update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
index 5608b1ff8580f76d7d690f56cc21abbb048f435c..888b969696dba7be6a3e48e8bb058e437dcbace5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg_fpbs.ma
@@ -12,69 +12,76 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/fdeq_fqup.ma".
-include "basic_2/static/fdeq_fdeq.ma".
+include "static_2/static/feqx_feqx.ma".
 include "basic_2/rt_transition/fpbq_fpb.ma".
+include "basic_2/rt_computation/fpbs_fqup.ma".
 include "basic_2/rt_computation/fpbg.ma".
 
 (* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
 
 (* Advanced forward lemmas **************************************************)
 
-lemma fpbg_fwd_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2.
-                     â¦\83G1, L1, T1â¦\84 >[h,o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 â\89¥[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 *
+lemma fpbg_fwd_fpbs: ∀h,G1,G2,L1,L2,T1,T2.
+                     â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 *
 /3 width=5 by fpbs_strap2, fpb_fpbq/
 qed-.
 
-(* Advanced properties with degree-based equivalence on closures ************)
+(* Advanced properties with sort-irrelevant equivalence on closures *********)
 
 (* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma fdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
-                       â\88\80G1,L1,T1. â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
-elim (fdeq_fpb_trans …  H1 … H0) -G -L -T
-/4 width=9 by fpbs_strap2, fpbq_fdeq, ex2_3_intro/
+lemma feqx_fpbg_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ >[h] ❪G2,L2,T2❫ →
+                       â\88\80G1,L1,T1. â\9dªG1,L1,T1â\9d« â\89\9b â\9dªG,L,Tâ\9d« â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+#h #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
+elim (feqx_fpb_trans …  H1 … H0) -G -L -T
+/4 width=9 by fpbs_strap2, fpbq_feqx, ex2_3_intro/
 qed-.
 
 (* Properties with parallel proper rst-reduction on closures ****************)
 
-lemma fpb_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                      â¦\83G1, L1, T1â¦\84 â\89»[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 →
-                      â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84.
+lemma fpb_fpbg_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
+                      â\9dªG1,L1,T1â\9d« â\89»[h] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« >[h] â\9dªG2,L2,T2â\9d« →
+                      â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
 /3 width=5 by fpbg_fwd_fpbs, ex2_3_intro/ qed-.
 
 (* Properties with parallel rst-reduction on closures ***********************)
 
-lemma fpbq_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
-                       â¦\83G1, L1, T1â¦\84 â\89½[h, o] â¦\83G, L, Tâ¦\84 â\86\92 â¦\83G, L, Tâ¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 →
-                       â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+lemma fpbq_fpbg_trans: ∀h,G1,G,G2,L1,L,L2,T1,T,T2.
+                       â\9dªG1,L1,T1â\9d« â\89½[h] â\9dªG,L,Tâ\9d« â\86\92 â\9dªG,L,Tâ\9d« >[h] â\9dªG2,L2,T2â\9d« →
+                       â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
 elim (fpbq_inv_fpb … H1) -H1
-/2 width=5 by fdeq_fpbg_trans, fpb_fpbg_trans/
+/2 width=5 by feqx_fpbg_trans, fpb_fpbg_trans/
 qed-.
 
 (* Properties with parallel rst-compuutation on closures ********************)
 
-lemma fpbs_fpbg_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                       â\88\80G2,L2,T2. â¦\83G, L, Tâ¦\84 >[h, o] â¦\83G2, L2, T2â¦\84 â\86\92 â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
+lemma fpbs_fpbg_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+                       â\88\80G2,L2,T2. â\9dªG,L,Tâ\9d« >[h] â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpbq_fpbg_trans/
 qed-.
 
+(* Advanced properties with plus-iterated structural successor for closures *)
+
+lemma fqup_fpbg_trans (h):
+      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ⬂+ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ >[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ >[h] ❪G2,L2,T2❫.
+/3 width=5 by fpbs_fpbg_trans, fqup_fpbs/ qed-.
+
 (* Advanced inversion lemmas of parallel rst-computation on closures ********)
 
 (* Basic_2A1: was: fpbs_fpbg *)
-lemma fpbs_inv_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                     â\88¨â\88¨ â¦\83G1, L1, T1â¦\84 â\89\9b[h, o] â¦\83G2, L2, T2â¦\84
-                      | â¦\83G1, L1, T1â¦\84 >[h, o] â¦\83G2, L2, T2â¦\84.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
+lemma fpbs_inv_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ →
+                     â\88¨â\88¨ â\9dªG1,L1,T1â\9d« â\89\9b â\9dªG2,L2,T2â\9d«
+                      | â\9dªG1,L1,T1â\9d« >[h] â\9dªG2,L2,T2â\9d«.
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
 [ /2 width=1 by or_introl/
 | #G #G2 #L #L2 #T #T2 #_ #H2 * #H1
   elim (fpbq_inv_fpb … H2) -H2 #H2
-  [ /3 width=5 by fdeq_trans, or_introl/
-  | elim (fdeq_fpb_trans … H1 … H2) -G -L -T
-    /4 width=5 by ex2_3_intro, or_intror, fdeq_fpbs/
-  | /3 width=5 by fpbg_fdeq_trans, or_intror/
+  [ /3 width=5 by feqx_trans, or_introl/
+  | elim (feqx_fpb_trans … H1 … H2) -G -L -T
+    /4 width=5 by ex2_3_intro, or_intror, feqx_fpbs/
+  | /3 width=5 by fpbg_feqx_trans, or_intror/
   | /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
   ]
 ]
@@ -82,12 +89,12 @@ qed-.
 
 (* Advanced properties of parallel rst-computation on closures **************)
 
-lemma fpbs_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, o] ⦃F2, K2, T2⦄ →
-                      â\88\80G2,L2,U2. â¦\83F2, K2, T2â¦\84 â\89»[h, o] â¦\83G2, L2, U2â¦\84 →
-                      â\88\83â\88\83G1,L1,U1. â¦\83F1, K1, T1â¦\84 â\89»[h, o] â¦\83G1, L1, U1â¦\84 & â¦\83G1, L1, U1â¦\84 â\89¥[h, o] â¦\83G2, L2, U2â¦\84.
-#h #o #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
-[ #H12 #G2 #L2 #U2 #H2 elim (fdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
-  /3 width=5 by fdeq_fpbs, ex2_3_intro/
+lemma fpbs_fpb_trans: ∀h,F1,F2,K1,K2,T1,T2. ❪F1,K1,T1❫ ≥[h] ❪F2,K2,T2❫ →
+                      â\88\80G2,L2,U2. â\9dªF2,K2,T2â\9d« â\89»[h] â\9dªG2,L2,U2â\9d« →
+                      â\88\83â\88\83G1,L1,U1. â\9dªF1,K1,T1â\9d« â\89»[h] â\9dªG1,L1,U1â\9d« & â\9dªG1,L1,U1â\9d« â\89¥[h] â\9dªG2,L2,U2â\9d«.
+#h #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
+[ #H12 #G2 #L2 #U2 #H2 elim (feqx_fpb_trans … H12 … H2) -F2 -K2 -T2
+  /3 width=5 by feqx_fpbs, ex2_3_intro/
 | * #H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9
   @(ex2_3_intro … H4) -H4 /3 width=5 by fpbs_strap1, fpb_fpbq/
 ]