refactoring ...

[helm.git] / matita / matita / contribs / lambda / paths / trace.ma

diff --git a/matita/matita/contribs/lambda/paths/trace.ma b/matita/matita/contribs/lambda/paths/trace.ma
new file mode 100644 (file)
index 0000000..53b9798
--- /dev/null
+++ b/matita/matita/contribs/lambda/paths/trace.ma
@@ -0,0 +1,54 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "paths/path.ma".
+
+(* TRACE ********************************************************************)
+
+(* Policy: trace metavariables: r, s *)
+definition trace: Type[0] ≝ list path.
+
+(* Note: a "whd" computation contracts just redexes in the whd *)
+definition is_whd: predicate trace ≝ All … in_whd.
+
+lemma is_whd_dx: ∀s. is_whd s → is_whd (dx:::s).
+#s elim s -s //
+#p #s #IHs * /3 width=1/ 
+qed.
+
+lemma is_whd_append: ∀r. is_whd r → ∀s. is_whd s → is_whd (r@s).
+#r elim r -r //
+#q #r #IHr * /3 width=1/
+qed.
+
+definition ho_compatible_rc: predicate (trace→relation term) ≝ λR.
+                             ∀s,A1,A2. R s A1 A2 → R (rc:::s) (𝛌.A1) (𝛌.A2).
+
+definition ho_compatible_sn: predicate (trace→relation term) ≝ λR.
+                             ∀s,B1,B2,A. R s B1 B2 → R (sn:::s) (@B1.A) (@B2.A).
+
+definition ho_compatible_dx: predicate (trace→relation term) ≝ λR.
+                             ∀s,B,A1,A2. R s A1 A2 → R (dx:::s) (@B.A1) (@B.A2).
+
+lemma lstar_compatible_rc: ∀R. compatible_rc R → ho_compatible_rc (lstar … R).
+#R #HR #s #A1 #A2 #H @(lstar_ind_l ????????? H) -s -A1 // /3 width=3/
+qed.
+
+lemma lstar_compatible_sn: ∀R. compatible_sn R → ho_compatible_sn (lstar … R).
+#R #HR #s #B1 #B2 #A #H @(lstar_ind_l ????????? H) -s -B1 // /3 width=3/
+qed.
+
+lemma lstar_compatible_dx: ∀R. compatible_dx R → ho_compatible_dx (lstar … R).
+#R #HR #s #B #A1 #A2 #H @(lstar_ind_l ????????? H) -s -A1 // /3 width=3/
+qed.