X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flpxs_cpxs.ma;h=fe6047de015bef2baaf357d5c33e544bbbb1ddda;hb=7c9d99dfb049d726491b71f07ba6a9b088b30166;hp=611aab47bd68cbf362050ae69f517f6364f8d9d9;hpb=db020b4218272e2e35641ce3bc3b0a9b3afda899;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma
index 611aab47b..fe6047de0 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma
@@ -14,22 +14,23 @@
 
 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 context-sensitive extended rt-computation for terms ******)
 
 (* Basic_2A1: was: cpxs_bind2 *)
-lemma cpxs_bind_dx (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.
+lemma cpxs_bind_alt (G):
+      ∀L,V1,V2. ❨G,L❩ ⊢ V1 ⬈* V2 →
+      ∀I,T1,T2. ❨G,L.ⓑ[I]V2❩ ⊢ T1 ⬈* T2 →
+      ∀p. ❨G,L❩ ⊢ ⓑ[p,I]V1.T1 ⬈* ⓑ[p,I]V2.T2.
 /4 width=5 by lpxs_cpxs_trans, lpxs_pair, cpxs_bind/ qed.
 
 (* Inversion lemmas with context-sensitive ext rt-computation for terms *****)
 
-lemma cpxs_inv_abst1 (h) (G): ∀p,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.
-#h #G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/
+lemma cpxs_inv_abst1 (G):
+      ∀p,L,V1,T1,U2. ❨G,L❩ ⊢ ⓛ[p]V1.T1 ⬈* U2 →
+      ∃∃V2,T2. ❨G,L❩ ⊢ V1 ⬈* V2 & ❨G,L.ⓛV1❩ ⊢ T1 ⬈* T2 & U2 = ⓛ[p]V2.T2.
+#G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /2 width=5 by ex3_2_intro/
 #U0 #U2 #_ #HU02 * #V0 #T0 #HV10 #HT10 #H destruct
 elim (cpx_inv_abst1 … HU02) -HU02 #V2 #T2 #HV02 #HT02 #H destruct
 lapply (lpxs_cpx_trans … HT02 (L.ⓛV1) ?)
@@ -37,12 +38,11 @@ lapply (lpxs_cpx_trans … HT02 (L.ⓛV1) ?)
 qed-.
 
 (* Basic_2A1: was: cpxs_inv_abbr1 *)
-lemma cpxs_inv_abbr1_dx (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 = Ⓣ.
-#h #p #G #L #V1 #T1 #U2 #H
+lemma cpxs_inv_abbr1_dx (p) (G) (L):
+      ∀V1,T1,U2. ❨G,L❩ ⊢ ⓓ[p]V1.T1 ⬈* U2 →
+      ∨∨ ∃∃V2,T2. ❨G,L❩ ⊢ V1 ⬈* V2 & ❨G,L.ⓓV1❩ ⊢ T1 ⬈* T2 & U2 = ⓓ[p]V2.T2
+       | ∃∃T2. ❨G,L.ⓓV1❩ ⊢ T1 ⬈* T2 & ⇧[1] U2 ≘ T2 & p = Ⓣ.
+#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