milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
index 279ee212eb6529b2ea9abd5c092f47d1ea9f3c8a..c313dc7ab16fe63aace1e44776e8bbf4c1400481 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
@@ -17,23 +17,23 @@ include "basic_2/rt_computation/cpxs.ma".
 
 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
 
-(* Properties with degree-based equivalence for terms ***********************)
+(* Properties with sort-irrelevant equivalence for terms ********************)
 
-lemma tdeq_cpxs_trans: ∀h,o,U1,T1. U1 ≛[h, o] T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
-                       ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛[h, o] T2.
-#h #o #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
+lemma tdeq_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → 
+                       ∃∃U2. ⦃G, L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛ T2.
+#h #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
 /3 width=3 by ex2_intro, cpxs_strap1/
 qed-.
 
 (* Note: this requires tdeq to be symmetric *)
 (* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
-lemma cpxs_tdneq_fwd_step_sn: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛[h, o] T2 → ⊥) →
-                              ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛[h, o] T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛[h, o] T2.
-#h #o #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
+lemma cpxs_tdneq_fwd_step_sn: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) →
+                              ∃∃T,T0. ⦃G, L⦄ ⊢ T1 ⬈[h] T & T1 ≛ T → ⊥ & ⦃G, L⦄ ⊢ T ⬈*[h] T0 & T0 ≛ T2.
+#h #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
 [ #H elim H -H //
 | #T1 #T0 #HT10 #HT02 #IH #Hn12
-  elim (tdeq_dec h o T1 T0) [ -HT10 -HT02 #H10 | -IH #Hn10 ]
+  elim (tdeq_dec T1 T0) [ -HT10 -HT02 #H10 | -IH #Hn10 ]
   [ elim IH -IH /3 width=3 by tdeq_trans/ -Hn12
     #T3 #T4 #HT03 #Hn03 #HT34 #H42
     elim (tdeq_cpx_trans … H10 … HT03) -HT03 #T5 #HT15 #H53