ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / rtmap_pushs.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_pushs.ma b/matita/matita/contribs/lambdadelta/ground/relocation/rtmap_pushs.ma
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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/notation/functions/upspoonstar_2.ma".
+include "ground/relocation/rtmap_eq.ma".
+
+(* RELOCATION MAP ***********************************************************)
+
+rec definition pushs (f:rtmap) (n:nat) on n: rtmap ≝ match n with
+[ O ⇒ f | S m ⇒ ⫯(pushs f m) ].
+
+interpretation "pushs (rtmap)" 'UpSpoonStar n f = (pushs f n).
+
+(* Basic_inversion lemmas *****************************************************)
+
+lemma eq_inv_pushs_sn: ∀n,f1,g2. ⫯*[n] f1 ≡ g2 →
+                       ∃∃f2. f1 ≡ f2 & ⫯*[n] f2 = g2.
+#n elim n -n /2 width=3 by ex2_intro/
+#n #IH #f1 #g2 #H elim (eq_inv_px … H) -H [|*: // ]
+#f0 #Hf10 #H1 elim (IH … Hf10) -IH -Hf10 #f2 #Hf12 #H2 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+lemma eq_inv_pushs_dx: ∀n,f2,g1. g1 ≡ ⫯*[n] f2 →
+                       ∃∃f1. f1 ≡ f2 & ⫯*[n] f1 = g1.
+#n elim n -n /2 width=3 by ex2_intro/
+#n #IH #f2 #g1 #H elim (eq_inv_xp … H) -H [|*: // ]
+#f0 #Hf02 #H1 elim (IH … Hf02) -IH -Hf02 #f1 #Hf12 #H2 destruct
+/2 width=3 by ex2_intro/
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma pushs_O: ∀f. f = ⫯*[0] f.
+// qed.
+
+lemma pushs_S: ∀f,n. ⫯⫯*[n] f = ⫯*[↑n] f.
+// qed.
+
+lemma pushs_eq_repl: ∀n. eq_repl (λf1,f2. ⫯*[n] f1 ≡ ⫯*[n] f2).
+#n elim n -n /3 width=5 by eq_push/
+qed.
+
+(* Advanced properties ******************************************************)
+
+lemma pushs_xn: ∀n,f. ⫯*[n] ⫯f = ⫯*[↑n] f.
+#n elim n -n //
+qed.