renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / fpb_lfdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
index e37aa68f0cbcf33aeefde144b890f6ee1e825205..ee1dea03e54872df688166ef5604346f41b8cd2a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
@@ -14,23 +14,37 @@
 
 include "basic_2/static/lfdeq_fqus.ma".
 include "basic_2/rt_transition/cpx_lfdeq.ma".
-include "basic_2/rt_transition/lfpx_lfdeq.ma".
+include "basic_2/rt_transition/lpx_lfdeq.ma".
 include "basic_2/rt_transition/fpb.ma".
 
 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
 
 (* Properties with degree-based equivalence for local environments **********)
 
+lemma tdeq_fpb_trans: ∀h,o,U2,U1. U2 ≛[h, o] U1 →
+                      ∀G1,G2,L1,L2,T1. ⦃G1, L1, U1⦄ ≻[h, o] ⦃G2, L2, T1⦄ → 
+                      ∃∃L,T2. ⦃G1, L1, U2⦄ ≻[h, o] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
+[ #G2 #L2 #T1 #H
+  elim (tdeq_fqu_trans … H … HU21) -H
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #T1 #HUT1 #HnUT1
+  elim (tdeq_cpx_trans … HU21 … HUT1) -HUT1
+  /6 width=5 by fpb_cpx, tdeq_canc_sn, tdeq_trans, ex3_2_intro/
+| /6 width=5 by fpb_lpx, lfpx_tdeq_div, tdeq_lfdeq_conf, ex3_2_intro/
+]
+qed-.
+
 (* Basic_2A1: was just: lleq_fpb_trans *)
-lemma lfdeq_fpb_trans: â\88\80h,o,F,K1,K2,T. K1 â\89¡[h, o, T] K2 →
+lemma lfdeq_fpb_trans: â\88\80h,o,F,K1,K2,T. K1 â\89\9b[h, o, T] K2 →
                        ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
-                       â\88\83â\88\83L1,U0. â¦\83F, K1, Tâ¦\84 â\89»[h, o] â¦\83G, L1, U0â¦\84 & U0 â\89¡[h, o] U & L1 â\89¡[h, o, U] L2.
+                       â\88\83â\88\83L1,U0. â¦\83F, K1, Tâ¦\84 â\89»[h, o] â¦\83G, L1, U0â¦\84 & U0 â\89\9b[h, o] U & L1 â\89\9b[h, o, U] L2.
 #h #o #F #K1 #K2 #T #HT #G #L2 #U * -G -L2 -U
 [ #G #L2 #U #H2 elim (lfdeq_fqu_trans … H2 … HT) -K2
   /3 width=5 by fpb_fqu, ex3_2_intro/
 | #U #HTU #HnTU elim (lfdeq_cpx_trans … HT … HTU) -HTU
-  /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf_sn, ex3_2_intro/
-| #L2 #HKL2 #HnKL2 elim (lfdeq_lfpx_trans … HKL2 … HT) -HKL2
-  /6 width=5 by fpb_lfpx, lfdeq_canc_sn, ex3_2_intro/ (* 2 lleq_canc_sn *)
+  /5 width=10 by fpb_cpx, cpx_lfdeq_conf_sn, tdeq_trans, tdeq_lfdeq_conf, ex3_2_intro/
+| #L2 #HKL2 #HnKL2 elim (lfdeq_lpx_trans … HKL2 … HT) -HKL2
+  /6 width=5 by fpb_lpx, (* 2x *) lfdeq_canc_sn, ex3_2_intro/
 ]
 qed-.