advances non lfsx ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
new file mode 100644 (file)
index 0000000..5ea3071
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
@@ -0,0 +1,69 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_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 ****)
+
+axiom pippo: ∀h,o,p,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
+             ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] L & L ≡[h, o, V] L2.
+
+(* Advanced properties ******************************************************)
+
+lemma lfsx_lfdeq_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                        ∀L2. L1 ≡[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
+#h #o #G #L1 #T #H @(lfsx_ind … H) -L1
+#L1 #_ #IHL1 #L2 #HL12 @lfsx_intro
+#L #HL2 #HnL2 elim (lfdeq_lfpx_trans … HL2 … HL12) -HL2
+/4 width=5 by lfdeq_repl/
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+(* Basic_2A1: was: lsx_fwd_bind_sn *)
+lemma lfsx_fwd_bind_sn: ∀h,o,p,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓑ{p,I}V.T] 𝐒⦃L⦄ →
+                        G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄.
+#h #o #p #I #G #L #V #T #H @(lfsx_ind … H) -L
+#L1 #_ #IHL1 @lfsx_intro
+#L2 #H #HnL12 elim (pippo … o p I … T H) -H
+/6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_bind_sn/
+qed-.
+(*
+lemma lfsx_fwd_flat_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
+                       G ⊢ ⬈*[h, o, V, l] L.
+#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
+#L1 #_ #IHL1 @lfsx_intro
+#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_sn/
+qed-.
+
+lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
+                       G ⊢ ⬈*[h, o, T, l] L.
+#h #o #I #G #L #V #T #l #H @(lfsx_ind … H) -L
+#L1 #_ #IHL1 @lfsx_intro
+#L2 #HL12 #HV @IHL1 /3 width=3 by lfdeq_fwd_flat_dx/
+qed-.
+
+lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ②{I}V.T, l] L →
+                       G ⊢ ⬈*[h, o, V, l] L.
+#h #o * /2 width=4 by lfsx_fwd_bind_sn, lfsx_fwd_flat_sn/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T,l. G ⊢ ⬈*[h, o, ⓕ{I}V.T, l] L →
+                    G ⊢ ⬈*[h, o, V, l] L ∧ G ⊢ ⬈*[h, o, T, l] L.
+/3 width=3 by lfsx_fwd_flat_sn, lfsx_fwd_flat_dx, conj/ qed-.
+*)
\ No newline at end of file