universary milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lleq.ma
index f8790c5d918229b077c40a70e6256f7be146ac03..be3e0f0b5f62263a03fc9f89cb6344ebeecc6610 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lleq.ma
@@ -12,20 +12,28 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/reduction/lpx_leq.ma".
+include "basic_2/reduction/cpx_lleq.ma".
 include "basic_2/computation/cpxs.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
 
 (* Properties on lazy equivalence for local environments ********************)
 
-lemma lleq_cpxs_trans: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
-                       â\88\80L1. L1 â\8b\95[0, T1] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[h, g] T2.
-#h #g #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
-/4 width=6 by lleq_cpx_conf_dx, lleq_cpx_trans, cpxs_strap2/
+lemma lleq_cpxs_trans: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, o] T2 →
+                       â\88\80L1. L1 â\89¡[T1, 0] L2 â\86\92 â¦\83G, L1â¦\84 â\8a¢ T1 â\9e¡*[h, o] T2.
+#h #o #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
+/4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/
 qed-.
 
-lemma lleq_cpxs_conf_dx: ∀h,g,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, g] T2 →
-                         ∀L1. L1 ⋕[0, T1] L2 → L1 ⋕[0, T2] L2.
-#h #g #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by lleq_cpx_conf_dx/
+lemma cpxs_lleq_conf: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, o] T2 →
+                      ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ➡*[h, o] T2.
+/3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-.
+
+lemma cpxs_lleq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡*[h, o] T2 →
+                         ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/
 qed-.
+
+lemma cpxs_lleq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡*[h, o] T2 →
+                         ∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
+/4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ qed-.