update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_pat.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_pat.ma
deleted file mode 100644 (file)
index b652722..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_pat_pat.ma
+++ /dev/null
@@ -1,121 +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_lt_pred.ma".
-include "ground/relocation/gr_pat.ma".
-
-(* POSITIVE APPLICATION FOR GENERIC RELOCATION MAPS *************************)
-
-(* Main constructions *******************************************************)
-
-(*** at_monotonic *)
-theorem gr_pat_monotonic:
-        ∀j2,i2,f. @❪i2,f❫ ≘ j2 → ∀j1,i1. @❪i1,f❫ ≘ j1 →
-        i1 < i2 → j1 < j2.
-#j2 elim j2 -j2
-[ #i2 #f #H2f elim (gr_pat_inv_unit_dx … H2f) -H2f //
-  #g #H21 #_ #j1 #i1 #_ #Hi elim (plt_ge_false … Hi) -Hi //
-| #j2 #IH #i2 #f #H2f * //
-  #j1 #i1 #H1f #Hi elim (plt_inv_gen … Hi)
-  #_ #Hi2 elim (gr_pat_inv_succ_bi … H2f (↓i2)) -H2f [1,3: * |*: // ]
-  #g #H2g #H
-  [ elim (gr_pat_inv_push_succ … H1f … H) -f
-    /4 width=8 by plt_inv_succ_bi, plt_succ_bi/
-  | /4 width=8 by gr_pat_inv_next_succ, plt_succ_bi/
-  ]
-]
-qed-.
-
-(*** at_inv_monotonic *)
-theorem gr_pat_inv_monotonic:
-        ∀j1,i1,f. @❪i1,f❫ ≘ j1 → ∀j2,i2. @❪i2,f❫ ≘ j2 →
-        j1 < j2 → i1 < i2.
-#j1 elim j1 -j1
-[ #i1 #f #H1f elim (gr_pat_inv_unit_dx … H1f) -H1f //
-  #g * -i1 #H #j2 #i2 #H2f #Hj lapply (plt_des_gen … Hj) -Hj
-  #H22 elim (gr_pat_inv_push_succ … H2f … (↓j2) H) -f //
-| #j1 #IH *
-  [ #f #H1f elim (gr_pat_inv_unit_succ … H1f) -H1f [ |*: // ]
-    #g #H1g #H #j2 #i2 #H2f #Hj elim (plt_inv_succ_sn … Hj) -Hj
-    /3 width=7 by gr_pat_inv_next_succ/
-  | #i1 #f #H1f #j2 #i2 #H2f #Hj elim (plt_inv_succ_sn … Hj) -Hj
-    #Hj #H22 elim (gr_pat_inv_succ_bi … H1f) -H1f [1,4: * |*: // ]
-    #g #Hg #H
-    [ elim (gr_pat_inv_push_succ … H2f … (↓j2) H) -f
-      /3 width=7 by plt_succ_bi/
-    | /3 width=7 by gr_pat_inv_next_succ/
-    ]
-  ]
-]
-qed-.
-
-(*** at_mono *)
-theorem gr_pat_mono (f) (i):
-        ∀i1. @❪i,f❫ ≘ i1 → ∀i2. @❪i,f❫ ≘ i2 → i2 = i1.
-#f #i #i1 #H1 #i2 #H2 elim (pnat_split_lt_eq_gt i2 i1) //
-#Hi elim (plt_ge_false i i)
-/2 width=6 by gr_pat_inv_monotonic/
-qed-.
-
-(*** at_inj *)
-theorem gr_pat_inj (f) (i):
-        ∀i1. @❪i1,f❫ ≘ i → ∀i2. @❪i2,f❫ ≘ i → i1 = i2.
-#f #i #i1 #H1 #i2 #H2 elim (pnat_split_lt_eq_gt i2 i1) //
-#Hi elim (plt_ge_false i i)
-/2 width=6 by gr_pat_monotonic/
-qed-.
-
-(*** at_div_comm *)
-theorem gr_pat_div_comm (f2) (g2) (f1) (g1):
-        H_gr_pat_div f2 g2 f1 g1 → H_gr_pat_div g2 f2 g1 f1.
-#f2 #g2 #f1 #g1 #IH #jg #jf #j #Hg #Hf
-elim (IH … Hf Hg) -IH -j /2 width=3 by ex2_intro/
-qed-.
-
-(*** at_div_pp *)
-theorem gr_pat_div_push_bi (f2) (g2) (f1) (g1):
-        H_gr_pat_div f2 g2 f1 g1 → H_gr_pat_div (⫯f2) (⫯g2) (⫯f1) (⫯g1).
-#f2 #g2 #f1 #g1 #IH #jf #jg #j #Hf #Hg
-elim (gr_pat_inv_push … Hf) -Hf [1,2: * |*: // ]
-[ #H1 #H2 destruct -IH
-  lapply (gr_pat_inv_push_unit … Hg ???) -Hg [4: |*: // ] #H destruct
-  /3 width=3 by gr_pat_refl, ex2_intro/
-| #xf #i #Hf2 #H1 #H2 destruct
-  lapply (gr_pat_inv_push_succ … Hg ????) -Hg [5: * |*: // ] #xg #Hg2 #H destruct
-  elim (IH … Hf2 Hg2) -IH -i /3 width=9 by gr_pat_push, ex2_intro/
-]
-qed-.
-
-(*** at_div_nn *)
-theorem gr_pat_div_next_bi (f2) (g2) (f1) (g1):
-        H_gr_pat_div f2 g2 f1 g1 → H_gr_pat_div (↑f2) (↑g2) (f1) (g1).
-#f2 #g2 #f1 #g1 #IH #jf #jg #j #Hf #Hg
-elim (gr_pat_inv_next … Hf) -Hf [ |*: // ] #i #Hf2 #H destruct
-lapply (gr_pat_inv_next_succ … Hg ????) -Hg [5: |*: // ] #Hg2
-elim (IH … Hf2 Hg2) -IH -i /2 width=3 by ex2_intro/
-qed-.
-
-(*** at_div_np *)
-theorem gr_pat_div_next_push (f2) (g2) (f1) (g1):
-        H_gr_pat_div f2 g2 f1 g1 → H_gr_pat_div (↑f2) (⫯g2) (f1) (↑g1).
-#f2 #g2 #f1 #g1 #IH #jf #jg #j #Hf #Hg
-elim (gr_pat_inv_next … Hf) -Hf [ |*: // ] #i #Hf2 #H destruct
-lapply (gr_pat_inv_push_succ … Hg ????) -Hg [5: * |*: // ] #xg #Hg2 #H destruct
-elim (IH … Hf2 Hg2) -IH -i /3 width=7 by gr_pat_next, ex2_intro/
-qed-.
-
-(*** at_div_pn *)
-theorem gr_pat_div_push_next (f2) (g2) (f1) (g1):
-        H_gr_pat_div f2 g2 f1 g1 → H_gr_pat_div (⫯f2) (↑g2) (↑f1) (g1).
-/4 width=6 by gr_pat_div_next_push, gr_pat_div_comm/ qed-.