- more background for the exclusion binder

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lifts_lifts_bind.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma
new file mode 100644 (file)
index 0000000..10ad3cc
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_lifts_bind.ma
@@ -0,0 +1,34 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/lifts_lifts.ma".
+include "basic_2/relocation/lifts_bind.ma".
+
+(* GENERIC RELOCATION FOR BINDERS *******************************************)
+
+(* Main properties **********************************************************)
+
+theorem liftsb_div3: ∀f2,I,I2. ⬆*[f2] I2 ≡ I → ∀f,I1. ⬆*[f] I1 ≡ I →
+                     ∀f1. f2 ⊚ f1 ≡ f → ⬆*[f1] I1 ≡ I2.
+#f2 #I #I2 * -I -I2 #I [2: #V #V2 #HV2 ] #f #I1 #H
+[ elim (liftsb_inv_pair_dx … H) | lapply (liftsb_inv_unit_dx … H) ] -H
+/3 width=6 by lifts_div3, ext2_pair, ext2_unit/
+qed-.
+
+theorem liftsb_trans: ∀f1,I1,I. ⬆*[f1] I1 ≡ I → ∀f2,I2. ⬆*[f2] I ≡ I2 →
+                      ∀f. f2 ⊚ f1 ≡ f → ⬆*[f] I1 ≡ I2.
+#f1 #I1 #I * -I1 -I #I1 [2: #V1 #V #HV1 ] #f2 #I2 #H
+[ elim (liftsb_inv_pair_sn … H) | lapply (liftsb_inv_unit_sn … H) ] -H
+/3 width=6 by lifts_trans, ext2_pair, ext2_unit/
+qed-.