- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / append / cl_shift.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cl_shift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cl_shift.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/append/cl_shift.etc
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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/grammar/lenv_append.ma".
+
+(* SHIFT OF A CLOSURE *******************************************************)
+
+let rec shift L T on L ≝ match L with
+[ LAtom       ⇒ T
+| LPair L I V ⇒ shift L (-ⓑ{I} V. T)
+].
+
+interpretation "shift (closure)" 'Append L T = (shift L T).
+
+(* Basic properties *********************************************************)
+
+lemma shift_append_assoc: ∀L,K. ∀T:term. (L @@ K) @@ T = L @@ K @@ T.
+#L #K elim K -K // normalize //
+qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma shift_inj: ∀L1,L2. ∀T1,T2:term. L1 @@ T1 = L2 @@ T2 → |L1| = |L2| →
+                 L1 = L2 ∧ T1 = T2.
+#L1 elim L1 -L1
+[ * normalize /2 width=1/
+  #L2 #I2 #V2 #T1 #T2 #_ <plus_n_Sm #H destruct
+| #L1 #H1 #V1 #IH * normalize
+  [ #T1 #T2 #_ <plus_n_Sm #H destruct
+  | #L2 #I2 #V2 #T1 #T2 #H1 #H2
+    elim (IH … H1) -IH -H1 /2 width=1/ -H2 #H1 #H2 destruct /2 width=1/
+  ]
+]
+qed-.