ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / etc / relocation / trace_snot.etc

diff --git a/matita/matita/contribs/lambdadelta/ground/etc/relocation/trace_snot.etc b/matita/matita/contribs/lambdadelta/ground/etc/relocation/trace_snot.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/ground/etc/relocation/trace_snot.etc
@@ -0,0 +1,50 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_2/notation/functions/complement_1.ma".
+include "ground_2/relocation/trace.ma".
+
+(* RELOCATION TRACE *********************************************************)
+
+let rec snot (t:trace) on t ≝ match t with
+[ nil      ⇒ ◊
+| cons b t ⇒ (¬ b) @ snot t
+].
+
+interpretation
+   "complement (trace)"
+   'Complement t = (snot t).
+
+(* Basic properties *********************************************************)
+
+lemma snot_empty: ∁ (◊) = ◊.
+// qed.
+
+lemma snot_inh: ∀t,b. ∁ (b@t) = (¬ b) @ ∁ t.
+// qed.
+
+lemma snot_true: ∀t. ∁ (Ⓣ @ t) = Ⓕ @ ∁ t.
+// qed.
+
+lemma snot_false: ∀t. ∁ (Ⓕ @ t) = Ⓣ @ ∁ t.
+// qed.
+
+lemma snot_length: ∀t. |∁ t| = |t|.
+#t elim t -t normalize //
+qed.
+
+lemma snot_colength: ∀t. ∥∁ t∥ = |t| - ∥t∥.
+#t elim t -t //
+* /2 width=1 by minus_Sn_m/
+qed.