ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_isfin.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
deleted file mode 100644 (file)
index 3a9d265..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_isfin.ma
+++ /dev/null
@@ -1,96 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/isfinite_1.ma".
-include "ground_2/relocation/rtmap_fcla.ma".
-
-(* RELOCATION MAP ***********************************************************)
-
-definition isfin: predicate rtmap ≝
-                  λf. ∃n. 𝐂❪f❫ ≘ n.
-
-interpretation "test for finite colength (rtmap)"
-   'IsFinite f = (isfin f).
-
-(* Basic eliminators ********************************************************)
-
-lemma isfin_ind (R:predicate rtmap): (∀f.  𝐈❪f❫ → R f) →
-                                     (∀f. 𝐅❪f❫ → R f → R (⫯f)) →
-                                     (∀f. 𝐅❪f❫ → R f → R (↑f)) →
-                                     ∀f. 𝐅❪f❫ → R f.
-#R #IH1 #IH2 #IH3 #f #H elim H -H
-#n #H elim H -f -n /3 width=2 by ex_intro/
-qed-.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma isfin_inv_push: ∀g. 𝐅❪g❫ → ∀f. ⫯f = g → 𝐅❪f❫.
-#g * /3 width=4 by fcla_inv_px, ex_intro/
-qed-.
-
-lemma isfin_inv_next: ∀g. 𝐅❪g❫ → ∀f. ↑f = g → 𝐅❪f❫.
-#g * #n #H #f #H0 elim (fcla_inv_nx … H … H0) -g
-/2 width=2 by ex_intro/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma isfin_eq_repl_back: eq_repl_back … isfin.
-#f1 * /3 width=4 by fcla_eq_repl_back, ex_intro/
-qed-.
-
-lemma isfin_eq_repl_fwd: eq_repl_fwd … isfin.
-/3 width=3 by isfin_eq_repl_back, eq_repl_sym/ qed-.
-
-lemma isfin_isid: ∀f. 𝐈❪f❫ → 𝐅❪f❫.
-/3 width=2 by fcla_isid, ex_intro/ qed.
-
-lemma isfin_push: ∀f. 𝐅❪f❫ → 𝐅❪⫯f❫.
-#f * /3 width=2 by fcla_push, ex_intro/
-qed.
-
-lemma isfin_next: ∀f. 𝐅❪f❫ → 𝐅❪↑f❫.
-#f * /3 width=2 by fcla_next, ex_intro/
-qed.
-
-(* Properties with iterated push ********************************************)
-
-lemma isfin_pushs: ∀n,f. 𝐅❪f❫ → 𝐅❪⫯*[n]f❫.
-#n elim n -n /3 width=3 by isfin_push/
-qed.
-
-(* Inversion lemmas with iterated push **************************************)
-
-lemma isfin_inv_pushs: ∀n,g. 𝐅❪⫯*[n]g❫ → 𝐅❪g❫.
-#n elim n -n /3 width=3 by isfin_inv_push/
-qed.
-
-(* Properties with tail *****************************************************)
-
-lemma isfin_tl: ∀f. 𝐅❪f❫ → 𝐅❪⫱f❫.
-#f elim (pn_split f) * #g #H #Hf destruct
-/3 width=3 by isfin_inv_push, isfin_inv_next/
-qed.
-
-(* Inversion lemmas with tail ***********************************************)
-
-lemma isfin_inv_tl: ∀f. 𝐅❪⫱f❫ → 𝐅❪f❫.
-#f elim (pn_split f) * /2 width=1 by isfin_next, isfin_push/
-qed-.
-
-(* Inversion lemmas with iterated tail **************************************)
-
-lemma isfin_inv_tls: ∀n,f. 𝐅❪⫱*[n]f❫ → 𝐅❪f❫.
-#n elim n -n /3 width=1 by isfin_inv_tl/
-qed-.