update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma
index 9389dd099a3baa6d7fe71f060627318fe40b61ae..2eda15369ba2c0c8e57b4447dd430f877e162f6e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_lfdeq.ma
@@ -12,18 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/lfdeq_lfdeq.ma".
 include "basic_2/rt_transition/lfpx_lfdeq.ma".
 include "basic_2/rt_computation/lfpxs_fqup.ma".
 
 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
 
+(* Properties with degree-based equivalence on terms ************************)
+
+lemma lfpxs_tdeq_trans: ∀h,o,G. s_r_confluent1 … (cdeq h o) (lfpxs h G).
+#h #o #G #L1 #T1 #T2 #HT12 #L2 #H @(lfpxs_ind_sn … H) -L2
+/3 width=6 by lfpxs_step_dx, lfpx_tdeq_conf/
+qed-.
+
+lemma tdeq_lfpxs_trans: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+                        ∀G,L1,L2. ⦃G, L1⦄ ⊢⬈*[h, T2] L2 → ⦃G, L1⦄ ⊢⬈*[h, T1] L2.
+/3 width=4 by lfpxs_tdeq_trans, tdeq_sym/ qed-.
+
 (* Properties with degree-based equivalence on referred entries *************)
 
 (* Basic_2A1: was: lleq_lpxs_trans *)
 lemma lfdeq_lfpxs_trans: ∀h,o,G,L2,K2,T. ⦃G, L2⦄ ⊢ ⬈*[h, T] K2 →
-                         â\88\80L1. L1 â\89¡[h, o, T] L2 →
-                         â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] K1 & K1 â\89¡[h, o, T] K2.
+                         â\88\80L1. L1 â\89\9b[h, o, T] L2 →
+                         â\88\83â\88\83K1. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] K1 & K1 â\89\9b[h, o, T] K2.
 #h #o #G #L2 #K2 #T #H @(lfpxs_ind_sn … H) -K2 /2 width=3 by ex2_intro/
 #K #K2 #_ #HK2 #IH #L1 #HT elim (IH … HT) -L2
 #L #HL1 #HT elim (lfdeq_lfpx_trans … HK2 … HT) -K
@@ -31,8 +41,8 @@ lemma lfdeq_lfpxs_trans: ∀h,o,G,L2,K2,T. ⦃G, L2⦄ ⊢ ⬈*[h, T] K2 →
 qed-.
 
 (* Basic_2A1: was: lpxs_nlleq_inv_step_sn *)
-lemma lfpxs_lfdneq_inv_step_sn: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89¡[h, o, T] L2 → ⊥) →
-                                â\88\83â\88\83L,L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L & L1 â\89¡[h, o, T] L â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, T] L0 & L0 â\89¡[h, o, T] L2.
+lemma lfpxs_lfdneq_inv_step_sn: â\88\80h,o,G,L1,L2,T. â¦\83G, L1â¦\84 â\8a¢ â¬\88*[h, T] L2 â\86\92 (L1 â\89\9b[h, o, T] L2 → ⊥) →
+                                â\88\83â\88\83L,L0. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, T] L & L1 â\89\9b[h, o, T] L â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ â¬\88*[h, T] L0 & L0 â\89\9b[h, o, T] L2.
 #h #o #G #L1 #L2 #T #H @(lfpxs_ind_dx … H) -L1
 [ #H elim H -H //
 | #L1 #L #H1 #H2 #IH2 #H12 elim (lfdeq_dec h o L1 L T) #H