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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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15 include "basic_2/static/lfdeq_lfdeq.ma".
16 include "basic_2/rt_transition/lfpx_lfdeq.ma".
17 include "basic_2/rt_computation/lfsx.ma".
19 (* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
21 (* Advanced properties ******************************************************)
23 lemma lfsx_lfdeq_trans: āh,o,G,L1,T. G ā¢ ā¬*[h, o, T] šā¦L1ā¦ ā
24 āL2. L1 ā”[h, o, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
25 #h #o #G #L1 #T #H @(lfsx_ind ā¦ H) -L1
26 #L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
27 #L #HL2 #HnL2 elim (lfdeq_lfpx_trans ā¦ HL2 ā¦ HL12) -HL2
28 /4 width=5 by lfdeq_repl/
31 (* Advanced forward lemmas **************************************************)
33 (* Basic_2A1: includes: lsx_fwd_bind_sn lsx_fwd_flat_sn *)
34 (* Basic_2A1: was: lsx_fwd_pair_sn *)
35 lemma lfsx_fwd_pair_sn: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā”{I}V.T] šā¦Lā¦ ā
36 G ā¢ ā¬*[h, o, V] šā¦Lā¦.
37 #h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
38 #L1 #_ #IHL1 @lfsx_intro
39 #L2 #H #HnL12 elim (lfpx_pair_sn_split ā¦ o I ā¦ T H) -H
40 /6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
44 (* Basic_2A1: was: lsx_fwd_flat_dx *)
45 lemma lfsx_fwd_flat_dx: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
46 G ā¢ ā¬*[h, o, T] šā¦Lā¦.
47 #h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
48 #L1 #_ #IHL1 @lfsx_intro
49 #L2 #H #HnL12 elim (lfpx_flat_dx_split ā¦ o I ā¦ V ā¦ H) -H
50 /6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_flat_dx/
53 (* Advanced inversion lemmas ************************************************)
55 (* Basic_2A1: was: lsx_inv_flat *)
56 lemma lfsx_inv_flat: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
57 G ā¢ ā¬*[h, o, V] šā¦Lā¦ ā§ G ā¢ ā¬*[h, o, T] šā¦Lā¦.
58 /3 width=3 by lfsx_fwd_pair_sn, lfsx_fwd_flat_dx, conj/ qed-.