update in basic_2

+ lemma csx_fsb proved

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
index 74eae9335e51fd82f0e20a12add8b9ecfb0a8779..82c5eb62ace479bc97e9076b2dc491eea5728b70 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
@@ -67,6 +67,10 @@ lemma ffdeq_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2
                         ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by fpbs_strap2, fpbq_ffdeq/ qed-.
 
+lemma tdeq_lfdeq_lfpx_fpbs: ∀h,o,T1,T2. T1 ≛[h, o] T2 → ∀L1,L0. L1 ≛[h, o, T2] L0 →
+                            ∀G,L2. ⦃G, L0⦄ ⊢ ⬈[h, T2] L2 → ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, T2⦄.
+/4 width=5 by ffdeq_fpbs, fpbs_strap1, fpbq_lfpx, ffdeq_intro_dx/ qed.
+
 (* Basic_2A1: removed theorems 3:
               fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs
 *)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma
index 4cef4f3964870a6391e26b4bd5a36ece4f326699..ce248aeb1f104c24e80afe60fb7e0c4bdcfade85 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma
@@ -24,6 +24,10 @@ lemma tdeq_fpbs_trans: ∀h,o,T1,T. T1 ≛[h, o] T →
                        ∀G1,G2,L1,L2,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by ffdeq_fpbs_trans, tdeq_ffdeq/ qed-.
 
+lemma fpbs_tdeq_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T⦄ →
+                       ∀T2. T ≛[h, o] T2 →  ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+/3 width=5 by fpbs_ffdeq_trans, tdeq_ffdeq/ qed-.
+
 (* Properties with plus-iterated structural successor for closures **********)
 
 lemma fqup_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma
index 5a8c400b53834feed34d4e74fd4450d75e390145..9bccf418d7d0265727ece8c9ed67e284b6a3888b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lfpxs.ma
@@ -49,6 +49,10 @@ lemma lfpxs_ffdeq_fpbs: ∀h,o,G1,L1,L,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, T1] L →
                         ∀G2,L2,T2. ⦃G1, L, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
 /3 width=3 by lfpxs_fpbs_trans, ffdeq_fpbs/ qed.
 
+lemma fpbs_lfpx_trans: ∀h,o,G1,G2,L1,L,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L, T2⦄ →
+                       ∀L2. ⦃G2, L⦄ ⊢ ⬈[h, T2] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+/3 width=3 by fpbs_lfpxs_trans, lfpx_lfpxs/ qed-.
+
 (* Properties with star-iterated structural successor for closures **********)
 
 (* Basic_2A1: uses: fqus_lpxs_fpbs *)
@@ -64,6 +68,16 @@ lemma cpxs_fqus_lfpxs_fpbs: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →
                             ∀L2.⦃G2, L⦄ ⊢ ⬈*[h, T2] L2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
 /3 width=5 by cpxs_fqus_fpbs, fpbs_lfpxs_trans/ qed.
 
+lemma fpbs_cpxs_tdeq_fqup_lfpx_trans: ∀h,o,G1,G3,L1,L3,T1,T3. ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G3, L3, T3⦄ →
+                                      ∀T4. ⦃G3, L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛[h, o] T5 →
+                                      ∀G2,L4,T2. ⦃G3, L3, T5⦄ ⊐+ ⦃G2, L4, T2⦄ →
+                                      ∀L2. ⦃G2, L4⦄ ⊢ ⬈[h, T2] L2 → ⦃G1, L1, T1⦄ ≥ [h, o] ⦃G2, L2, T2⦄.
+#h #o #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
+@(fpbs_lfpx_trans … HL42) -L2 (**) (* full auto too slow *)
+@(fpbs_fqup_trans … H34) -G2 -L4 -T2
+/3 width=3 by fpbs_cpxs_trans, fpbs_tdeq_trans/ 
+qed-.
+
 (* Advanced properties ******************************************************)
 
 lemma fpbs_intro_fstar: ∀h,o,G1,L1,T1,T. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] T →

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
index 925beb513f1e215a87a89e0676688f201cbbfd56..62fd4fe1089c6764132e16d84c4883846d96d9a8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb.ma
@@ -41,6 +41,7 @@ lemma fsb_ind_alt: ∀h,o. ∀R: relation3 …. (
 /4 width=1 by fsb_intro/
 qed-.
 
-(* Basic_2A1: removed theorems 5:
+(* Basic_2A1: removed theorems 6:
               fsba_intro fsba_ind_alt fsba_fpbs_trans fsb_fsba fsba_inv_fsb
+              aaa_fsba
 *)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
index 58325a948d0d7c3d1af8d59cd8e6e983a98d78ac..6d25d649b6a9b19765619a2415bc848085bcb942 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
@@ -12,59 +12,67 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/fpbs_fpb.ma".
-include "basic_2/computation/fpbs_fpbs.ma".
-include "basic_2/computation/csx_fpbs.ma".
-include "basic_2/computation/lsx_csx.ma".
-include "basic_2/computation/fsb_alt.ma".
+include "basic_2/rt_computation/lfsx_csx.ma".
+include "basic_2/rt_computation/fpbs_cpx.ma".
+include "basic_2/rt_computation/fpbs_csx.ma".
+include "basic_2/rt_computation/fsb_fpbg.ma".
 
