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: uses: lsx_fwd_flat_dx *)
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 ************************************************)
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-.