update in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / reqg_length.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/reqg_length.ma b/matita/matita/contribs/lambdadelta/static_2/static/reqg_length.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 "static_2/relocation/lifts_teqg.ma".
+include "static_2/static/rex_length.ma".
+include "static_2/static/rex_fsle.ma".
+include "static_2/static/reqg.ma".
+
+(* GENERIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***********)
+
+(* Advanved properties with free variables inclusion ************************)
+
+lemma reqg_fsge_comp (S):
+      reflexive … S →
+      rex_fsge_compatible (ceqg S).
+#S #HS #L1 #L2 #T * #f1 #Hf1 #HL12
+lapply (frees_seqg_conf … Hf1 … HL12)
+lapply (sex_fwd_length … HL12)
+/3 width=8 by lveq_length_eq, ex4_4_intro/ (**) (* full auto fails *)
+qed-.
+
+(* Properties with length for local environments ****************************)
+
+(* Basic_2A1: uses: lleq_sort *)
+lemma reqg_sort_length (S):
+      ∀L1,L2. |L1| = |L2| → ∀s. L1 ≛[S,⋆s] L2.
+/2 width=1 by rex_sort_length/ qed.
+
+(* Basic_2A1: uses: lleq_gref *)
+lemma reqg_gref_length (S):
+      ∀L1,L2. |L1| = |L2| → ∀l. L1 ≛[S,§l] L2.
+/2 width=1 by rex_gref_length/ qed.
+
+lemma reqg_unit_length (S):
+      ∀L1,L2. |L1| = |L2| →
+      ∀I. L1.ⓤ[I] ≛[S,#0] L2.ⓤ[I].
+/2 width=1 by rex_unit_length/ qed.
+
+(* Basic_2A1: uses: lleq_lift_le lleq_lift_ge *)
+lemma reqg_lifts_bi (S):
+      ∀L1,L2. |L1| = |L2| → ∀K1,K2,T. K1 ≛[S,T] K2 →
+      ∀b,f. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
+      ∀U. ⇧*[f] T ≘ U → L1 ≛[S,U] L2.
+/3 width=9 by rex_lifts_bi, teqg_lifts_sn/ qed-.
+
+(* Forward lemmas with length for local environments ************************)
+
+(* Basic_2A1: lleq_fwd_length *)
+lemma reqg_fwd_length (S):
+      ∀L1,L2. ∀T:term. L1 ≛[S,T] L2 → |L1| = |L2|.
+/2 width=3 by rex_fwd_length/ qed-.