update in static_2 and basic_2

[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 b188e7880b23f30c40e3a56c134fd00384bab86d..d7a1ccae06e091ef9a0396aa2af7c639a53cdae3 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
@@ -12,9 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/ffdeq_fqup.ma".
-include "basic_2/static/ffdeq_ffdeq.ma".
+include "static_2/static/fdeq_fdeq.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 *****************************)
@@ -30,11 +30,11 @@ qed-.
 (* Advanced properties with degree-based equivalence on closures ************)
 
 (* Basic_2A1: uses: fleq_fpbg_trans *)
-lemma ffdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
-                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
+lemma fdeq_fpbg_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >[h, o] ⦃G2, L2, T2⦄ →
+                       ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
 #h #o #G #G2 #L #L2 #T #T2 * #G0 #L0 #T0 #H0 #H02 #G1 #L1 #T1 #H1
-elim (ffdeq_fpb_trans …  H1 … H0) -G -L -T
-/4 width=9 by fpbs_strap2, fpbq_ffdeq, ex2_3_intro/
+elim (fdeq_fpb_trans …  H1 … H0) -G -L -T
+/4 width=9 by fpbs_strap2, fpbq_fdeq, ex2_3_intro/
 qed-.
 
 (* Properties with parallel proper rst-reduction on closures ****************)
@@ -51,7 +51,7 @@ lemma fpbq_fpbg_trans: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2.
                        ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
 #h #o #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
 elim (fpbq_inv_fpb … H1) -H1
-/2 width=5 by ffdeq_fpbg_trans, fpb_fpbg_trans/
+/2 width=5 by fdeq_fpbg_trans, fpb_fpbg_trans/
 qed-.
 
 (* Properties with parallel rst-compuutation on closures ********************)
@@ -61,6 +61,13 @@ lemma fpbs_fpbg_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L
 #h #o #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) (o):
+      ∀G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ⊐+ ⦃G,L,T⦄ →
+      ∀G2,L2,T2. ⦃G,L,T⦄ >[h,o] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h,o] ⦃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 *)
@@ -71,10 +78,10 @@ lemma fpbs_inv_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2,
 [ /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 ffdeq_trans, or_introl/
-  | elim (ffdeq_fpb_trans … H1 … H2) -G -L -T
-    /4 width=5 by ex2_3_intro, or_intror, ffdeq_fpbs/
-  | /3 width=5 by fpbg_ffdeq_trans, or_intror/
+  [ /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/
   | /4 width=5 by fpbg_fpbq_trans, fpb_fpbq, or_intror/
   ]
 ]
@@ -86,8 +93,8 @@ lemma fpbs_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≥[h, o] ⦃F2
                       ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
                       ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
 #h #o #F1 #F2 #K1 #K2 #T1 #T2 #H elim (fpbs_inv_fpbg … H) -H
-[ #H12 #G2 #L2 #U2 #H2 elim (ffdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
-  /3 width=5 by ffdeq_fpbs, ex2_3_intro/
+[ #H12 #G2 #L2 #U2 #H2 elim (fdeq_fpb_trans … H12 … H2) -F2 -K2 -T2
+  /3 width=5 by fdeq_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/
 ]