made executable again

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

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 72c12b91e721c5591db79a5afad97bc0f5f45f6b..f49c3d568d571da048814ea011cb8ea8d4d7b94e 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
@@ -12,34 +12,49 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "static_2/s_computation/fqus_fqup.ma".
-include "static_2/static/feqx_fqup.ma".
-include "basic_2/rt_computation/fpbs_fqus.ma".
+include "basic_2/rt_transition/fpb_fqup.ma".
+include "basic_2/rt_computation/fpbs.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-(* Advanced properties ******************************************************)
+(* Advanced eliminators *****************************************************)
+
+lemma fpbs_ind:
+      ∀G1,L1,T1. ∀Q:relation3 genv lenv term. Q G1 L1 T1 →
+      (∀G,G2,L,L2,T,T2. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ → ❨G,L,T❩ ≽ ❨G2,L2,T2❩ → Q G L T → Q G2 L2 T2) →
+      ∀G2,L2,T2. ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩ → Q G2 L2 T2.
+/3 width=8 by tri_TC_star_ind/ qed-.
 
-lemma teqx_fpbs_trans: ∀h,T1,T. T1 ≛ T →
-                       ∀G1,G2,L1,L2,T2. ❪G1,L1,T❫ ≥[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-/3 width=5 by feqx_fpbs_trans, teqx_feqx/ qed-.
+lemma fpbs_ind_dx:
+      ∀G2,L2,T2. ∀Q:relation3 genv lenv term. Q G2 L2 T2 →
+      (∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≽ ❨G,L,T❩ → ❨G,L,T❩ ≥ ❨G2,L2,T2❩ → Q G L T → Q G1 L1 T1) →
+      ∀G1,L1,T1. ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩ → Q G1 L1 T1.
+/3 width=8 by tri_TC_star_ind_dx/ qed-.
 
-lemma fpbs_teqx_trans: ∀h,G1,G2,L1,L2,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T❫ →
-                       ∀T2. T ≛ T2 →  ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-/3 width=5 by fpbs_feqx_trans, teqx_feqx/ qed-.
+(* Advanced properties ******************************************************)
+
+lemma fpbs_refl:
+      tri_reflexive … fpbs.
+/2 width=1 by tri_inj/ qed.
 
 (* Properties with plus-iterated structural successor for closures **********)
 
-lemma fqup_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ⬂+ ❪G2,L2,T2❫ →
-                 ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
-/4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
+lemma fqup_fpbs:
+      ∀G1,G2,L1,L2,T1,T2. ❨G1,L1,T1❩ ⬂+ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/4 width=5 by fqu_fquq, fquq_fpb, tri_step/
 qed.
 
-lemma fpbs_fqup_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
-                       ∀G2,L2,T2. ❪G,L,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-/3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
-
-lemma fqup_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ →
-                       ∀G1,L1,T1. ❪G1,L1,T1❫ ⬂+ ❪G,L,T❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
-/3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.
+lemma fpbs_fqup_trans:
+      ∀G1,G,L1,L,T1,T. ❨G1,L1,T1❩ ≥ ❨G,L,T❩ →
+      ∀G2,L2,T2. ❨G,L,T❩ ⬂+ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/3 width=5 by fpbs_strap1, fqu_fpb/
+qed-.
+
+lemma fqup_fpbs_trans:
+      ∀G,G2,L,L2,T,T2. ❨G,L,T❩ ≥ ❨G2,L2,T2❩ →
+      ∀G1,L1,T1. ❨G1,L1,T1❩ ⬂+ ❨G,L,T❩ → ❨G1,L1,T1❩ ≥ ❨G2,L2,T2❩.
+#G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -T1
+/3 width=9 by fpbs_strap2, fqu_fpb/
+qed-.
\ No newline at end of file