TSort n) (THead (Flat Cast) t3 t2))).(let H9 \def (eq_ind T (TSort n)
533 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
534 \Rightarrow True | (TLRef _) \Rightarrow False | (THead _ _ _) \Rightarrow
535 False])) I (THead (Flat Cast) t3 t2) H8) in (False_ind ((eq T (TSort (next g
536 n)) t4) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)) H9))) c1 (sym_eq C c1 c0
537 H5) H6 H7)))) | (tau0_abbr c1 d v i H5 w H6) \Rightarrow (\lambda (H7: (eq C
538 c1 c0)).(\lambda (H8: (eq T (TLRef i) (THead (Flat Cast) t3 t2))).(\lambda
539 (H9: (eq T (lift (S i) O w) t4)).(eq_ind C c0 (\lambda (c2: C).((eq T (TLRef
540 i) (THead (Flat Cast) t3 t2)) \to ((eq T (lift (S i) O w) t4) \to ((getl i c2
541 (CHead d (Bind Abbr) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Flat Cast)
542 t3 t2) t4)))))) (\lambda (H10: (eq T (TLRef i) (THead (Flat Cast) t3
543 t2))).(let H11 \def (eq_ind T (TLRef i) (\lambda (e: T).(match e in T return
544 (\lambda (_: T).Prop) with [(TSort _) \Rightarrow False | (TLRef _)
545 \Rightarrow True | (THead _ _ _) \Rightarrow False])) I (THead (Flat Cast) t3
546 t2) H10) in (False_ind ((eq T (lift (S i) O w) t4) \to ((getl i c0 (CHead d
547 (Bind Abbr) v)) \to ((tau0 g d v w) \to (ty3 g c0 (THead (Flat Cast) t3 t2)
548 t4)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5 H6)))) | (tau0_abst c1 d v i H5
549 w H6) \Rightarrow (\lambda (H7: (eq C c1 c0)).(\lambda (H8: (eq T (TLRef i)
550 (THead (Flat Cast) t3 t2))).(\lambda (H9: (eq T (lift (S i) O v) t4)).(eq_ind
551 C c0 (\lambda (c2: C).((eq T (TLRef i) (THead (Flat Cast) t3 t2)) \to ((eq T
552 (lift (S i) O v) t4) \to ((getl i c2 (CHead d (Bind Abst) v)) \to ((tau0 g d
553 v w) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))) (\lambda (H10: (eq T
554 (TLRef i) (THead (Flat Cast) t3 t2))).(let H11 \def (eq_ind T (TLRef i)
555 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
556 \Rightarrow False | (TLRef _) \Rightarrow True | (THead _ _ _) \Rightarrow
557 False])) I (THead (Flat Cast) t3 t2) H10) in (False_ind ((eq T (lift (S i) O
558 v) t4) \to ((getl i c0 (CHead d (Bind Abst) v)) \to ((tau0 g d v w) \to (ty3
559 g c0 (THead (Flat Cast) t3 t2) t4)))) H11))) c1 (sym_eq C c1 c0 H7) H8 H9 H5
560 H6)))) | (tau0_bind b c1 v t5 t6 H5) \Rightarrow (\lambda (H6: (eq C c1
561 c0)).(\lambda (H7: (eq T (THead (Bind b) v t5) (THead (Flat Cast) t3
562 t2))).(\lambda (H8: (eq T (THead (Bind b) v t6) t4)).(eq_ind C c0 (\lambda
563 (c2: C).((eq T (THead (Bind b) v t5) (THead (Flat Cast) t3 t2)) \to ((eq T
564 (THead (Bind b) v t6) t4) \to ((tau0 g (CHead c2 (Bind b) v) t5 t6) \to (ty3
565 g c0 (THead (Flat Cast) t3 t2) t4))))) (\lambda (H9: (eq T (THead (Bind b) v
566 t5) (THead (Flat Cast) t3 t2))).(let H10 \def (eq_ind T (THead (Bind b) v t5)
567 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
568 \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
569 (match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow True |
570 (Flat _) \Rightarrow False])])) I (THead (Flat Cast) t3 t2) H9) in (False_ind
571 ((eq T (THead (Bind b) v t6) t4) \to ((tau0 g (CHead c0 (Bind b) v) t5 t6)
572 \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4))) H10))) c1 (sym_eq C c1 c0 H6)
573 H7 H8 H5)))) | (tau0_appl c1 v t5 t6 H5) \Rightarrow (\lambda (H6: (eq C c1
574 c0)).(\lambda (H7: (eq T (THead (Flat Appl) v t5) (THead (Flat Cast) t3
575 t2))).(\lambda (H8: (eq T (THead (Flat Appl) v t6) t4)).(eq_ind C c0 (\lambda
576 (c2: C).((eq T (THead (Flat Appl) v t5) (THead (Flat Cast) t3 t2)) \to ((eq T
