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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/LAMBDA-TYPES/LambdaDelta-1/pr3/wcpr0".
19 include "pr3/props.ma".
21 include "wcpr0/getl.ma".
24 \forall (c1: C).(\forall (c2: C).((wcpr0 c2 c1) \to (\forall (t1:
25 T).(\forall (t2: T).((pr3 c1 t1 t2) \to (pr3 c2 t1 t2))))))
27 \lambda (c1: C).(\lambda (c2: C).(\lambda (H: (wcpr0 c2 c1)).(wcpr0_ind
28 (\lambda (c: C).(\lambda (c0: C).(\forall (t1: T).(\forall (t2: T).((pr3 c0
29 t1 t2) \to (pr3 c t1 t2)))))) (\lambda (c: C).(\lambda (t1: T).(\lambda (t2:
30 T).(\lambda (H0: (pr3 c t1 t2)).H0)))) (\lambda (c0: C).(\lambda (c3:
31 C).(\lambda (H0: (wcpr0 c0 c3)).(\lambda (_: ((\forall (t1: T).(\forall (t2:
32 T).((pr3 c3 t1 t2) \to (pr3 c0 t1 t2)))))).(\lambda (u1: T).(\lambda (u2:
33 T).(\lambda (H2: (pr0 u1 u2)).(\lambda (k: K).(\lambda (t1: T).(\lambda (t2:
34 T).(\lambda (H3: (pr3 (CHead c3 k u2) t1 t2)).(pr3_ind (CHead c3 k u1)
35 (\lambda (t: T).(\lambda (t0: T).(pr3 (CHead c0 k u1) t t0))) (\lambda (t:
36 T).(pr3_refl (CHead c0 k u1) t)) (\lambda (t0: T).(\lambda (t3: T).(\lambda
37 (H4: (pr2 (CHead c3 k u1) t3 t0)).(\lambda (t4: T).(\lambda (_: (pr3 (CHead
38 c3 k u1) t0 t4)).(\lambda (H6: (pr3 (CHead c0 k u1) t0 t4)).(pr3_t t0 t3
39 (CHead c0 k u1) (let H7 \def (match H4 in pr2 return (\lambda (c: C).(\lambda
40 (t: T).(\lambda (t5: T).(\lambda (_: (pr2 c t t5)).((eq C c (CHead c3 k u1))
41 \to ((eq T t t3) \to ((eq T t5 t0) \to (pr3 (CHead c0 k u1) t3 t0))))))))
42 with [(pr2_free c t5 t6 H7) \Rightarrow (\lambda (H8: (eq C c (CHead c3 k
43 u1))).(\lambda (H9: (eq T t5 t3)).(\lambda (H10: (eq T t6 t0)).(eq_ind C
44 (CHead c3 k u1) (\lambda (_: C).((eq T t5 t3) \to ((eq T t6 t0) \to ((pr0 t5
45 t6) \to (pr3 (CHead c0 k u1) t3 t0))))) (\lambda (H11: (eq T t5 t3)).(eq_ind
46 T t3 (\lambda (t: T).((eq T t6 t0) \to ((pr0 t t6) \to (pr3 (CHead c0 k u1)
47 t3 t0)))) (\lambda (H12: (eq T t6 t0)).(eq_ind T t0 (\lambda (t: T).((pr0 t3
48 t) \to (pr3 (CHead c0 k u1) t3 t0))) (\lambda (H13: (pr0 t3 t0)).(pr3_pr2
49 (CHead c0 k u1) t3 t0 (pr2_free (CHead c0 k u1) t3 t0 H13))) t6 (sym_eq T t6
50 t0 H12))) t5 (sym_eq T t5 t3 H11))) c (sym_eq C c (CHead c3 k u1) H8) H9 H10
51 H7)))) | (pr2_delta c d u i H7 t5 t6 H8 t H9) \Rightarrow (\lambda (H10: (eq
52 C c (CHead c3 k u1))).(\lambda (H11: (eq T t5 t3)).(\lambda (H12: (eq T t
53 t0)).(eq_ind C (CHead c3 k u1) (\lambda (c4: C).((eq T t5 t3) \to ((eq T t
54 t0) \to ((getl i c4 (CHead d (Bind Abbr) u)) \to ((pr0 t5 t6) \to ((subst0 i
55 u t6 t) \to (pr3 (CHead c0 k u1) t3 t0))))))) (\lambda (H13: (eq T t5
56 t3)).(eq_ind T t3 (\lambda (t7: T).((eq T t t0) \to ((getl i (CHead c3 k u1)
57 (CHead d (Bind Abbr) u)) \to ((pr0 t7 t6) \to ((subst0 i u t6 t) \to (pr3
58 (CHead c0 k u1) t3 t0)))))) (\lambda (H14: (eq T t t0)).(eq_ind T t0 (\lambda
59 (t7: T).((getl i (CHead c3 k u1) (CHead d (Bind Abbr) u)) \to ((pr0 t3 t6)
60 \to ((subst0 i u t6 t7) \to (pr3 (CHead c0 k u1) t3 t0))))) (\lambda (H15:
61 (getl i (CHead c3 k u1) (CHead d (Bind Abbr) u))).(\lambda (H16: (pr0 t3
62 t6)).(\lambda (H17: (subst0 i u t6 t0)).(ex3_2_ind C T (\lambda (e2:
63 C).(\lambda (u3: T).(getl i (CHead c0 k u1) (CHead e2 (Bind Abbr) u3))))
64 (\lambda (e2: C).(\lambda (_: T).(wcpr0 e2 d))) (\lambda (_: C).(\lambda (u3:
65 T).(pr0 u3 u))) (pr3 (CHead c0 k u1) t3 t0) (\lambda (x0: C).(\lambda (x1:
66 T).(\lambda (H18: (getl i (CHead c0 k u1) (CHead x0 (Bind Abbr)
67 x1))).(\lambda (_: (wcpr0 x0 d)).(\lambda (H20: (pr0 x1 u)).(ex2_ind T
68 (\lambda (t7: T).(subst0 i x1 t6 t7)) (\lambda (t7: T).(pr0 t7 t0)) (pr3
69 (CHead c0 k u1) t3 t0) (\lambda (x: T).(\lambda (H21: (subst0 i x1 t6
70 x)).(\lambda (H22: (pr0 x t0)).(pr3_sing (CHead c0 k u1) x t3 (pr2_delta
71 (CHead c0 k u1) x0 x1 i H18 t3 t6 H16 x H21) t0 (pr3_pr2 (CHead c0 k u1) x t0
72 (pr2_free (CHead c0 k u1) x t0 H22)))))) (pr0_subst0_back u t6 t0 i H17 x1
73 H20))))))) (wcpr0_getl_back (CHead c3 k u1) (CHead c0 k u1) (wcpr0_comp c0 c3
74 H0 u1 u1 (pr0_refl u1) k) i d u (Bind Abbr) H15))))) t (sym_eq T t t0 H14)))
75 t5 (sym_eq T t5 t3 H13))) c (sym_eq C c (CHead c3 k u1) H10) H11 H12 H7 H8
76 H9))))]) in (H7 (refl_equal C (CHead c3 k u1)) (refl_equal T t3) (refl_equal
77 T t0))) t4 H6))))))) t1 t2 (pr3_pr2_pr3_t c3 u2 t1 t2 k H3 u1 (pr2_free c3 u1
78 u2 H2)))))))))))))) c2 c1 H))).