partial commit in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / rdsx_fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_fqup.ma
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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/static/lfdeq_fqup.ma".
+include "basic_2/rt_computation/rdsx.ma".
+
+(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lsx_atom *)
+lemma lfsx_atom (h) (o) (G) (T): G ⊢ ⬈*[h, o, T] 𝐒⦃⋆⦄.
+#h #o #G #T
+@rdsx_intro #Y #H #HnT
+lapply (lpx_inv_atom_sn … H) -H #H destruct
+elim HnT -HnT //
+qed.
+
+(* Advanced forward lemmas **************************************************)
+
+(* Basic_2A1: uses: lsx_fwd_bind_dx *)
+(* Note: the exclusion binder (ⓧ) makes this more elegant and much simpler *)
+(* Note: the old proof without the exclusion binder requires lreq *)
+lemma rdsx_fwd_bind_dx (h) (o) (G):
+                       ∀p,I,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+                       G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓧ⦄.
+#h #o #G #p #I #L #V #T #H
+@(rdsx_ind … H) -L #L1 #_ #IH
+@rdsx_intro #Y #H #HT
+elim (lpx_inv_unit_sn … H) -H #L2 #HL12 #H destruct
+/4 width=4 by lfdeq_fwd_bind_dx_void/
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: uses: lsx_inv_bind *)
+lemma rdsx_inv_bind (h) (o) (G): ∀p,I,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+                                 ∧∧ G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ & G ⊢ ⬈*[h, o, T] 𝐒⦃L.ⓧ⦄.
+/3 width=4 by rdsx_fwd_pair_sn, rdsx_fwd_bind_dx, conj/ qed-.