- basic_2 : restricted refinement for free variables (lsubf): first results

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubf_frees.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubf_frees.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/lsubf.ma".
+
+(* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
+
+(* Properties with context-sensitive free variables *************************)
+
+lemma lsubf_free_trans: ∀f2,L2,T. L2 ⊢ 𝐅*⦃T⦄ ≡ f2 → ∀f,L1. ⦃L1, f⦄ ⫃𝐅* ⦃L2, f2⦄ →
+                        ∃∃f1. L1 ⊢ 𝐅*⦃T⦄ ≡ f1 & f1 ⊆ f.
+#f2 #L2 #T #H elim H -f2 -L2 -T
+[ #f2 #I #Hf2 #f #L1 #H elim (lsubf_inv_atom2 … H) -H
+  #H1 #H2 destruct /3 width=3 by frees_atom, sle_refl, ex2_intro/
+| #f2 #I #K2 #W #s #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
+  [ #g1 #K1 #H12 #H1 #H2
+  | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
+  ] destruct elim (IH … H12) -f2 -K2
+  /3 width=7 by frees_sort, sle_push, ex2_intro/
+| #f2 #I #K2 #W #_ #IH #f #L1 #H elim (lsubf_inv_next2 … H) -H *
+  [ #g1 #K1 #H12 #H1 #H2 destruct elim (IH … H12) -f2 -K2
+    /3 width=7 by frees_zero, sle_next, ex2_intro/
+  | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3 destruct
+    elim (IH … H12) -K2 #f1 #Hf1 #Hfg1
+    elim (sor_isfin_ex … f1 g ??)
+    /5 width=10 by frees_fwd_isfin, frees_flat, frees_zero, monotonic_sle_sor, sor_inv_sle_dx, sor_sle_sn, sle_next, ex2_intro/
+  ]
+| #f2 #I #K2 #W #i #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
+  [ #g1 #K1 #H12 #H1 #H2
+  | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
+  ] destruct elim (IH … H12) -f2 -K2
+  /3 width=7 by frees_lref, sle_push, ex2_intro/
+| #f2 #I #K2 #W #l #_ #IH #f #L1 #H elim (lsubf_inv_push2 … H) -H *
+  [ #g1 #K1 #H12 #H1 #H2
+  | #g #g1 #K1 #V #Hg #Hg1 #H12 #H1 #H2 #H3
+  ] destruct elim (IH … H12) -f2 -K2
+  /3 width=7 by frees_gref, sle_push, ex2_intro/
+| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
+| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f #L1 #H12
+ 
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