milestone update in basic_2, update in ground and static_2

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

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 10831ed7308c2195f552cbdfced23031d96a26f1..99d72a494a20df45b7054264d0448be4eeb6ef3b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_cpxs.ma
@@ -14,45 +14,48 @@
 
 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) ?)
 /3 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro/
 qed-.
 
-lemma cpxs_inv_abbr1 (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
-                               | ∃∃T2. ⦃G, L.ⓓV1⦄ ⊢ T1 ⬈*[h] T2 & ⬆*[1] U2 ≘ T2 & p = Ⓣ.
-#h #G #p #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by ex3_2_intro, or_introl/
+(* Basic_2A1: was: cpxs_inv_abbr1 *)
+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
   elim (cpx_inv_abbr1 … HU02) -HU02 *
   [ #V2 #T2 #HV02 #HT02 #H destruct
     lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?)
     /4 width=5 by lpxs_pair, cpxs_trans, cpxs_strap1, ex3_2_intro, or_introl/
-  | #T2 #HT02 #HUT2
-    lapply (lpxs_cpx_trans … HT02 (L.ⓓV1) ?) -HT02
-    /4 width=3 by lpxs_pair, cpxs_trans, ex3_intro, or_intror/
+  | #T2 #HT20 #HTU2 #Hp -V0
+    elim (cpx_lifts_sn … HTU2 (Ⓣ) … (L.ⓓV1) … HT20) -T2 [| /3 width=3 by drops_refl, drops_drop/ ] #U0 #HU20 #HTU0
+    /4 width=3 by cpxs_strap1, ex3_intro, or_intror/
   ]
 | #U1 #HTU1 #HU01 #Hp
-  elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01) -U0 /3 width=3 by drops_refl, drops_drop/ #U #HU2 #HU1
+  elim (cpx_lifts_sn … HU02 (Ⓣ) … (L.ⓓV1) … HU01) -U0 [| /3 width=3 by drops_refl, drops_drop/ ] #U #HU2 #HU1
   /4 width=3 by cpxs_strap1, ex3_intro, or_intror/
 ]
 qed-.