]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfpx.ma
73cee45379ef37200a9daf6c01581ffed6c27f85
[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpxs_lfpx.ma
1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15 include "basic_2/rt_transition/lfpx_fqup.ma".
16 include "basic_2/rt_transition/lfpx_cpx.ma".
17 include "basic_2/rt_computation/cpxs_drops.ma".
18 include "basic_2/rt_computation/cpxs_cpxs.ma".
19
20 (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
21
22 (* Properties with uncounted parallel rt-transition on referred entries *****)
23
24 lemma lfpx_cpxs_conf: ∀h,G. s_r_confluent1 … (cpxs h G) (lfpx h G).
25 /3 width=5 by lfpx_cpx_conf, s_r_conf1_LTC1/ qed-.
26
27 lemma lfpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (lfpx h G).
28 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 //
29 [ #G #L2 #s1 #L1 #H elim (lfpx_inv_sort … H) -H * /2 width=1 by cpx_cpxs/
30 | #I #G #L2 #V #V2 #W2 #_ #IH #HVW2 #Y1 #H
31   elim (lfpx_inv_zero_pair_dx … H) -H #L1 #V1 #HL1 #HV1 #H destruct
32   /5 width=3 by lfpx_cpx_conf, cpxs_delta, cpxs_strap2/
33 | #I2 #G #L2 #V2 #W2 #i #_ #IH #HVW2 #Y1 #H
34   elim (lfpx_inv_lref_bind_dx … H) -H #I1 #L1 #HL1 #H destruct
35   /4 width=3 by cpxs_lref, cpxs_strap2/
36 | #p #I #G #L2 #V #V2 #T #T2 #_ #_ #IHV #IHT #L1 #H
37   elim (lfpx_inv_bind … H) -H /3 width=1 by cpxs_bind/
38 | #I #G #L2 #V #V2 #T #T2 #_ #_ #IHV #IHT #L1 #H
39   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_flat/
40 | #G #L2 #V #T #T2 #T0 #_ #IH #HT02 #L1 #H
41   elim (lfpx_inv_bind … H) -H /3 width=3 by cpxs_zeta/
42 | #G #L2 #V #T #T2 #_ #IH #L1 #H
43   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_eps/
44 | #G #L2 #V #V2 #T #_ #IH #L1 #H
45   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_ee/
46 | #p #G #L2 #V #V2 #W #W2 #T #T2 #_ #_ #_ #IHV #IHW #IHT #L1 #H
47   elim (lfpx_inv_flat … H) -H #HV #H
48   elim (lfpx_inv_bind … H) -H /3 width=1 by cpxs_beta/
49 | #p #G #L2 #V #V2 #V0 #W #W2 #T #T2 #_ #_ #_ #IHV #IHW #IHT #HV20 #L1 #H
50   elim (lfpx_inv_flat … H) -H #HV #H
51   elim (lfpx_inv_bind … H) -H /3 width=3 by cpxs_theta/
52 ]
53 qed.
54
55 lemma lfpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (lfpx h G).
56 /3 width=6 by lfpx_cpx_conf, lfpx_cpx_trans, s_r_trans_LTC1/
57 qed-.
58
59 (* Advanced properties ******************************************************)
60
61 lemma cpx_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
62                  ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈[h] T2 →
63                  ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
64 /4 width=5 by lfpx_cpx_trans, cpxs_bind_dx, lfpx_pair/ qed.
65
66 lemma cpxs_bind2_dx: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
67                      ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
68                      ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
69 /4 width=5 by lfpx_cpxs_trans, cpxs_bind_dx, lfpx_pair/ qed.