577 (THead (Flat Appl) v t6) t4) \to ((tau0 g c2 t5 t6) \to (ty3 g c0 (THead
578 (Flat Cast) t3 t2) t4))))) (\lambda (H9: (eq T (THead (Flat Appl) v t5)
579 (THead (Flat Cast) t3 t2))).(let H10 \def (eq_ind T (THead (Flat Appl) v t5)
580 (\lambda (e: T).(match e in T return (\lambda (_: T).Prop) with [(TSort _)
581 \Rightarrow False | (TLRef _) \Rightarrow False | (THead k _ _) \Rightarrow
582 (match k in K return (\lambda (_: K).Prop) with [(Bind _) \Rightarrow False |
583 (Flat f) \Rightarrow (match f in F return (\lambda (_: F).Prop) with [Appl
584 \Rightarrow True | Cast \Rightarrow False])])])) I (THead (Flat Cast) t3 t2)
585 H9) in (False_ind ((eq T (THead (Flat Appl) v t6) t4) \to ((tau0 g c0 t5 t6)
586 \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4))) H10))) c1 (sym_eq C c1 c0 H6)
587 H7 H8 H5)))) | (tau0_cast c1 v1 v2 H5 t5 t6 H6) \Rightarrow (\lambda (H7: (eq
588 C c1 c0)).(\lambda (H8: (eq T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3
589 t2))).(\lambda (H9: (eq T (THead (Flat Cast) v2 t6) t4)).(eq_ind C c0
590 (\lambda (c2: C).((eq T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2))
591 \to ((eq T (THead (Flat Cast) v2 t6) t4) \to ((tau0 g c2 v1 v2) \to ((tau0 g
592 c2 t5 t6) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))) (\lambda (H10: (eq
593 T (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2))).(let H11 \def
594 (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_: T).T) with
595 [(TSort _) \Rightarrow t5 | (TLRef _) \Rightarrow t5 | (THead _ _ t)
596 \Rightarrow t])) (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2) H10) in
597 ((let H12 \def (f_equal T T (\lambda (e: T).(match e in T return (\lambda (_:
598 T).T) with [(TSort _) \Rightarrow v1 | (TLRef _) \Rightarrow v1 | (THead _ t
599 _) \Rightarrow t])) (THead (Flat Cast) v1 t5) (THead (Flat Cast) t3 t2) H10)
600 in (eq_ind T t3 (\lambda (t: T).((eq T t5 t2) \to ((eq T (THead (Flat Cast)
601 v2 t6) t4) \to ((tau0 g c0 t v2) \to ((tau0 g c0 t5 t6) \to (ty3 g c0 (THead
602 (Flat Cast) t3 t2) t4)))))) (\lambda (H13: (eq T t5 t2)).(eq_ind T t2
603 (\lambda (t: T).((eq T (THead (Flat Cast) v2 t6) t4) \to ((tau0 g c0 t3 v2)
604 \to ((tau0 g c0 t t6) \to (ty3 g c0 (THead (Flat Cast) t3 t2) t4)))))
605 (\lambda (H14: (eq T (THead (Flat Cast) v2 t6) t4)).(eq_ind T (THead (Flat
606 Cast) v2 t6) (\lambda (t: T).((tau0 g c0 t3 v2) \to ((tau0 g c0 t2 t6) \to
607 (ty3 g c0 (THead (Flat Cast) t3 t2) t)))) (\lambda (H15: (tau0 g c0 t3
608 v2)).(\lambda (H16: (tau0 g c0 t2 t6)).(let H_y \def (H1 t6 H16) in (let H_y0
609 \def (H3 v2 H15) in (let H17 \def (ty3_unique g c0 t2 t6 H_y t3 H0) in
610 (ex_ind T (\lambda (t: T).(ty3 g c0 v2 t)) (ty3 g c0 (THead (Flat Cast) t3
611 t2) (THead (Flat Cast) v2 t6)) (\lambda (x: T).(\lambda (H18: (ty3 g c0 v2
612 x)).(ex_ind T (\lambda (t: T).(ty3 g c0 t6 t)) (ty3 g c0 (THead (Flat Cast)
613 t3 t2) (THead (Flat Cast) v2 t6)) (\lambda (x0: T).(\lambda (H19: (ty3 g c0
614 t6 x0)).(ty3_conv g c0 (THead (Flat Cast) v2 t6) (THead (Flat Cast) x v2)
615 (ty3_cast g c0 t6 v2 (ty3_sconv g c0 t6 x0 H19 t3 v2 H_y0 H17) x H18) (THead
616 (Flat Cast) t3 t2) (THead (Flat Cast) v2 t3) (ty3_cast g c0 t2 t3 H0 v2 H_y0)
617 (pc3_thin_dx c0 t3 t6 (ty3_unique g c0 t2 t3 H0 t6 H_y) v2 Cast))))
618 (ty3_correct g c0 t2 t6 H_y)))) (ty3_correct g c0 t3 v2 H_y0))))))) t4 H14))
619 t5 (sym_eq T t5 t2 H13))) v1 (sym_eq T v1 t3 H12))) H11))) c1 (sym_eq C c1 c0
620 H7) H8 H9 H5 H6))))]) in (H5 (refl_equal C c0) (refl_equal T (THead (Flat
621 Cast) t3 t2)) (refl_equal T t4))))))))))))) c u t1 H))))).
projects / helm.git / blob