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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 (* Basic_2A1: uses: lsx_lleq_trans *)
24 lemma lfsx_lfdeq_trans: āh,o,G,L1,T. G ā¢ ā¬*[h, o, T] šā¦L1ā¦ ā
25 āL2. L1 ā”[h, o, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
26 #h #o #G #L1 #T #H @(lfsx_ind ā¦ H) -L1
27 #L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
28 #L #HL2 #HnL2 elim (lfdeq_lfpx_trans ā¦ HL2 ā¦ HL12) -HL2
29 /4 width=5 by lfdeq_repl/
32 (* Basic_2A1: uses: lsx_lpx_trans *)
33 lemma lfsx_lfpx_trans: āh,o,G,L1,T. G ā¢ ā¬*[h, o, T] šā¦L1ā¦ ā
34 āL2. ā¦G, L1ā¦ ā¢ ā¬[h, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
35 #h #o #G #L1 #T #H @(lfsx_ind ā¦ H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
36 elim (lfdeq_dec h o L1 L2 T) /3 width=4 by lfsx_lfdeq_trans, lfxs_refl/
39 (* Advanced forward lemmas **************************************************)
41 (* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
42 lemma lfsx_fwd_pair_sn: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā”{I}V.T] šā¦Lā¦ ā
43 G ā¢ ā¬*[h, o, V] šā¦Lā¦.
44 #h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
45 #L1 #_ #IHL1 @lfsx_intro
46 #L2 #H #HnL12 elim (lfpx_pair_sn_split ā¦ H o I T) -H
47 /6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
50 (* Basic_2A1: uses: lsx_fwd_flat_dx *)
51 lemma lfsx_fwd_flat_dx: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
52 G ā¢ ā¬*[h, o, T] šā¦Lā¦.
53 #h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
54 #L1 #_ #IHL1 @lfsx_intro
55 #L2 #H #HnL12 elim (lfpx_flat_dx_split ā¦ H o I V) -H
56 /6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_flat_dx/
59 (* Basic_2A1: uses: lsx_fwd_bind_dx *)
60 (* Note: the exclusion binder (ā§) makes this more elegant and much simpler *)
61 lemma lfsx_fwd_bind_dx: āh,o,p,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{p,I}V.T] šā¦Lā¦ ā
62 G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
63 #h #o #p #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
64 #L1 #_ #IH @lfsx_intro
65 #L2 #H #HT elim (lfpx_bind_dx_split_void ā¦ H o p I V) -H
66 /6 width=5 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_dx_void/
69 (* Advanced inversion lemmas ************************************************)
71 (* Basic_2A1: uses: lsx_inv_flat *)
72 lemma lfsx_inv_flat: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
73 G ā¢ ā¬*[h, o, V] šā¦Lā¦ ā§ G ā¢ ā¬*[h, o, T] šā¦Lā¦.
74 /3 width=3 by lfsx_fwd_pair_sn, lfsx_fwd_flat_dx, conj/ qed-.
76 (* Basic_2A1: uses: lsx_inv_bind *)
77 lemma lfsx_inv_bind: āh,o,p,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{p,I}V.T] šā¦Lā¦ ā
78 G ā¢ ā¬*[h, o, V] šā¦Lā¦ ā§ G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
79 /3 width=4 by lfsx_fwd_pair_sn, lfsx_fwd_bind_dx, conj/ qed-.