syntactic components detached from basic_2 become static_2

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

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma
new file mode 100644 (file)
index 0000000..7a39036
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubf_frees.ma
@@ -0,0 +1,51 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/static/lsubf.ma".
+
+(* RESTRICTED REFINEMENT FOR CONTEXT-SENSITIVE FREE VARIABLES ***************)
+
+(* Properties with context-sensitive free variables *************************)
+
+lemma lsubf_frees_trans: ∀f2,L2,T. L2 ⊢ 𝐅*⦃T⦄ ≘ f2 →
+                         ∀f1,L1. ⦃L1, f1⦄ ⫃𝐅* ⦃L2, f2⦄ → L1 ⊢ 𝐅*⦃T⦄ ≘ f1.
+#f2 #L2 #T #H elim H -f2 -L2 -T
+[ /3 width=5 by lsubf_fwd_isid_dx, frees_sort/
+| #f2 #i #Hf2 #g1 #Y1 #H
+  elim (lsubf_inv_atom2 … H) -H #Hg1 #H destruct
+  elim (eq_inv_pushs_dx … Hg1) -Hg1 #g #Hg #H destruct
+  elim (eq_inv_xn … Hg) -Hg
+  /3 width=3 by frees_atom, isid_eq_repl_fwd/
+| #f2 #I #K2 #W #_ #IH #g1 #Y1 #H elim (lsubf_inv_pair2 … H) -H *
+  [ #f1 #K1 #H12 #H1 #H2 destruct /3 width=1 by frees_pair/
+  | #f #f0 #f1 #K1 #V #H12 #Hf #Hf1 #H1 #H2 #H3 destruct
+    /4 width=5 by frees_pair, frees_flat/
+  ]
+| #f2 #I #L2 #Hf2 #g1 #Y1 #H elim (lsubf_inv_unit2 … H) -H *
+  [ #f1 #L1 #H12 #H1 #H2 destruct
+    /3 width=5 by lsubf_fwd_isid_dx, frees_unit/
+  | #f #f0 #f1 #J #L1 #V #H12 #Hf #Hf1 #H1 #H2 destruct
+    /5 width=9 by lsubf_fwd_isid_dx, frees_eq_repl_back, frees_pair, sor_isid_inv_sn/
+  ]
+| #f2 #I #L2 #i #_ #IH #g1 #L1 #H elim (lsubf_inv_push2 … H) -H
+  /3 width=1 by frees_lref/
+| /3 width=5 by lsubf_fwd_isid_dx, frees_gref/
+| #f2V #f2T #f2 #p #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+  elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 #f1V #g1T #HV #HT #Hf1
+  elim (lsubf_bind_tl_dx … (BPair I V) … HT) -HT #f1T #HT #H destruct
+  /3 width=5 by frees_bind/
+| #f2V #f2T #f2 #I #L2 #V #T #_ #_ #Hf2 #IHV #IHT #f1 #L1 #H12
+  elim (lsubf_inv_sor_dx … H12 … Hf2) -f2 /3 width=5 by frees_flat/
+]
+qed-.