syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / sex_length.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/sex_length.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/sex_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/syntax/lenv_length.ma".
+include "static_2/relocation/sex.ma".
+
+(* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
+
+(* Forward lemmas with length for local environments ************************)
+
+(* Note: "#f #I1 #I2 #L1 #L2 >length_bind >length_bind //" was needed to conclude *)
+lemma sex_fwd_length: ∀RN,RP,f,L1,L2. L1 ⪤[RN, RP, f] L2 → |L1| = |L2|.
+#RN #RP #f #L1 #L2 #H elim H -f -L1 -L2 //
+qed-.
+
+(* Properties with length for local environments ****************************)
+
+lemma sex_length_cfull: ∀L1,L2. |L1| = |L2| → ∀f. L1 ⪤[cfull, cfull, f] L2.
+#L1 elim L1 -L1
+[ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
+| #L1 #I1 #IH #Y2 #H #f
+  elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
+  elim (pn_split f) * #g #H destruct /3 width=1 by sex_next, sex_push/
+]
+qed.
+
+lemma sex_length_isid: ∀R,L1,L2. |L1| = |L2| →
+                       ∀f. 𝐈⦃f⦄ → L1 ⪤[R, cfull, f] L2.
+#R #L1 elim L1 -L1
+[ #Y2 #H >(length_inv_zero_sn … H) -Y2 //
+| #L1 #I1 #IH #Y2 #H #f #Hf
+  elim (length_inv_succ_sn … H) -H #I2 #L2 #HL12 #H destruct
+  elim (isid_inv_gen … Hf) -Hf #g #Hg #H destruct /3 width=1 by sex_push/
+]
+qed.