update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / grammar / lreq_lreq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/grammar/lreq_lreq.ma b/matita/matita/contribs/lambdadelta/basic_2A/grammar/lreq_lreq.ma
new file mode 100644 (file)
index 0000000..700b87d
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/grammar/lreq_lreq.ma
@@ -0,0 +1,49 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "ground_2A/ynat/ynat_plus.ma".
+include "basic_2A/grammar/lreq.ma".
+
+(* EQUIVALENCE FOR LOCAL ENVIRONMENTS ***************************************)
+
+(* Main properties **********************************************************)
+
+theorem lreq_trans: ∀l,m. Transitive … (lreq l m).
+#l #m #L1 #L2 #H elim H -L1 -L2 -l -m
+[ #l #m #X #H lapply (lreq_inv_atom1 … H) -H
+  #H destruct //
+| #I1 #I #L1 #L #V1 #V #_ #IHL1 #X #H elim (lreq_inv_zero1 … H) -H
+  #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by lreq_zero/
+| #I #L1 #L #V #m #_ #IHL1 #X #H elim (lreq_inv_pair1 … H) -H //
+  #L2 #HL2 #H destruct /3 width=1 by lreq_pair/
+| #I1 #I #L1 #L #V1 #V #l #m #_ #IHL1 #X #H elim (lreq_inv_succ1 … H) -H //
+  #I2 #L2 #V2 #HL2 #H destruct /3 width=1 by lreq_succ/
+]
+qed-.
+
+theorem lreq_canc_sn: ∀l,m,L,L1,L2. L ⩬[l, m] L1 → L ⩬[l, m] L2 → L1 ⩬[l, m] L2.
+/3 width=3 by lreq_trans, lreq_sym/ qed-.
+
+theorem lreq_canc_dx: ∀l,m,L,L1,L2. L1 ⩬[l, m] L → L2 ⩬[l, m] L → L1 ⩬[l, m] L2.
+/3 width=3 by lreq_trans, lreq_sym/ qed-.
+
+theorem lreq_join: ∀L1,L2,l,i. L1 ⩬[l, i] L2 →
+                   ∀m. L1 ⩬[i+l, m] L2 → L1 ⩬[l, i+m] L2.
+#L1 #L2 #l #i #H elim H -L1 -L2 -l -i //
+[ #I #L1 #L2 #V #m #_ #IHL12 #m #H
+  lapply (lreq_inv_succ … H ?) -H // >ypred_succ /3 width=1 by lreq_pair/
+| #I1 #I2 #L1 #L2 #V1 #V2 #l #m #_ #IHL12 #m #H
+  lapply (lreq_inv_succ … H ?) -H // >yplus_succ2 >ypred_succ /3 width=1 by lreq_succ/
+]
+qed-.