milestone update in basic_2, update in ground and static_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
index b0921440d36c723ed8c4d76c15db87d9e2ad519e..86dc07b45fa41b3723979cb35031ac83b490f35b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
@@ -12,38 +12,38 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lpx_rdeq.ma".
+include "basic_2/rt_transition/lpx_reqx.ma".
 include "basic_2/rt_computation/csx_drops.ma".
 
-(* STRONGLY NORMALIZING TERMS FOR UNBOUND PARALLEL RT-TRANSITION ************)
+(* STRONGLY NORMALIZING TERMS FOR EXTENDED PARALLEL RT-TRANSITION ***********)
 
 (* Advanced properties ******************************************************)
 
-lemma csx_tdeq_trans (h) (G):
-      ∀L,T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-      â\88\80T2. T1 â\89\9b T2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T2â¦\84.
-#h #G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
-@csx_intro #T1 #HT21 #HnT21 elim (tdeq_cpx_trans … HT2 … HT21) -HT21
-/4 width=5 by tdeq_repl/
+lemma csx_teqx_trans (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      â\88\80T2. T1 â\89\9b T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T2.
+#G #L #T1 #H @(csx_ind … H) -T1 #T #_ #IH #T2 #HT2
+@csx_intro #T1 #HT21 #HnT21 elim (teqx_cpx_trans … HT2 … HT21) -HT21
+/4 width=5 by teqx_repl/
 qed-.
 
-lemma csx_cpx_trans (h) (G):
-      ∀L,T1. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
-      â\88\80T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88[h] T2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83T2â¦\84.
-#h #G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
-elim (tdeq_dec T1 T2) /3 width=4 by csx_tdeq_trans/
+lemma csx_cpx_trans (G) (L):
+      ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
+      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T2.
+#G #L #T1 #H @(csx_ind … H) -T1 #T1 #HT1 #IHT1 #T2 #HLT12
+elim (teqx_dec T1 T2) /3 width=4 by csx_teqx_trans/
 qed-.
 
 (* Basic_1: was just: sn3_cast *)
-lemma csx_cast (h) (G):
-      ∀L,W. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃W⦄ →
-      â\88\80T. â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Tâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83â\93\9dW.Tâ¦\84.
-#h #G #L #W #HW @(csx_ind … HW) -W
+lemma csx_cast (G) (L):
+      ∀W. ❪G,L❫ ⊢ ⬈*𝐒 W →
+      â\88\80T. â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 T â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 â\93\9dW.T.
+#G #L #W #HW @(csx_ind … HW) -W
 #W #HW #IHW #T #HT @(csx_ind … HT) -T
 #T #HT #IHT @csx_intro
 #X #H1 #H2 elim (cpx_inv_cast1 … H1) -H1
 [ * #W0 #T0 #HLW0 #HLT0 #H destruct
-  elim (tdneq_inv_pair … H2) -H2
+  elim (tneqx_inv_pair … H2) -H2
   [ -W -T #H elim H -H //
   | -HW -IHT /3 width=3 by csx_cpx_trans/
   | -HW -HT -IHW /4 width=3 by csx_cpx_trans, cpx_pair_sn/
@@ -54,10 +54,10 @@ qed.
 
 (* Basic_1: was just: sn3_abbr *)
 (* Basic_2A1: was: csx_lref_bind *)
-lemma csx_lref_pair_drops (h) (G): 
-      ∀I,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V →
-      â¦\83G,Kâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Vâ¦\84 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83#iâ¦\84.
-#h #G #I #L #K #V #i #HLK #HV
+lemma csx_lref_pair_drops (G) (L):
+      ∀I,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V →
+      â\9dªG,Kâ\9d« â\8a¢ â¬\88*ð\9d\90\92 V â\86\92 â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 #i.
+#G #L #I #K #V #i #HLK #HV
 @csx_intro #X #H #Hi elim (cpx_inv_lref1_drops … H) -H
 [ #H destruct elim Hi //
 | -Hi * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HV1
@@ -70,19 +70,19 @@ qed.
 
 (* Basic_1: was: sn3_gen_def *)
 (* Basic_2A1: was: csx_inv_lref_bind *)
-lemma csx_inv_lref_pair_drops (h) (G):
-      ∀I,L,K,V,i. ⬇*[i] L ≘ K.ⓑ{I}V →
-      â¦\83G,Lâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83#iâ¦\84 â\86\92 â¦\83G,Kâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Vâ¦\84.
-#h #G #I #L #K #V #i #HLK #Hi
-elim (lifts_total V (ð\9d\90\94â\9d´â\86\91iâ\9dµ))
+lemma csx_inv_lref_pair_drops (G) (L):
+      ∀I,K,V,i. ⇩[i] L ≘ K.ⓑ[I]V →
+      â\9dªG,Lâ\9d« â\8a¢ â¬\88*ð\9d\90\92 #i â\86\92 â\9dªG,Kâ\9d« â\8a¢ â¬\88*ð\9d\90\92 V.
+#G #L #I #K #V #i #HLK #Hi
+elim (lifts_total V (ð\9d\90\94â\9d¨â\86\91iâ\9d©))
 /4 width=9 by csx_inv_lifts, csx_cpx_trans, cpx_delta_drops, drops_isuni_fwd_drop2/
 qed-.
 
-lemma csx_inv_lref_drops (h) (G):
-      ∀L,i. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃#i⦄ →
-      â\88¨â\88¨ â¬\87*[â\92»,ð\9d\90\94â\9d´iâ\9dµ] L ≘ ⋆
-       | â\88\83â\88\83I,K. â¬\87*[i] L â\89\98 K.â\93¤{I}
-       | â\88\83â\88\83I,K,V. â¬\87*[i] L â\89\98 K.â\93\91{I}V & â¦\83G,Kâ¦\84 â\8a¢ â¬\88*[h] ð\9d\90\92â¦\83Vâ¦\84.
-#h #G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
+lemma csx_inv_lref_drops (G) (L):
+      ∀i. ❪G,L❫ ⊢ ⬈*𝐒 #i →
+      â\88¨â\88¨ â\87©*[â\92»,ð\9d\90\94â\9d¨iâ\9d©] L ≘ ⋆
+       | â\88\83â\88\83I,K. â\87©[i] L â\89\98 K.â\93¤[I]
+       | â\88\83â\88\83I,K,V. â\87©[i] L â\89\98 K.â\93\91[I]V & â\9dªG,Kâ\9d« â\8a¢ â¬\88*ð\9d\90\92 V.
+#G #L #i #H elim (drops_F_uni L i) /2 width=1 by or3_intro0/
 * * /4 width=9 by csx_inv_lref_pair_drops, ex2_3_intro, ex1_2_intro, or3_intro2, or3_intro1/
 qed-.