(* Advanced properties ******************************************************)
(* Basic_2A1: uses: lsx_atom *)
-lemma lfsx_atom (h) (G) (T): G ā¢ ā¬*[h,T] šāŖāā«.
+lemma lfsx_atom (h) (G) (T): G ā¢ ā¬*š[h,T] ā.
#h #G #T
@rsx_intro #Y #H #HnT
lapply (lpx_inv_atom_sn ā¦ H) -H #H destruct
(* Note: the exclusion binder (ā§) makes this more elegant and much simpler *)
(* Note: the old proof without the exclusion binder requires lreq *)
lemma rsx_fwd_bind_dx_void (h) (G):
- āp,I,L,V,T. G ā¢ ā¬*[h,ā[p,I]V.T] šāŖLā« ā G ā¢ ā¬*[h,T] šāŖL.ā§ā«.
+ āp,I,L,V,T. G ā¢ ā¬*š[h,ā[p,I]V.T] L ā G ā¢ ā¬*š[h,T] L.ā§.
#h #G #p #I #L #V #T #H
@(rsx_ind ā¦ H) -L #L1 #_ #IH
@rsx_intro #Y #H #HT
(* Basic_2A1: uses: lsx_inv_bind *)
lemma rsx_inv_bind_void (h) (G):
- āp,I,L,V,T. G ā¢ ā¬*[h,ā[p,I]V.T] šāŖLā« ā
- ā§ā§ G ā¢ ā¬*[h,V] šāŖLā« & G ā¢ ā¬*[h,T] šāŖL.ā§ā«.
+ āp,I,L,V,T. G ā¢ ā¬*š[h,ā[p,I]V.T] L ā
+ ā§ā§ G ā¢ ā¬*š[h,V] L & G ā¢ ā¬*š[h,T] L.ā§.
/3 width=4 by rsx_fwd_pair_sn, rsx_fwd_bind_dx_void, conj/ qed-.