update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
index 414bfddd4043f18c280c069c3621d01356c17cb5..856fccf535b10d4e24607d69267a585a5496308e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
@@ -12,27 +12,36 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/lifts_tdeq.ma".
-include "basic_2/static/lfxs_lfxs.ma".
 include "basic_2/static/lfdeq_fqup.ma".
-include "basic_2/rt_transition/lfpx_frees.ma".
-include "basic_2/rt_transition/lfpx.ma". (**) (* should be in lfpx_frees.ma *)
+include "basic_2/static/lfdeq_lfdeq.ma".
+include "basic_2/rt_transition/lfpx_fsle.ma".
 
 (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
 
 (* Properties with degree-based equivalence for local environments **********)
 
-lemma lfpx_pair_sn_split: ∀h,o,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 →
-                          â\88\83â\88\83L. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, â\91¡{I}V.T] L & L â\89¡[h, o, V] L2.
-/3 width=5 by lfpx_frees_conf, lfxs_pair_sn_split/ qed-.
+lemma lfpx_pair_sn_split: ∀h,G,L1,L2,V. ⦃G, L1⦄ ⊢ ⬈[h, V] L2 → ∀o,I,T.
+                          â\88\83â\88\83L. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, â\91¡{I}V.T] L & L â\89\9b[h, o, V] L2.
+/3 width=5 by lfpx_fsge_comp, lfxs_pair_sn_split/ qed-.
 
-lemma lfpx_flat_dx_split: ∀h,o,I,G,L1,L2,V,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 →
-                          â\88\83â\88\83L. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, â\93\95{I}V.T] L & L â\89¡[h, o, T] L2.
-/3 width=5 by lfpx_frees_conf, lfxs_flat_dx_split/ qed-.
+lemma lfpx_flat_dx_split: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → ∀o,I,V.
+                          â\88\83â\88\83L. â¦\83G, L1â¦\84 â\8a¢ â¬\88[h, â\93\95{I}V.T] L & L â\89\9b[h, o, T] L2.
+/3 width=5 by lfpx_fsge_comp, lfxs_flat_dx_split/ qed-.
 
-lemma lfpx_bind_dx_split: ∀h,o,p,I,G,L1,L2,V1,T. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L2 →
-                          ∃∃L,V. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V1.T] L & L.ⓑ{I}V ≡[h, o, T] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V.
-/3 width=5 by lfpx_frees_conf, lfxs_bind_dx_split/ qed-.
+lemma lfpx_bind_dx_split: ∀h,I,G,L1,L2,V1,T. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈[h, T] L2 → ∀o,p.
+                          ∃∃L,V. ⦃G, L1⦄ ⊢ ⬈[h, ⓑ{p,I}V1.T] L & L.ⓑ{I}V ≛[h, o, T] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V.
+/3 width=5 by lfpx_fsge_comp, lfxs_bind_dx_split/ qed-.
+
+lemma lfpx_bind_dx_split_void: ∀h,G,K1,L2,T. ⦃G, K1.ⓧ⦄ ⊢ ⬈[h, T] L2 → ∀o,p,I,V.
+                               ∃∃K2. ⦃G, K1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] K2 & K2.ⓧ ≛[h, o, T] L2.
+/3 width=5 by lfpx_fsge_comp, lfxs_bind_dx_split_void/ qed-.
+
+lemma lfpx_tdeq_conf: ∀h,o,G. s_r_confluent1 … (cdeq h o) (lfpx h G).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+
+lemma lfpx_tdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+                     ∀G,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, T2] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T1] L2.
+/2 width=5 by tdeq_lfxs_div/ qed-.
 
 lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (cpx h G) (cdeq h o).
 #h #o #G #L0 #T0 #T1 #H @(cpx_ind … H) -G -L0 -T0 -T1 /2 width=3 by ex2_intro/
@@ -115,45 +124,45 @@ lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (
 qed-.
 
