X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flfpxs_cpxs.ma;h=a5288e11a4d1bf10045e8f20ad25482e4bdfea07;hb=05b047be6817f430c8c72fd9b0902df8bb9f579e;hp=e565bdc6760bce3a70789419767d65c57ed5f02f;hpb=56dd0e9f60e0dabfb587b014755fd4dad27960bb;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma
index e565bdc67..a5288e11a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfpxs_cpxs.ma
@@ -15,35 +15,33 @@
 include "basic_2/rt_computation/cpxs_lfpx.ma".
 include "basic_2/rt_computation/lfpxs_fqup.ma".
 
-(* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
+(* UNBOUND PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ******)
 
-(* Properties with uncounted context-sensitive rt-computation for terms *****)
+(* Properties with unbound context-sensitive rt-computation for terms *******)
 
-lemma lfpxs_pair: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
-                  ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ⬈*[h, T] L.ⓑ{I}V2.
-#h #G #L #V1 #V2 #H @(cpxs_ind … H) -V2
-/3 width=3 by lfpxs_strap1, lfpx_pair/
-qed.
+(* Basic_2A1: uses: lpxs_pair lpxs_pair_refl *)
+lemma lfpxs_pair_refl: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
+                       ∀I,T. ⦃G, L.ⓑ{I}V1⦄ ⊢ ⬈*[h, T] L.ⓑ{I}V2.
+/2 width=1 by tc_lfxs_pair_refl/ qed.
 
-(* Basic_2A1: was just: lpxs_cpx_trans *)
 lemma lfpxs_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (lfpxs h G).
-/3 width=5 by s_r_trans_LTC2, lfpx_cpxs_trans/ qed-.
+#h #G @s_r_trans_CTC2 @lfpx_cpxs_trans (**) (* auto fails *)
+qed-.
 
-(* Note: lfpxs_cpx_conf does not hold, thus we cannot invoke s_r_trans_LTC1 *)
-(* Basic_2A1: was just: lpxs_cpxs_trans *)
+(* Note: lfpxs_cpx_conf does not hold, thus we cannot invoke s_r_trans_CTC1 *)
 lemma lfpxs_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (lfpxs h G).
-#h #G @s_r_to_s_rs_trans @s_r_trans_LTC2
+#h #G @s_r_to_s_rs_trans @s_r_trans_CTC2
 @s_rs_trans_TC1 /2 width=3 by lfpx_cpxs_trans/ (**) (* full auto too slow *)
 qed-.
 
-(* Advanced properties on uncounted rt-computation for terms ****************)
+(* Advanced properties on unbound rt-computation for terms ******************)
 
 lemma cpxs_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 →
                   ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
                   ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
-/4 width=3 by lfpxs_cpxs_trans, lfpxs_pair, cpxs_bind/ qed.
+/4 width=3 by lfpxs_cpxs_trans, lfpxs_pair_refl, cpxs_bind/ qed.
 
-(* Advanced inversion lemmas on uncounted rt-computation for terms **********)
+(* Advanced inversion lemmas on unbound rt-computation for terms ************)
 
 lemma cpxs_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2 →
                       ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓛV1⦄ ⊢ T1 ⬈*[h] T2 &
@@ -52,27 +50,27 @@ lemma cpxs_inv_abst1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓛ{p}V1.T1 ⬈*[h] U2
 #U0 #U2 #_ #HU02 * #V0 #T0 #HV10 #HT10 #H destruct
 elim (cpx_inv_abst1 … HU02) -HU02 #V2 #T2 #HV02 #HT02 #H destruct
 lapply (lfpxs_cpx_trans … HT02 (L.ⓛV1) ?)
-/3 width=5 by lfpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro/
+/3 width=5 by lfpxs_pair_refl, cpxs_trans, cpxs_strap1, ex3_2_intro/
 qed-.
 
 lemma cpxs_inv_abbr1: ∀h,p,G,L,V1,T1,U2. ⦃G, L⦄ ⊢ ⓓ{p}V1.T1 ⬈*[h] U2 → (
                       ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 &
                                U2 = ⓓ{p}V2.T2
                       ) ∨
-                      ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≡ T2 & p = true.
+                      ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = true.
 #h #p #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
 #U0 #U2 #_ #HU02 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct
   elim (cpx_inv_abbr1 … HU02) -HU02 *
   [ #V2 #T2 #HV02 #HT02 #H destruct
     lapply (lfpxs_cpx_trans … HT02 (L.ⓓV1) ?)
-    /4 width=5 by lfpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
+    /4 width=5 by lfpxs_pair_refl, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
   | #T2 #HT02 #HUT2
     lapply (lfpxs_cpx_trans … HT02 (L.ⓓV1) ?) -HT02
-    /4 width=3 by lfpxs_pair, cpxs_trans, ex3_intro, or_intror/
+    /4 width=3 by lfpxs_pair_refl, cpxs_trans, ex3_intro, or_intror/
   ]
 | #U1 #HTU1 #HU01
-  elim (cpx_lifts … HU02 (Ⓣ) … (L.ⓓV1) … HU01)
+  elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01)
   /4 width=3 by cpxs_strap1, drops_refl, drops_drop, ex3_intro, or_intror/
 ]
 qed-.