advances on cpx_lfxs_conf_fle

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
index 8c8679a475f0159e3af37f42569e2058da066e06..0f34a15b3acb8763af3ffc7af3fa9c7fe993937a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_etc.ma
@@ -1,3 +1,17 @@
-(* Basic_2A1: was just: lprs_lpxs *)
-lemma lprs_lfpxs: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡*[h, o] L2.
-/3 width=3 by lpr_lpx, monotonic_TC/ qed.
+
+include "basic_2/static/lfxs_lex.ma".
+include "basic_2/rt_transition/cpx_etc.ma".
+include "basic_2/rt_computation/lfpxs_lpxs.ma".
+
+lemma R_fle_comp_LTC: ∀R. R_fle_compatible R → R_fle_compatible (LTC … R).
+#R #HR #L #T1 #T2 #H elim H -T2
+/3 width=3 by fle_trans_dx/
+qed-.
+lemma lfpxs_cpx_conf: ∀h,G. s_r_confluent1 … (cpx h G) (lfpxs h G).
+#h #G #L1 #T1 #T2 #HT12 #L2 #H
+elim (tc_lfxs_inv_lex_lfeq … H) -H #L #HL1 #HL2
+lapply (lfxs_lex … HL1 T1) #H
+elim (cpx_lfxs_conf_fle … HT12 … H) -HT12 -H // #_ #HT21 #_
+@(lfpxs_lpxs_lfeq … HL1) -HL1
+@(fle_lfxs_trans … HL2) //
+qed-.