 lemma cpx_tdeq_conf: ∀h,o,G,L. ∀T0:term. ∀T1. ⦃G, L⦄ ⊢ T0 ⬈[h] T1 →
-                     â\88\80T2. T0 â\89¡[h, o] T2 →
-                     â\88\83â\88\83T. T1 â\89¡[h, o] T & ⦃G, L⦄ ⊢ T2 ⬈[h] T.
+                     â\88\80T2. T0 â\89\9b[h, o] T2 →
+                     â\88\83â\88\83T. T1 â\89\9b[h, o] T & ⦃G, L⦄ ⊢ T2 ⬈[h] T.
 #h #o #G #L #T0 #T1 #HT01 #T2 #HT02
 elim (cpx_tdeq_conf_lexs … HT01 … HT02 L … L) -HT01 -HT02
 /2 width=3 by lfxs_refl, ex2_intro/
 qed-.
 
-lemma tdeq_cpx_trans: â\88\80h,o,G,L,T2. â\88\80T0:term. T2 â\89¡[h, o] T0 →
+lemma tdeq_cpx_trans: â\88\80h,o,G,L,T2. â\88\80T0:term. T2 â\89\9b[h, o] T0 →
                       ∀T1. ⦃G, L⦄ ⊢ T0 ⬈[h] T1 → 
-                      â\88\83â\88\83T. â¦\83G, Lâ¦\84 â\8a¢ T2 â¬\88[h] T & T â\89¡[h, o] T1.
+                      â\88\83â\88\83T. â¦\83G, Lâ¦\84 â\8a¢ T2 â¬\88[h] T & T â\89\9b[h, o] T1.
 #h #o #G #L #T2 #T0 #HT20 #T1 #HT01
 elim (cpx_tdeq_conf … HT01 T2) -HT01 /3 width=3 by tdeq_sym, ex2_intro/
 qed-.
 
 (* Basic_2A1: uses: cpx_lleq_conf *)
 lemma cpx_lfdeq_conf: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
-                      â\88\80L2. L0 â\89¡[h, o, T0] L2 →
-                      â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88[h] T & T1 â\89¡[h, o] T.
+                      â\88\80L2. L0 â\89\9b[h, o, T0] L2 →
+                      â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88[h] T & T1 â\89\9b[h, o] T.
 #h #o #G #L0 #T0 #T1 #HT01 #L2 #HL02
 elim (cpx_tdeq_conf_lexs … HT01 T0 … L0 … HL02) -HT01 -HL02
 /2 width=3 by lfxs_refl, ex2_intro/
 qed-.
 
 (* Basic_2A1: uses: lleq_cpx_trans *)
-lemma lfdeq_cpx_trans: â\88\80h,o,G,L2,L0,T0. L2 â\89¡[h, o, T0] L0 →
+lemma lfdeq_cpx_trans: â\88\80h,o,G,L2,L0,T0. L2 â\89\9b[h, o, T0] L0 →
                        ∀T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
-                       â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88[h] T & T â\89¡[h, o] T1.
+                       â\88\83â\88\83T. â¦\83G, L2â¦\84 â\8a¢ T0 â¬\88[h] T & T â\89\9b[h, o] T1.
 #h #o #G #L2 #L0 #T0 #HL20 #T1 #HT01
 elim (cpx_lfdeq_conf … o … HT01 L2) -HT01
 /3 width=3 by lfdeq_sym, tdeq_sym, ex2_intro/
 qed-.
 
 lemma lfpx_lfdeq_conf: ∀h,o,G,T. confluent2 … (lfpx h G T) (lfdeq h o T).
-/3 width=6 by lfpx_frees_conf, cpx_tdeq_conf_lexs, frees_lfdeq_conf_lexs, lfxs_conf/ qed-.
+/3 width=6 by lfpx_fsge_comp, lfdeq_fsge_comp, cpx_tdeq_conf_lexs, lfxs_conf/ qed-.
 
 (* Basic_2A1: uses: lleq_lpx_trans *)
 lemma lfdeq_lfpx_trans: ∀h,o,G,T,L2,K2. ⦃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 #T #L2 #K2 #HLK2 #L1 #HL12
 elim (lfpx_lfdeq_conf … o … HLK2 L1)
 /3 width=3 by lfdeq_sym, ex2_intro/