milestone in basic_2

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

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 e86c302b8217c848917bcad34c3c9ee1e5105131..2d33b783e834e333b2b3e0547d4b0343a659c0c0 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/rdsx_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⦄.
-#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
+lemma fsb_inv_csx: ∀h,G,L,T. ≥[h] 𝐒⦃G, L, T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+#h #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,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+                    ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h] ⦃G2, L2, T2⦄ → ≥[h] 𝐒⦃G2, L2, T2⦄.
+#h #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 (fpbs_csx_conf … H10) // -HT1 #HT0
+generalize in match IHu; -IHu generalize in match H10; -H10
+@(rdsx_ind … (csx_rdsx … 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 *)
+  | #G3 #L3 #T3 #H03 #_
+    elim (lpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
+    elim (tdeq_dec 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_rdeq_lpx_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_lpx_trans/
     ]
   ]
 ]
 qed.
 
-lemma csx_fsb: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ⦥[h, o] ⦃G, L, T⦄.
+lemma csx_fsb: ∀h,G,L,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ≥[h] 𝐒⦃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 →
-                               (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                               R G1 L1 T1
+lemma csx_ind_fpb: ∀h. ∀Q:relation3 genv lenv term.
+                   (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
+                               (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                               Q G1 L1 T1
                    ) →
-                   â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\86\92 R G L T.
+                   â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92  Q 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) →
-                                R G1 L1 T1
+lemma csx_ind_fpbg: ∀h. ∀Q:relation3 genv lenv term.
+                    (â\88\80G1,L1,T1. â¦\83G1, L1â¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T1â¦\84 →
+                                (∀G2,L2,T2. ⦃G1, L1, T1⦄ >[h] ⦃G2, L2, T2⦄ → Q G2 L2 T2) →
+                                Q G1 L1 T1
                     ) →
-                    â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\8a*[h, o] T â\86\92 R G L T.
+                    â\88\80G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92  Q G L T.
 /4 width=4 by fsb_inv_csx, csx_fsb, fsb_ind_fpbg/ qed-.