milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_reqx.ma
index 29deb02390f28d93936f637b0d4a2a3a8c8b47fb..886c4dffbbb72af5e83efd2fdd546e3092996e7b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_reqx.ma
@@ -15,16 +15,15 @@
 include "basic_2/rt_transition/lpx_reqx.ma".
 include "basic_2/rt_computation/lpxs_lpx.ma".
 
-(* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
+(* EXTENDED PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS *************)
 
 (* Properties with sort-irrelevant equivalence on referred entries **********)
 
 (* Basic_2A1: uses: lleq_lpxs_trans *)
-lemma reqx_lpxs_trans (h) (G) (T:term):
-                      ∀L2,K2. ❪G,L2❫ ⊢ ⬈*[h] K2 →
-                      ∀L1. L1 ≛[T] L2 →
-                      ∃∃K1. ❪G,L1❫ ⊢ ⬈*[h] K1 & K1 ≛[T] K2.
-#h #G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
+lemma reqx_lpxs_trans (G) (T:term):
+      ∀L2,K2. ❪G,L2❫ ⊢ ⬈* K2 → ∀L1. L1 ≛[T] L2 →
+      ∃∃K1. ❪G,L1❫ ⊢ ⬈* K1 & K1 ≛[T] K2.
+#G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
 #L #L2 #HL2 #_ #IH #L1 #HT
 elim (reqx_lpx_trans … HL2 … HT) -L #L #HL1 #HT
 elim (IH … HT) -L2 #K #HLK #HT
@@ -32,11 +31,10 @@ elim (IH … HT) -L2 #K #HLK #HT
 qed-.
 
 (* Basic_2A1: uses: lpxs_nlleq_inv_step_sn *)
-lemma lpxs_rneqx_inv_step_sn (h) (G) (T:term):
-                             ∀L1,L2. ❪G,L1❫ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) →
-                             ∃∃L,L0. ❪G,L1❫ ⊢ ⬈[h] L & L1 ≛[T] L → ⊥ &
-                                     ❪G,L❫ ⊢ ⬈*[h] L0 & L0 ≛[T] L2.
-#h #G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
+lemma lpxs_rneqx_inv_step_sn (G) (T:term):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈* L2 → (L1 ≛[T] L2 → ⊥) →
+      ∃∃L,L0. ❪G,L1❫ ⊢ ⬈ L & L1 ≛[T] L → ⊥ & ❪G,L❫ ⊢ ⬈* L0 & L0 ≛[T] L2.
+#G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
 [ #H elim H -H //
 | #L1 #L #H1 #H2 #IH2 #H12 elim (reqx_dec L1 L T) #H
   [ -H1 -H2 elim IH2 -IH2 /3 width=3 by reqx_trans/ -H12