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 "basic_1/csubc/drop.ma".
19 theorem drop1_csubc_trans:
20 \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2:
21 C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C
22 (\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))
24 \lambda (g: G).(\lambda (hds: PList).(let TMP_3 \def (\lambda (p:
25 PList).(\forall (c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1:
26 C).((csubc g e2 e1) \to (let TMP_1 \def (\lambda (c1: C).(drop1 p c1 e1)) in
27 (let TMP_2 \def (\lambda (c1: C).(csubc g c2 c1)) in (ex2 C TMP_1
28 TMP_2))))))))) in (let TMP_8 \def (\lambda (c2: C).(\lambda (e2: C).(\lambda
29 (H: (drop1 PNil c2 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e2 e1)).(let
30 H_y \def (drop1_gen_pnil c2 e2 H) in (let TMP_4 \def (\lambda (c: C).(csubc g
31 c e1)) in (let H1 \def (eq_ind_r C e2 TMP_4 H0 c2 H_y) in (let TMP_5 \def
32 (\lambda (c1: C).(drop1 PNil c1 e1)) in (let TMP_6 \def (\lambda (c1:
33 C).(csubc g c2 c1)) in (let TMP_7 \def (drop1_nil e1) in (ex_intro2 C TMP_5
34 TMP_6 e1 TMP_7 H1)))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda
35 (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: C).(\forall (e2:
36 C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e2 e1) \to (ex2 C (\lambda
37 (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c2 c1)))))))))).(\lambda
38 (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n n0 p) c2 e2)).(\lambda
39 (e1: C).(\lambda (H1: (csubc g e2 e1)).(let H_x \def (drop1_gen_pcons c2 e2 p
40 n n0 H0) in (let H2 \def H_x in (let TMP_9 \def (\lambda (c3: C).(drop n n0
41 c2 c3)) in (let TMP_10 \def (\lambda (c3: C).(drop1 p c3 e2)) in (let TMP_12
42 \def (\lambda (c1: C).(let TMP_11 \def (PCons n n0 p) in (drop1 TMP_11 c1
43 e1))) in (let TMP_13 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_14
44 \def (ex2 C TMP_12 TMP_13) in (let TMP_33 \def (\lambda (x: C).(\lambda (H3:
45 (drop n n0 c2 x)).(\lambda (H4: (drop1 p x e2)).(let H_x0 \def (H x e2 H4 e1
46 H1) in (let H5 \def H_x0 in (let TMP_15 \def (\lambda (c1: C).(drop1 p c1
47 e1)) in (let TMP_16 \def (\lambda (c1: C).(csubc g x c1)) in (let TMP_18 \def
48 (\lambda (c1: C).(let TMP_17 \def (PCons n n0 p) in (drop1 TMP_17 c1 e1))) in
49 (let TMP_19 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_20 \def (ex2 C
50 TMP_18 TMP_19) in (let TMP_32 \def (\lambda (x0: C).(\lambda (H6: (drop1 p x0
51 e1)).(\lambda (H7: (csubc g x x0)).(let H_x1 \def (drop_csubc_trans g c2 x n0
52 n H3 x0 H7) in (let H8 \def H_x1 in (let TMP_21 \def (\lambda (c1: C).(drop n
53 n0 c1 x0)) in (let TMP_22 \def (\lambda (c1: C).(csubc g c2 c1)) in (let
54 TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (PCons n n0 p) in (drop1 TMP_23
55 c1 e1))) in (let TMP_25 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_26
56 \def (ex2 C TMP_24 TMP_25) in (let TMP_31 \def (\lambda (x1: C).(\lambda (H9:
