update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_lt.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_lt.ma
deleted file mode 100644 (file)
index 648c27f..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_lt.ma
+++ /dev/null
@@ -1,79 +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/arith/pnat_pred.ma".
-include "ground/arith/pnat_lt.ma".
-include "ground/relocation/gr_pat.ma".
-
-(* POSITIVE APPLICATION FOR GENERIC RELOCATION MAPS *************************)
-
-(* Destructions with plt and ple ********************************************)
-
-(*** at_increasing *)
-lemma gr_pat_increasing (i2) (i1) (f):
-      @❪i1,f❫ ≘ i2 → i1 ≤ i2.
-#i2 elim i2 -i2
-[ #i1 #f #Hf elim (gr_pat_inv_unit_dx … Hf) -Hf //
-| #i2 #IH * //
-  #i1 #f #Hf elim (gr_pat_inv_succ_bi … Hf) -Hf [1,4: * |*: // ]
-  /3 width=2 by ple_succ_bi, ple_succ_dx/
-]
-qed-.
-
-(*** at_increasing_strict *)
-lemma gr_pat_increasing_strict (g) (i1) (i2):
-      @❪i1,g❫ ≘ i2 → ∀f. ↑f = g →
-      ∧∧ i1 < i2 & @❪i1,f❫ ≘ ↓i2.
-#g #i1 #i2 #Hg #f #H elim (gr_pat_inv_next … Hg … H) -Hg -H
-/4 width=2 by conj, gr_pat_increasing, ple_succ_bi/
-qed-.
-
-(*** at_fwd_id_ex *)
-lemma gr_pat_des_id (f) (i): @❪i,f❫ ≘ i → ⫯⫰f = f.
-#f elim (gr_map_split_tl f) //
-#H #i #Hf elim (gr_pat_inv_next … Hf … H) -Hf -H
-#j2 #Hg #H destruct lapply (gr_pat_increasing … Hg) -Hg
-#H elim (plt_ge_false … H) -H //
-qed-.
-
-(* Constructions with ple ***************************************************)
-
-(*** at_le_ex *)
-lemma gr_pat_le_ex (j2) (i2) (f):
-      @❪i2,f❫ ≘ j2 → ∀i1. i1 ≤ i2 →
-      ∃∃j1. @❪i1,f❫ ≘ j1 & j1 ≤ j2.
-#j2 elim j2 -j2 [2: #j2 #IH ] #i2 #f #Hf
-[ elim (gr_pat_inv_succ_dx … Hf) -Hf [1,3: * |*: // ]
-  #g [ #x2 ] #Hg [ #H2 ] #H0
-  [ * /3 width=3 by gr_pat_refl, ex2_intro/
-    #i1 #Hi12 destruct lapply (ple_inv_succ_bi … Hi12) -Hi12
-    #Hi12 elim (IH … Hg … Hi12) -x2 -IH
-    /3 width=7 by gr_pat_push, ex2_intro, ple_succ_bi/
-  | #i1 #Hi12 elim (IH … Hg … Hi12) -IH -i2
-    /3 width=5 by gr_pat_next, ex2_intro, ple_succ_bi/
-  ]
-| elim (gr_pat_inv_unit_dx … Hf) -Hf //
-  #g * -i2 #H2 #i1 #Hi12 <(ple_inv_unit_dx … Hi12)
-  /3 width=3 by gr_pat_refl, ex2_intro/
-]
-qed-.
-
-(*** at_id_le *)
-lemma gr_pat_id_le (i1) (i2):
-      i1 ≤ i2 → ∀f. @❪i2,f❫ ≘ i2 → @❪i1,f❫ ≘ i1.
-#i1 #i2 #H
-@(ple_ind_alt … H) -i1 -i2 [ #i2 | #i1 #i2 #_ #IH ] #f #Hf
-lapply (gr_pat_des_id … Hf) #H <H in Hf; -H
-/4 width=7 by gr_pat_inv_succ_push_succ, gr_pat_push, gr_pat_refl/
-qed-.