milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma
index 292dc54e1609be9441ec59872869e10e29865fba..58c6d29ff80fa85669ee32b746c279b8669bb09e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_rdeq.ma
@@ -17,33 +17,33 @@ include "basic_2/rt_computation/cpxs_tdeq.ma".
 
 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties with degree-based equivalence for local environments **********)
+(* Properties with sort-irrelevant equivalence for local environments *******)
 
 (* Basic_2A1: was just: lleq_cpxs_trans *) 
-lemma rdeq_cpxs_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
-                       ∀L2. L2 ≛[h, o, T0] L0 →
-                       ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛[h, o] T1.
-#h #o #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
+lemma rdeq_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 (rdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2
-elim (IH L2) -IH /2 width=4 by cpx_rdeq_conf_dx/ -L0 #U2 #H3 #H4
+elim (IH L2) -IH /2 width=5 by cpx_rdeq_conf_dx/ -L0 #U2 #H3 #H4
 elim (tdeq_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
 /3 width=5 by cpxs_strap2, tdeq_trans, ex2_intro/
 qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf *) 
-lemma cpxs_rdeq_conf: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
-                      ∀L2. L0 ≛[h, o, T0] L2 →
-                      ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛[h, o] T1.
+lemma cpxs_rdeq_conf: ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
+                      ∀L2. L0 ≛[T0] L2 →
+                      ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
 /3 width=3 by rdeq_cpxs_trans, rdeq_sym/ qed-.
 
 (* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
-lemma cpxs_rdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L1. L1 ≛[h, o, T1] L2 → L1 ≛[h, o, T2] L2.
-#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_rdeq_conf_dx/
+lemma cpxs_rdeq_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_rdeq_conf_dx/
 qed-.
 
 (* Basic_2A1: was just: lleq_conf_sn *) 
-lemma cpxs_rdeq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 →
-                         ∀L2. L1 ≛[h, o, T1] L2 → L1 ≛[h, o, T2] L2.
+lemma cpxs_rdeq_conf_sn: ∀h,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 →
+                         ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
 /4 width=6 by cpxs_rdeq_conf_dx, rdeq_sym/ qed-.