milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_rdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_rdeq.ma
index 3526c22c2c3c748d9f300cf972535e6ae75e4534..2bc873339eb4826b50af090c2cc512498b5c996e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_rdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_rdeq.ma
@@ -17,13 +17,14 @@ include "basic_2/rt_computation/lpxs_lpx.ma".
 
 (* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
 
-(* Properties with degree-based equivalence on referred entries *************)
+(* Properties with sort-irrelevant equivalence on referred entries **********)
 
 (* Basic_2A1: uses: lleq_lpxs_trans *)
-lemma rdeq_lpxs_trans (h) (o) (G) (T:term): ∀L2,K2. ⦃G, L2⦄ ⊢ ⬈*[h] K2 →
-                                            ∀L1. L1 ≛[h, o, T] L2 →
-                                            ∃∃K1. ⦃G, L1⦄ ⊢ ⬈*[h] K1 & K1 ≛[h, o, T] K2.
-#h #o #G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
+lemma rdeq_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/
 #L #L2 #HL2 #_ #IH #L1 #HT
 elim (rdeq_lpx_trans … HL2 … HT) -L #L #HL1 #HT
 elim (IH … HT) -L2 #K #HLK #HT
@@ -31,13 +32,13 @@ elim (IH … HT) -L2 #K #HLK #HT
 qed-.
 
 (* Basic_2A1: uses: lpxs_nlleq_inv_step_sn *)
-lemma lpxs_rdneq_inv_step_sn (h) (o) (G) (T:term):
-                             ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[h, o, T] L2 → ⊥) →
-                             ∃∃L,L0. ⦃G, L1⦄ ⊢ ⬈[h] L & L1 ≛[h, o, T] L → ⊥ &
-                                     ⦃G, L⦄ ⊢ ⬈*[h] L0 & L0 ≛[h, o, T] L2.
-#h #o #G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
+lemma lpxs_rdneq_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
 [ #H elim H -H //
-| #L1 #L #H1 #H2 #IH2 #H12 elim (rdeq_dec h o L1 L T) #H
+| #L1 #L #H1 #H2 #IH2 #H12 elim (rdeq_dec L1 L T) #H
   [ -H1 -H2 elim IH2 -IH2 /3 width=3 by rdeq_trans/ -H12
     #L0 #L3 #H1 #H2 #H3 #H4 lapply (rdeq_rdneq_trans … H … H2) -H2
     #H2 elim (rdeq_lpx_trans … H1 … H) -L