update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / prelift_label.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/prelift_label.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 "delayed_updating/notation/functions/uparrow_2.ma".
+include "delayed_updating/syntax/label.ma".
+include "ground/relocation/tr_pap.ma".
+
+(* PRELIFT FOR LABEL ********************************************************)
+
+definition prelift_label (f) (l): label ≝
+match l with
+[ label_d n ⇒ 𝗱(f＠⧣❨n❩)
+| label_m   ⇒ 𝗺
+| label_L   ⇒ 𝗟
+| label_A   ⇒ 𝗔
+| label_S   ⇒ 𝗦
+].
+
+interpretation
+  "prelift (label)"
+  'UpArrow f l = (prelift_label f l).
+
+(* Basic constructions ******************************************************)
+
+lemma prelift_label_d (f) (n):
+      (𝗱(f＠⧣❨n❩)) = ↑[f]𝗱n.
+// qed.
+
+lemma prelift_label_m (f):
+      (𝗺) = ↑[f]𝗺.
+// qed.
+
+lemma prelift_label_L (f):
+      (𝗟) = ↑[f]𝗟.
+// qed.
+
+lemma prelift_label_A (f):
+      (𝗔) = ↑[f]𝗔.
+// qed.
+
+lemma prelift_label_S (f):
+      (𝗦) = ↑[f]𝗦.
+// qed.