update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
index 64be00b99ccc3150af51ecf8aa0a16bb103b3964..ee504e981c8907ad4cbe693676fb1dacde6b2f5b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
@@ -15,35 +15,34 @@
 include "basic_2/rt_transition/cpx_reqx.ma".
 include "basic_2/rt_computation/cpxs_teqx.ma".
 
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
 
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
 (* Basic_2A1: was just: lleq_cpxs_trans *)
-lemma reqx_cpxs_trans: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
-                       ∀L2. L2 ≛[T0] L0 →
-                       ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
-#h #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
-#T0 #T #HT0 #_ #IH #L2 #HL2
-elim (reqx_cpx_trans … HL2 … HT0) #U1 #H1 #H2
-elim (IH L2) -IH /2 width=5 by cpx_reqx_conf_dx/ -L0 #U2 #H3 #H4
-elim (teqx_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
-/3 width=5 by cpxs_strap2, teqx_trans, ex2_intro/
+lemma reqx_cpxs_trans (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L2 ≛[T0] L0 → ❪G,L2❫ ⊢ T0 ⬈* T1.
+#G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 //
+#T0 #T #H0T0 #_ #IH #L2 #HL2
+lapply (reqx_cpx_trans … HL2 … H0T0) #H2T0
+lapply (IH L2 ?) -IH /2 width=5 by cpx_reqx_conf_dx/ -L0 #H2T1
+/2 width=3 by cpxs_strap2/
 qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf *)
-lemma cpxs_reqx_conf: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
-                      ∀L2. L0 ≛[T0] L2 →
-                      ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
+lemma cpxs_reqx_conf (G):
+      ∀L0,T0,T1. ❪G,L0❫ ⊢ T0 ⬈* T1 → ∀L2. L0 ≛[T0] L2 → ❪G,L2❫ ⊢ T0 ⬈* T1.
 /3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf_dx *)
-lemma cpxs_reqx_conf_dx: ∀h,G,L2,T1,T2. ⦃G,L2⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
-#h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
+lemma cpxs_reqx_conf_dx (G):
+      ∀L2,T1,T2. ❪G,L2❫ ⊢ T1 ⬈* T2 →
+      ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
+#G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
 qed-.
 
 (* Basic_2A1: was just: lleq_conf_sn *)
-lemma cpxs_reqx_conf_sn: ∀h,G,L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
+lemma cpxs_reqx_conf_sn (G):
+      ∀L1,T1,T2. ❪G,L1❫ ⊢ T1 ⬈* T2 →
+      ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
 /4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.