- commit of the "s_computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / s_computation / fqup_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/s_computation/fqup_drops.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/relocation/drops.ma".
+include "basic_2/s_computation/fqup.ma".
+
+(* PLUS-ITERATED SUPCLOSURE *************************************************)
+
+(* Properties with generic slicing for local environments *******************)
+
+lemma fqup_drops_succ: ∀G,K,T,l,L,U. ⬇*[⫯l] L ≡ K → ⬆*[⫯l] T ≡ U →
+                       ⦃G, L, U⦄ ⊐+ ⦃G, K, T⦄.
+#G #K #T #l elim l -l
+[ #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
+  #I #Y #V #HY #H destruct <(drops_fwd_isid … HY) -K
+  /3 width=1 by fqu_fqup, fqu_drop/
+| #l #IH #L #U #HLK #HTU elim (drops_inv_succ … HLK) -HLK
+  #I #Y #V #HY #H destruct
+  elim (lifts_split_trans … HTU … (𝐔❴⫯l❵) (𝐔❴1❵)) -HTU
+  /4 width=5 by fqup_strap2, fqu_drop/
+]
+qed.
+
+lemma fqup_drops_strap1: ∀G1,G2,L1,K1,K2,T1,T2,U1,l. ⬇*[l] L1 ≡ K1 → ⬆*[l] T1 ≡ U1 →
+                         ⦃G1, K1, T1⦄ ⊐ ⦃G2, K2, T2⦄ → ⦃G1, L1, U1⦄ ⊐+ ⦃G2, K2, T2⦄.
+#G1 #G2 #L1 #K1 #K2 #T1 #T2 #U1 *
+[ #HLK1 #HTU1 #HT12
+  >(drops_fwd_isid … HLK1) -L1 //
+  <(lifts_fwd_isid … HTU1) -U1 /2 width=1 by fqu_fqup/
+| /3 width=5 by fqup_strap1, fqup_drops_succ/
+]
+qed-.
+
+lemma fqup_lref: ∀I,G,L,K,V,i. ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, L, #i⦄ ⊐+ ⦃G, K, V⦄.
+/2 width=6 by fqup_drops_strap1/ qed.