update in static_2

[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 92fd0dd561db4a353e4de4dc056af4850f4e689b..b815ae960744b3fc72209e00788c2ab66d122cbc 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/feqx_fqus.ma".
-include "static_2/static/feqx_feqx.ma".
+include "static_2/static/feqg_fqus.ma".
+include "static_2/static/feqg_feqg.ma".
 include "basic_2/rt_computation/cpxs_fqus.ma".
-include "basic_2/rt_computation/cpxs_feqx.ma".
-include "basic_2/rt_computation/lpxs_feqx.ma".
+include "basic_2/rt_computation/cpxs_feqg.ma".
+include "basic_2/rt_computation/lpxs_feqg.ma".
 include "basic_2/rt_computation/fpbs_cpxs.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
@@ -46,7 +46,7 @@ qed-.
 (* Basic_2A1: uses: lpxs_lleq_fpbs *)
 lemma lpxs_feqx_fpbs:
       ∀G1,L1,L,T1. ❪G1,L1❫ ⊢ ⬈* L →
-      â\88\80G2,L2,T2. â\9dªG1,L,T1â\9d« â\89\9b ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+      â\88\80G2,L2,T2. â\9dªG1,L,T1â\9d« â\89\85 ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=3 by lpxs_fpbs_trans, feqx_fpbs/ qed.
 
 lemma fpbs_lpx_trans:
@@ -71,7 +71,7 @@ lemma cpxs_fqus_lpxs_fpbs:
 
 lemma fpbs_cpxs_teqx_fqup_lpx_trans:
       ∀G1,G3,L1,L3,T1,T3. ❪G1,L1,T1❫ ≥  ❪G3,L3,T3❫ →
-      â\88\80T4. â\9dªG3,L3â\9d« â\8a¢ T3 â¬\88* T4 â\86\92 â\88\80T5. T4 â\89\9b T5 →
+      â\88\80T4. â\9dªG3,L3â\9d« â\8a¢ T3 â¬\88* T4 â\86\92 â\88\80T5. T4 â\89\85 T5 →
       ∀G2,L4,T2. ❪G3,L3,T5❫ ⬂+ ❪G2,L4,T2❫ →
       ∀L2. ❪G2,L4❫ ⊢ ⬈ L2 → ❪G1,L1,T1❫ ≥  ❪G2,L2,T2❫.
 #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
@@ -87,7 +87,7 @@ lemma fpbs_intro_star:
       ∀G1,L1,T1,T. ❪G1,L1❫ ⊢ T1 ⬈* T →
       ∀G,L,T0. ❪G1,L1,T❫ ⬂* ❪G,L,T0❫ →
       ∀L0. ❪G,L❫ ⊢ ⬈* L0 →
-      â\88\80G2,L2,T2. â\9dªG,L0,T0â\9d« â\89\9b ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ .
+      â\88\80G2,L2,T2. â\9dªG,L0,T0â\9d« â\89\85 ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ .
 /3 width=5 by cpxs_fqus_lpxs_fpbs, fpbs_strap1, fpbq_feqx/ qed.
 
 (* Advanced inversion lemmas *************************************************)
@@ -95,9 +95,9 @@ lemma fpbs_intro_star:
 (* Basic_2A1: uses: fpbs_inv_alt *)
 lemma fpbs_inv_star:
       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ →
-      â\88\83â\88\83G,L,L0,T,T0. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* T & â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG,L,T0â\9d« & â\9dªG,Lâ\9d« â\8a¢ â¬\88* L0 & â\9dªG,L0,T0â\9d« â\89\9b ❪G2,L2,T2❫.
+      â\88\83â\88\83G,L,L0,T,T0. â\9dªG1,L1â\9d« â\8a¢ T1 â¬\88* T & â\9dªG1,L1,Tâ\9d« â¬\82* â\9dªG,L,T0â\9d« & â\9dªG,Lâ\9d« â\8a¢ â¬\88* L0 & â\9dªG,L0,T0â\9d« â\89\85 ❪G2,L2,T2❫.
 #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind_dx … H) -G1 -L1 -T1
-[ /2 width=9 by ex4_5_intro/
+[ /3 width=9 by feqg_refl, ex4_5_intro/
 | #G1 #G0 #L1 #L0 #T1 #T0 * -G0 -L0 -T0
   [ #G0 #L0 #T0 #H10 #_ * #G3 #L3 #L4 #T3 #T4 #HT03 #H34 #HL34 #H42
     elim (fquq_cpxs_trans … HT03 … H10) -T0
@@ -109,10 +109,10 @@ lemma fpbs_inv_star:
     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 (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/
+    elim (feqg_cpxs_trans … H10 … HT03) -T0 // #T0 #HT10 #H03
+    elim (feqg_fqus_trans … H03 … H34) -G0 -L0 -T3 // #G0 #L0 #T3 #H03 #H34
+    elim (feqg_lpxs_trans … H34 … HL34) -L3 // #L3 #HL03 #H34
+    /3 width=13 by feqg_trans, ex4_5_intro/
   ]
 ]
 qed-.