(* *)
(**************************************************************************)
-include "basic_2/static/lfdeq_lfdeq.ma".
include "basic_2/rt_transition/lfpx_lfdeq.ma".
include "basic_2/rt_computation/lfsx.ma".
-(* STRONGLY NORMALIZING LOCAL ENV.S FOR UNCOUNTED PARALLEL RT-TRANSITION ****)
+(* 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
- Ć¢\88\80L2. L1 Ć¢\89Ā”[h, o, T] L2 ā G ā¢ ā¬*[h, o, T] šā¦L2ā¦.
+ Ć¢\88\80L2. L1 Ć¢\89\9b[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: includes: lsx_fwd_bind_sn lsx_fwd_flat_sn *)
-(* Basic_2A1: was: lsx_fwd_pair_sn *)
+(* 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¦ o I ā¦ T H) -H
-/6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
+#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: was: lsx_fwd_flat_dx *)
+(* 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¦ o I ā¦ V ā¦ H) -H
-/6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_flat_dx/
+#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: was: lsx_inv_flat *)
+(* 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-.