+++ /dev/null
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-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/rt_transition/lfpx_lfdeq.ma".
-include "basic_2/rt_computation/lfsx.ma".
-
-(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNBOUND PARALLEL RT-TRANSITION ******)
-
-(* Advanced properties ******************************************************)
-
-(* Basic_2A1: uses: lsx_lleq_trans *)
-lemma lfsx_lfdeq_trans: āh,o,G,L1,T. G ā¢ ā¬*[h, o, T] šā¦L1ā¦ ā
- āL2. L1 ā[h, o, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
-#h #o #G #L1 #T #H @(lfsx_ind ā¦ H) -L1
-#L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
-#L #HL2 #HnL2 elim (lfdeq_lfpx_trans ā¦ HL2 ā¦ HL12) -HL2
-/4 width=5 by lfdeq_repl/
-qed-.
-
-(* Basic_2A1: uses: lsx_lpx_trans *)
-lemma lfsx_lfpx_trans: āh,o,G,L1,T. G ā¢ ā¬*[h, o, T] šā¦L1ā¦ ā
- āL2. ā¦G, L1ā¦ ā¢ ā¬[h, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
-#h #o #G #L1 #T #H @(lfsx_ind ā¦ H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
-elim (lfdeq_dec h o L1 L2 T) /3 width=4 by lfsx_lfdeq_trans, lfxs_refl/
-qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-(* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
-lemma lfsx_fwd_pair_sn: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā”{I}V.T] šā¦Lā¦ ā
- G ā¢ ā¬*[h, o, V] šā¦Lā¦.
-#h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #H #HnL12 elim (lfpx_pair_sn_split ā¦ H o I T) -H
-/6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
-qed-.
-
-(* Basic_2A1: uses: lsx_fwd_flat_dx *)
-lemma lfsx_fwd_flat_dx: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
- G ā¢ ā¬*[h, o, T] šā¦Lā¦.
-#h #o #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
-#L1 #_ #IHL1 @lfsx_intro
-#L2 #H #HnL12 elim (lfpx_flat_dx_split ā¦ H o I V) -H
-/6 width=3 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_flat_dx/
-qed-.
-
-(* Basic_2A1: uses: lsx_fwd_bind_dx *)
-(* Note: the exclusion binder (ā§) makes this more elegant and much simpler *)
-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
- G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
-#h #o #p #I #G #L #V #T #H @(lfsx_ind ā¦ H) -L
-#L1 #_ #IH @lfsx_intro
-#L2 #H #HT elim (lfpx_bind_dx_split_void ā¦ H o p I V) -H
-/6 width=5 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_dx_void/
-qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-(* Basic_2A1: uses: lsx_inv_flat *)
-lemma lfsx_inv_flat: āh,o,I,G,L,V,T. G ā¢ ā¬*[h, o, ā{I}V.T] šā¦Lā¦ ā
- G ā¢ ā¬*[h, o, V] šā¦Lā¦ ā§ G ā¢ ā¬*[h, o, T] šā¦Lā¦.
-/3 width=3 by lfsx_fwd_pair_sn, lfsx_fwd_flat_dx, conj/ qed-.
-
-(* Basic_2A1: uses: lsx_inv_bind *)
-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
- G ā¢ ā¬*[h, o, V] šā¦Lā¦ ā§ G ā¢ ā¬*[h, o, T] šā¦L.ā§ā¦.
-/3 width=4 by lfsx_fwd_pair_sn, lfsx_fwd_bind_dx, conj/ qed-.