-(* "QRST" STRONGLY NORMALIZING CLOSURES *************************************)
+(* STRONGLY NORMALIZING CLOSURES FOR PARALLEL RST-TRANSITION ****************)
 
-(* Advanced propreties on context-sensitive extended normalizing terms ******)
+(* Inversion lemmas with context-sensitive stringly rt-normalizing terms ****)
 
-lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
-                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦥[h, o] ⦃G2, L2, T2⦄.
+lemma fsb_inv_csx: ∀h,o,G,L,T. ≥[h, o] 𝐒⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+#h #o #G #L #T #H @(fsb_ind_alt … H) -G -L -T /5 width=1 by csx_intro, fpb_cpx/
+qed-.
+
+(* Propreties with context-sensitive stringly rt-normalizing terms **********)
+
+lemma csx_fsb_fpbs: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
+                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ≥[h, o] 𝐒⦃G2, L2, T2⦄.
 #h #o #G1 #L1 #T1 #H @(csx_ind … H) -T1
-#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind … G2 L2 T2) -G2 -L2 -T2
-#G0 #L0 #T0 #IHu #H10 lapply (csx_fpbs_conf … H10) // -HT1
-#HT0 generalize in match IHu; -IHu generalize in match H10; -H10
-@(lsx_ind … (csx_lsx … HT0 0)) -L0
+#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind (Ⓣ) … G2 L2 T2) -G2 -L2 -T2
+#G0 #L0 #T0 #IHu #H10 
+lapply (fpbs_csx_conf … H10) // -HT1 #HT0
+generalize in match IHu; -IHu generalize in match H10; -H10
+@(lfsx_ind … (csx_lfsx … HT0)) -L0
 #L0 #_ #IHd #H10 #IHu @fsb_intro
 #G2 #L2 #T2 * -G2 -L2 -T2 [ -IHd -IHc | -IHu -IHd |  ]
 [ /4 width=5 by fpbs_fqup_trans, fqu_fqup/
-| #T2 #HT02 #HnT02 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0
+| #T2 #HT02 #HnT02
+  elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0
   /3 width=4 by/
 | #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
-  [ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
-  | #G3 #L3 #T3 #H03 #_ elim (lpx_fqup_trans … H03 … HL02) -L2
-    #L4 #T4 elim (eq_term_dec T0 T4) [ -IHc | -IHu ]
-    [ #H destruct /5 width=5 by fsb_fpbs_trans, lpxs_fpbs, fpbs_fqup_trans, lpx_lpxs/
-    | #HnT04 #HT04 #H04 #HL43 elim (cpxs_neq_inv_step_sn … HT04 HnT04) -HT04 -HnT04
-      #T2 #HT02 #HnT02 #HT24 elim (fpbs_cpx_trans_neq … H10 … HT02 HnT02) -T0
-      lapply (fpbs_intro_alt … G3 … L4 … L3 L3 … T3 … HT24 ? ? ?) -HT24
-      /3 width=8 by fpbs_trans, lpx_lpxs, fqup_fqus/ (**) (* full auto too slow *)
+  [ /3 width=3 by fpbs_lfpxs_trans, lfpx_lfpxs/
+  | #G3 #L3 #T3 #H03 #_
+    elim (lfpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
+    elim (tdeq_dec h o T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
+    [ elim (tdeq_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
+      /4 width=7 by fsb_fpbs_trans, tdeq_lfdeq_lfpx_fpbs, fpbs_fqup_trans/
+    | elim (cpxs_tdneq_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
+      elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
+      /3 width=14 by fpbs_cpxs_tdeq_fqup_lfpx_trans/
     ]
   ]
 ]
 qed.
 
-lemma csx_fsb: â\88\80h,o,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\86\92 ⦥[h, o] ⦃G, L, T⦄.
+lemma csx_fsb: â\88\80h,o,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â\89¥[h, o] ð\9d\90\92⦃G, L, T⦄.
 /2 width=5 by csx_fsb_fpbs/ qed.
 
 (* Advanced eliminators *****************************************************)
 
 lemma csx_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
-                   (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\8a*[h, o] T1 →
+                   (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83T1â¦\84 →
                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                R G1 L1 T1
                    ) →
-                   â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T → R G L T.
+                   â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_alt/ qed-.
 
 lemma csx_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
-                    (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\8a*[h, o] T1 →
-                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≛[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                    (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83T1â¦\84 →
+                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                 R G1 L1 T1
                     ) →
-                    â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T → R G L T.
+                    â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, o] ð\9d\90\92â¦\83Tâ¦\84 → R G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
index fc893a1d2ef694c8033da058babfb2a8509f7e73..2c46eff5d2de289af7d9e0809b036ada0d8f4ec2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/partial.txt
@@ -8,4 +8,4 @@ lfsx.ma lfsx_drops.ma lfsx_fqup.ma lfsx_lpx.ma lfsx_lpxs.ma lfsx_lfpxs.ma lfsx_c
 lsubsx.ma lsubsx_lfsx.ma lsubsx_lsubsx.ma
 fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_cpx.ma fpbs_fpb.ma fpbs_cpxs.ma fpbs_lpxs.ma fpbs_lfpxs.ma fpbs_csx.ma fpbs_fpbs.ma
 fpbg.ma fpbg_fqup.ma fpbg_cpxs.ma fpbg_lfpxs.ma fpbg_fpbs.ma fpbg_fpbg.ma
-fsb.ma fsb_ffdeq.ma fsb_fpbg.ma
+fsb.ma fsb_ffdeq.ma fsb_csx.ma fsb_fpbg.ma