57 (drop n n0 x1 x0)).(\lambda (H10: (csubc g c2 x1)).(let TMP_28 \def (\lambda
58 (c1: C).(let TMP_27 \def (PCons n n0 p) in (drop1 TMP_27 c1 e1))) in (let
59 TMP_29 \def (\lambda (c1: C).(csubc g c2 c1)) in (let TMP_30 \def (drop1_cons
60 x1 x0 n n0 H9 e1 p H6) in (ex_intro2 C TMP_28 TMP_29 x1 TMP_30 H10))))))) in
61 (ex2_ind C TMP_21 TMP_22 TMP_26 TMP_31 H8)))))))))))) in (ex2_ind C TMP_15
62 TMP_16 TMP_20 TMP_32 H5)))))))))))) in (ex2_ind C TMP_9 TMP_10 TMP_14 TMP_33
63 H2)))))))))))))))))) in (PList_ind TMP_3 TMP_8 TMP_34 hds))))).
65 theorem csubc_drop1_conf_rev:
66 \forall (g: G).(\forall (hds: PList).(\forall (c2: C).(\forall (e2:
67 C).((drop1 hds c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C
68 (\lambda (c1: C).(drop1 hds c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))
70 \lambda (g: G).(\lambda (hds: PList).(let TMP_3 \def (\lambda (p:
71 PList).(\forall (c2: C).(\forall (e2: C).((drop1 p c2 e2) \to (\forall (e1:
72 C).((csubc g e1 e2) \to (let TMP_1 \def (\lambda (c1: C).(drop1 p c1 e1)) in
73 (let TMP_2 \def (\lambda (c1: C).(csubc g c1 c2)) in (ex2 C TMP_1
74 TMP_2))))))))) in (let TMP_8 \def (\lambda (c2: C).(\lambda (e2: C).(\lambda
75 (H: (drop1 PNil c2 e2)).(\lambda (e1: C).(\lambda (H0: (csubc g e1 e2)).(let
76 H_y \def (drop1_gen_pnil c2 e2 H) in (let TMP_4 \def (\lambda (c: C).(csubc g
77 e1 c)) in (let H1 \def (eq_ind_r C e2 TMP_4 H0 c2 H_y) in (let TMP_5 \def
78 (\lambda (c1: C).(drop1 PNil c1 e1)) in (let TMP_6 \def (\lambda (c1:
79 C).(csubc g c1 c2)) in (let TMP_7 \def (drop1_nil e1) in (ex_intro2 C TMP_5
80 TMP_6 e1 TMP_7 H1)))))))))))) in (let TMP_34 \def (\lambda (n: nat).(\lambda
81 (n0: nat).(\lambda (p: PList).(\lambda (H: ((\forall (c2: C).(\forall (e2:
82 C).((drop1 p c2 e2) \to (\forall (e1: C).((csubc g e1 e2) \to (ex2 C (\lambda
83 (c1: C).(drop1 p c1 e1)) (\lambda (c1: C).(csubc g c1 c2)))))))))).(\lambda
84 (c2: C).(\lambda (e2: C).(\lambda (H0: (drop1 (PCons n n0 p) c2 e2)).(\lambda
85 (e1: C).(\lambda (H1: (csubc g e1 e2)).(let H_x \def (drop1_gen_pcons c2 e2 p
86 n n0 H0) in (let H2 \def H_x in (let TMP_9 \def (\lambda (c3: C).(drop n n0
87 c2 c3)) in (let TMP_10 \def (\lambda (c3: C).(drop1 p c3 e2)) in (let TMP_12
88 \def (\lambda (c1: C).(let TMP_11 \def (PCons n n0 p) in (drop1 TMP_11 c1
89 e1))) in (let TMP_13 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_14
90 \def (ex2 C TMP_12 TMP_13) in (let TMP_33 \def (\lambda (x: C).(\lambda (H3:
91 (drop n n0 c2 x)).(\lambda (H4: (drop1 p x e2)).(let H_x0 \def (H x e2 H4 e1
92 H1) in (let H5 \def H_x0 in (let TMP_15 \def (\lambda (c1: C).(drop1 p c1
93 e1)) in (let TMP_16 \def (\lambda (c1: C).(csubc g c1 x)) in (let TMP_18 \def
94 (\lambda (c1: C).(let TMP_17 \def (PCons n n0 p) in (drop1 TMP_17 c1 e1))) in
95 (let TMP_19 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_20 \def (ex2 C
96 TMP_18 TMP_19) in (let TMP_32 \def (\lambda (x0: C).(\lambda (H6: (drop1 p x0
97 e1)).(\lambda (H7: (csubc g x0 x)).(let H_x1 \def (csubc_drop_conf_rev g c2 x
98 n0 n H3 x0 H7) in (let H8 \def H_x1 in (let TMP_21 \def (\lambda (c1:
99 C).(drop n n0 c1 x0)) in (let TMP_22 \def (\lambda (c1: C).(csubc g c1 c2))
100 in (let TMP_24 \def (\lambda (c1: C).(let TMP_23 \def (PCons n n0 p) in
101 (drop1 TMP_23 c1 e1))) in (let TMP_25 \def (\lambda (c1: C).(csubc g c1 c2))
102 in (let TMP_26 \def (ex2 C TMP_24 TMP_25) in (let TMP_31 \def (\lambda (x1:
103 C).(\lambda (H9: (drop n n0 x1 x0)).(\lambda (H10: (csubc g x1 c2)).(let
104 TMP_28 \def (\lambda (c1: C).(let TMP_27 \def (PCons n n0 p) in (drop1 TMP_27
105 c1 e1))) in (let TMP_29 \def (\lambda (c1: C).(csubc g c1 c2)) in (let TMP_30
106 \def (drop1_cons x1 x0 n n0 H9 e1 p H6) in (ex_intro2 C TMP_28 TMP_29 x1
107 TMP_30 H10))))))) in (ex2_ind C TMP_21 TMP_22 TMP_26 TMP_31 H8)))))))))))) in
108 (ex2_ind C TMP_15 TMP_16 TMP_20 TMP_32 H5)))))))))))) in (ex2_ind C TMP_9
109 TMP_10 TMP_14 TMP_33 H2)))))))))))))))))) in (PList_ind TMP_3 TMP_8 TMP_34