- partial commit of rt_transition ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpg_lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/static/lsubr.ma".
+include "basic_2/rt_transition/cpg.ma".
+
+(* CONTEXT-SENSITIVE GENERIC PARALLEL RT-TRANSITION FOR TERMS ***************)
+
+(* Properties with restricted refinement for local environments *************)
+
+lemma lsubr_cpg_trans: ∀h,r,G. lsub_trans … (cpg h r G) lsubr.
+#h #r #G #L1 #T1 #T2 #H elim H -r -G -L1 -T1 -T2
+[ //
+| /2 width=2 by cpg_st/
+| #r #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
+  elim (lsubr_inv_abbr2 … H) -H #L2 #HL21 #H destruct
+  /3 width=3 by cpg_delta/
+| #r #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
+  elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
+  /4 width=3 by cpg_delta, cpg_lt, cpg_ct/
+| #r #I1 #G #L1 #V1 #T1 #U1 #i #_ #HTU1 #IH #X #H
+  elim (lsubr_fwd_pair2 … H) -H #I2 #L2 #V2 #HL21 #H destruct
+  /3 width=3 by cpt_lref/
+|6,11: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/
+|7,9,10: /3 width=1 by cpg_flat, cpg_eps, cpg_ct/
+|8,12: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/
+]
+qed-.