update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
index 0271355147c99dbe80f9edd5baae151608a9aaf5..10433b26797d273bbd9d27195818649a7cbbe4e6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
@@ -12,34 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/tdeq_tdeq.ma".
+include "basic_2/rt_transition/lfpx_lfdeq.ma".
 include "basic_2/rt_computation/cpxs.ma".
-include "basic_2/rt_transition/cpx_lfdeq.ma".
-include "basic_2/static/lfdeq_fqup.ma".
-include "basic_2/rt_transition/lfpx_fqup.ma".
 
 (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
 
-axiom tdeq_dec: ∀h,o,T1,T2. Decidable (tdeq h o T1 T2).
+(* Properties with degree-based equivalence for terms ***********************)
 
-axiom tdeq_canc_sn: ∀h,o. left_cancellable … (tdeq h o).
-
-lemma tdeq_cpx_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 → 
-                      ∃∃U2.  ⦃G, L⦄ ⊢ U1 ⬈[h] U2 & U2 ≡[h, o] T2.
-#h #o #U1 #T1 #HUT1 #G #L #T2 #HT12
-elim (cpx_tdeq_conf_lexs … o … HT12 … U1 … L … L) /3 width=3 by tdeq_sym, ex2_intro/
-qed-.
-
-lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≡[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
-                       ∃∃U2.  ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≡[h, o] T2.
+lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≛[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
+                       ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛[h, o] T2.
 #h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
 /3 width=3 by ex2_intro, cpxs_strap1/
 qed-.
 
 (* Note: this requires tdeq to be symmetric *)
-lemma cpxs_tdneq_inv_step_sn: â\88\80h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89¡[h, o] T2 → ⊥) →
-                              â\88\83â\88\83T,T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T & T1 â\89¡[h, o] T â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h] T0 & T0 â\89¡[h, o] T2.
+lemma cpxs_tdneq_inv_step_sn: â\88\80h,o,G,L,T1,T2. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 (T1 â\89\9b[h, o] T2 → ⊥) →
+                              â\88\83â\88\83T,T0. â¦\83G, Lâ¦\84 â\8a¢ T1 â¬\88[h] T & T1 â\89\9b[h, o] T â\86\92 â\8a¥ & â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h] T0 & T0 â\89\9b[h, o] T2.
 #h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
 [ #H elim H -H //
 | #T1 #T #H1 #H2 #IH #Hn12 elim (tdeq_dec h o T1 T) #H destruct
@@ -51,5 +40,3 @@ lemma cpxs_tdneq_inv_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
   ]
 ]
 qed-.
-
-(* Basic_2A1: removed theorems 1: cpxs_neq_inv_step_sn *)