update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / lift_i / lift_constructors.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_constructors.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_constructors.etc
new file mode 100644 (file)
index 0000000..4eeb2ab
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_constructors.etc
@@ -0,0 +1,47 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/lift_prototerm_eq.ma".
+include "delayed_updating/substitution/lift_path_uni.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+
+(* LIFT FOR PROTOTERM *******************************************************)
+
+lemma lift_iref_bi (t1) (t2) (n):
+      t1 ⇔ t2 → 𝛗n.t1 ⇔ 𝛗n.t2.
+/2 width=1 by subset_equivalence_ext_f1_bi/
+qed.
+
+lemma lift_iref_sn (f) (t:prototerm) (n:pnat):
+      (𝛗f＠⧣❨n❩.t) ⊆ ↑[f](𝛗n.t).
+#f #t #n #p * #q #Hq #H0 destruct
+@(ex2_intro … (𝗱n◗𝗺◗q))
+/2 width=1 by in_comp_iref/
+qed-.
+
+lemma lift_iref_dx (f) (t) (n:pnat):
+      ↑[f](𝛗n.t) ⊆ 𝛗f＠⧣❨n❩.t.
+#f #t #n #p * #q #Hq #H0 destruct
+elim (in_comp_inv_iref … Hq) -Hq #p #H0 #Hp destruct
+/2 width=1 by in_comp_iref/
+qed-.
+
+lemma lift_iref (f) (t) (n:pnat):
+      (𝛗f＠⧣❨n❩.t) ⇔ ↑[f](𝛗n.t).
+/3 width=1 by conj, lift_iref_sn, lift_iref_dx/
+qed.
+
+lemma lift_iref_uni (t) (m) (n):
+      (𝛗(n+m).t) ⇔ ↑[𝐮❨m❩](𝛗n.t).
+// qed.