- second precommit for rtmap

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / etc / relocation / trace_isun.etc

diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/trace_isun.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/relocation/trace_isun.etc
new file mode 100644 (file)
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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 "ground_2/notation/relations/isuniform_1.ma".
+include "ground_2/relocation/trace_isid.ma".
+
+(* RELOCATION TRACE *********************************************************)
+
+inductive isun: predicate trace ≝
+| isun_id   : ∀t. 𝐈⦃t⦄ → isun t
+| isun_false: ∀t. isun t → isun (Ⓕ@t)
+.
+
+interpretation "test for uniformity (trace)"
+   'IsUniform t = (isun t).
+
+(* Basic inversion lennas ***************************************************)
+
+fact isun_inv_true_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓣ@u → 𝐈⦃u⦄.
+#t * -t
+[ #t #Ht #u #H destruct /2 width=1 by isid_inv_true/
+| #t #_ #u #H destruct
+]
+qed-.
+
+lemma isun_inv_true: ∀t. 𝐔⦃Ⓣ@t⦄ → 𝐈⦃t⦄.
+/2 width=3 by isun_inv_true_aux/ qed-.
+
+fact isun_inv_false_aux: ∀t. 𝐔⦃t⦄ → ∀u. t = Ⓕ@u → 𝐔⦃u⦄.
+#t * -t 
+[ #t #Ht #u #H destruct elim (isid_inv_false … Ht)
+| #t #Ht #u #H destruct //
+]
+qed-.
+
+lemma isun_inv_false: ∀t. 𝐔⦃Ⓕ@t⦄ → 𝐔⦃t⦄.
+/2 width=3 by isun_inv_false_aux/ qed-.