λδ-2B is released

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
index 07df0c6245afb41534f18f6407593caacc5c3dfc..f01561bc24af4902c9bc26026bf5196e66da383b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
@@ -12,11 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/static/fdeq_fqus.ma".
-include "static_2/static/fdeq_fdeq.ma".
+include "static_2/static/feqx_fqus.ma".
+include "static_2/static/feqx_feqx.ma".
 include "basic_2/rt_computation/cpxs_fqus.ma".
-include "basic_2/rt_computation/cpxs_fdeq.ma".
-include "basic_2/rt_computation/lpxs_fdeq.ma".
+include "basic_2/rt_computation/cpxs_feqx.ma".
+include "basic_2/rt_computation/lpxs_feqx.ma".
 include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
@@ -41,9 +41,9 @@ lemma lpxs_fpbs_trans: ∀h,G1,G2,L,L2,T1,T2. ⦃G1,L,T1⦄ ≥[h] ⦃G2,L2,T2
 qed-.
 
 (* Basic_2A1: uses: lpxs_lleq_fpbs *)
-lemma lpxs_fdeq_fpbs: ∀h,G1,L1,L,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] L →
+lemma lpxs_feqx_fpbs: ∀h,G1,L1,L,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] L →
                       ∀G2,L2,T2. ⦃G1,L,T1⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-/3 width=3 by lpxs_fpbs_trans, fdeq_fpbs/ qed.
+/3 width=3 by lpxs_fpbs_trans, feqx_fpbs/ qed.
 
 lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L,T2⦄ →
                       ∀L2. ⦃G2,L⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
@@ -51,41 +51,41 @@ lemma fpbs_lpx_trans: ∀h,G1,G2,L1,L,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L,T2⦄
 
 (* Properties with star-iterated structural successor for closures **********)
 
-lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â\8a\90* ⦃G2,L,T2⦄ →
+lemma fqus_lpxs_fpbs: â\88\80h,G1,G2,L1,L,T1,T2. â¦\83G1,L1,T1â¦\84 â¬\82* ⦃G2,L,T2⦄ →
                       ∀L2. ⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
 /3 width=3 by fpbs_lpxs_trans, fqus_fpbs/ qed.
 
 (* Properties with unbound context-sensitive parallel rt-computation ********)
 
 lemma cpxs_fqus_lpxs_fpbs: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
-                           â\88\80G2,L,T2. â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G2,L,T2⦄ →
+                           â\88\80G2,L,T2. â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G2,L,T2⦄ →
                            ∀L2.⦃G2,L⦄ ⊢ ⬈*[h] L2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
 /3 width=5 by cpxs_fqus_fpbs, fpbs_lpxs_trans/ qed.
 
-lemma fpbs_cpxs_tdeq_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1,L1,T1⦄ ≥ [h] ⦃G3,L3,T3⦄ →
+lemma fpbs_cpxs_teqx_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1,L1,T1⦄ ≥ [h] ⦃G3,L3,T3⦄ →
                                      ∀T4. ⦃G3,L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
-                                     â\88\80G2,L4,T2. â¦\83G3,L3,T5â¦\84 â\8a\90+ ⦃G2,L4,T2⦄ →
+                                     â\88\80G2,L4,T2. â¦\83G3,L3,T5â¦\84 â¬\82+ ⦃G2,L4,T2⦄ →
                                      ∀L2. ⦃G2,L4⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥ [h] ⦃G2,L2,T2⦄.
-#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
+#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
 @(fpbs_fqup_trans … H34) -G2 -L4 -T2
-/3 width=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/
+/3 width=3 by fpbs_cpxs_trans, fpbs_teqx_trans/
 qed-.
 
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: uses: fpbs_intro_alt *)
 lemma fpbs_intro_star: ∀h,G1,L1,T1,T. ⦃G1,L1⦄ ⊢ T1 ⬈*[h] T →
-                       â\88\80G,L,T0. â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G,L,T0⦄ →
+                       â\88\80G,L,T0. â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G,L,T0⦄ →
                        ∀L0. ⦃G,L⦄ ⊢ ⬈*[h] L0 →
                        ∀G2,L2,T2. ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ .
-/3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_fdeq/ qed.
+/3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_feqx/ qed.
 
 (* Advanced inversion lemmas *************************************************)
 
 (* Basic_2A1: uses: fpbs_inv_alt *)
 lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ →
-                     â\88\83â\88\83G,L,L0,T,T0. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] T & â¦\83G1,L1,Tâ¦\84 â\8a\90* ⦃G,L,T0⦄
+                     â\88\83â\88\83G,L,L0,T,T0. â¦\83G1,L1â¦\84 â\8a¢ T1 â¬\88*[h] T & â¦\83G1,L1,Tâ¦\84 â¬\82* ⦃G,L,T0⦄
                                   & ⦃G,L⦄ ⊢ ⬈*[h] L0 & ⦃G,L0,T0⦄ ≛ ⦃G2,L2,T2⦄.
 #h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
 [ /2 width=9 by ex4_5_intro/
@@ -100,10 +100,10 @@ lemma fpbs_inv_star: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2
     elim (lpx_fqus_trans … H34 … HL10) -L0
     /3 width=9 by lpxs_step_sn, cpxs_trans, ex4_5_intro/
   | #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42
-    elim (fdeq_cpxs_trans … H10 … HT03) -T0 #T0 #HT10 #H03
-    elim (fdeq_fqus_trans … H03 … H34) -G0 -L0 -T3 #G0 #L0 #T3 #H03 #H34
-    elim (fdeq_lpxs_trans … H34 … HL34) -L3 #L3 #HL03 #H34
-    /3 width=13 by fdeq_trans, ex4_5_intro/
+    elim (feqx_cpxs_trans … H10 … HT03) -T0 #T0 #HT10 #H03
+    elim (feqx_fqus_trans … H03 … H34) -G0 -L0 -T3 #G0 #L0 #T3 #H03 #H34
+    elim (feqx_lpxs_trans … H34 … HL34) -L3 #L3 #HL03 #H34
+    /3 width=13 by feqx_trans, ex4_5_intro/
   ]
 ]
 qed-.