milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fpbc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fpbc.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/rt_transition/fpbc_feqg.ma".
+include "basic_2/rt_transition/fpbc_fpb.ma".
+include "basic_2/rt_computation/fpbs_feqg.ma".
+
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
+
+(* Properties with proper parallel rst-reduction on closures ****************)
+
+lemma fpbc_fpbs:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+/3 width=1 by fpb_fpbs, fpbc_fwd_fpb/ qed.
+
+(* Inversion lemmas with proper parallel rst-reduction on closures **********)
+
+lemma fpbs_inv_fpbc_sn:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ →
+      ∨∨ ❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫
+       | ∃∃G,L,T. ❪G1,L1,T1❫ ≻ ❪G,L,T❫ & ❪G,L,T❫ ≥ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
+[ /3 width=1 by feqg_refl, or_introl/
+| #G #G2 #L #L2 #T #T2 #_ #H2 * [ #H1 | * #G0 #L0 #T0 #H10 #H0 ]
+  elim (fpb_inv_fpbc … H2) -H2 #H2
+  [ /3 width=5 by feqg_trans, or_introl/
+  | lapply (feqg_fpbc_trans … H1 … H2) -G -L -T //
+    /3 width=5 by fpb_fpbs, ex2_3_intro, or_intror/
+  | /4 width=12 by fpbs_feqg_trans, ex2_3_intro, or_intror/
+  | /5 width=9 by fpbs_strap1, fpbc_fwd_fpb, ex2_3_intro, or_intror/
+  ]
+]
+qed-.