update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_nat.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_nat.ma
deleted file mode 100644 (file)
index a70e01c..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_nat.ma
+++ /dev/null
@@ -1,73 +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/nat_lt_pred.ma".
-include "ground/relocation/gr_nat.ma".
-
-(* NON-NEGATIVE APPLICATION FOR GENERIC RELOCATION MAPS *****************************)
-
-(* Main destructions ********************************************************)
-
-theorem gr_nat_monotonic (k2) (l2) (f):
-        @↑❪l2,f❫ ≘ k2 → ∀k1,l1. @↑❪l1,f❫ ≘ k1 → l1 < l2 → k1 < k2.
-#k2 @(nat_ind_succ … k2) -k2
-[ #l2 #f #H2f elim (gr_nat_inv_zero_dx … H2f) -H2f //
-  #g #H21 #_ #k1 #l1 #_ #Hi destruct
-  elim (nlt_inv_zero_dx … Hi)
-| #k2 #IH #l2 #f #H2f #k1 @(nat_ind_succ … k1) -k1 //
-  #k1 #_ #l1 #H1f #Hl elim (nlt_inv_gen … Hl)
-  #_ #Hl2 elim (gr_nat_inv_succ_bi … H2f (↓l2)) -H2f [1,3: * |*: // ]
-  #g #H2g #H
-  [ elim (gr_nat_inv_push_succ … H1f … H) -f
-    /4 width=8 by nlt_inv_succ_bi, nlt_succ_bi/
-  | /4 width=8 by gr_nat_inv_next_succ, nlt_succ_bi/
-  ]
-]
-qed-.
-
-theorem gr_nat_inv_monotonic (k1) (l1) (f):
-        @↑❪l1,f❫ ≘ k1 → ∀k2,l2. @↑❪l2,f❫ ≘ k2 → k1 < k2 → l1 < l2.
-#k1 @(nat_ind_succ … k1) -k1
-[ #l1 #f #H1f elim (gr_nat_inv_zero_dx … H1f) -H1f //
-  #g * -l1 #H #k2 #l2 #H2f #Hk
-  lapply (nlt_des_gen … Hk) -Hk #H22
-  elim (gr_nat_inv_push_succ … H2f … (↓k2) H) -f //
-| #k1 #IH #l1 @(nat_ind_succ … l1) -l1
-  [ #f #H1f elim (gr_nat_inv_zero_succ … H1f) -H1f [ |*: // ]
-    #g #H1g #H #k2 #l2 #H2f #Hj elim (nlt_inv_succ_sn … Hj) -Hj
-    /3 width=7 by gr_nat_inv_next_succ/
-  | #l1 #_ #f #H1f #k2 #l2 #H2f #Hj elim (nlt_inv_succ_sn … Hj) -Hj
-    #Hj #H22 elim (gr_nat_inv_succ_bi … H1f) -H1f [1,4: * |*: // ]
-    #g #Hg #H
-    [ elim (gr_nat_inv_push_succ … H2f … (↓k2) H) -f
-      /3 width=7 by nlt_succ_bi/
-    | /3 width=7 by gr_nat_inv_next_succ/
-    ]
-  ]
-]
-qed-.
-
-theorem gr_nat_mono (f) (l) (l1) (l2):
-        @↑❪l,f❫ ≘ l1 → @↑❪l,f❫ ≘ l2 → l2 = l1.
-#f #l #l1 #l2 #H1 #H2 elim (nat_split_lt_eq_gt l2 l1) //
-#Hi elim (nlt_ge_false l l)
-/2 width=6 by gr_nat_inv_monotonic/
-qed-.
-
-theorem gr_nat_inj (f) (l1) (l2) (l):
-        @↑❪l1,f❫ ≘ l → @↑❪l2,f❫ ≘ l → l1 = l2.
-#f #l1 #l2 #l #H1 #H2 elim (nat_split_lt_eq_gt l2 l1) //
-#Hi elim (nlt_ge_false l l)
-/2 width=6 by gr_nat_monotonic/
-qed-.