update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_fcla.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_fcla.ma
deleted file mode 100644 (file)
index 3540561..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_fcla.ma
+++ /dev/null
@@ -1,71 +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/xoa/ex_3_1.ma".
-include "ground/xoa/ex_4_2.ma".
-include "ground/arith/nat_plus.ma".
-include "ground/arith/nat_le_max.ma".
-include "ground/relocation/gr_fcla_eq.ma".
-include "ground/relocation/gr_sor_isi.ma".
-
-(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
-
-(* Constructions with gr_fcla ***********************************************)
-
-(*** sor_fcla_ex *)
-lemma gr_sor_fcla_bi:
-      ∀f1,n1. 𝐂❪f1❫ ≘ n1 → ∀f2,n2. 𝐂❪f2❫ ≘ n2 →
-      ∃∃f,n. f1 ⋓ f2 ≘ f & 𝐂❪f❫ ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
-#f1 #n1 #Hf1 elim Hf1 -f1 -n1 /3 width=6 by gr_sor_isi_sn, ex4_2_intro/
-#f1 #n1 #Hf1 #IH #f2 #n2 * -f2 -n2 /3 width=6 by gr_fcla_push, gr_fcla_next, ex4_2_intro, gr_sor_isi_dx/
-#f2 #n2 #Hf2 elim (IH … Hf2) -IH -Hf2 -Hf1 [2,4: #f #n <nplus_succ_dx ] (* * full auto fails *)
-[ /3 width=7 by gr_fcla_next, gr_sor_push_next, nle_max_sn_succ_dx, nle_succ_bi, ex4_2_intro/
-| /4 width=7 by gr_fcla_next, gr_sor_next_bi, nle_succ_dx, nle_succ_bi, ex4_2_intro/
-| /3 width=7 by gr_fcla_push, gr_sor_push_bi, ex4_2_intro/
-| /3 width=7 by gr_fcla_next, gr_sor_next_push, nle_max_sn_succ_sn, nle_succ_bi, ex4_2_intro/
-]
-qed-.
-
-(* Destructions with gr_fcla ************************************************)
-
-(*** sor_fcla *)
-lemma gr_sor_inv_fcla_bi:
-      ∀f1,n1. 𝐂❪f1❫ ≘ n1 → ∀f2,n2. 𝐂❪f2❫ ≘ n2 → ∀f. f1 ⋓ f2 ≘ f →
-      ∃∃n. 𝐂❪f❫ ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
-#f1 #n1 #Hf1 #f2 #n2 #Hf2 #f #Hf elim (gr_sor_fcla_bi … Hf1 … Hf2) -Hf1 -Hf2
-/4 width=6 by gr_sor_mono, gr_fcla_eq_repl_back, ex3_intro/
-qed-.
-
-(* Destructions with gr_fcla ************************************************)
-
-(*** sor_fwd_fcla_sn_ex *)
-lemma gr_sor_des_fcla_sn:
-      ∀f,n. 𝐂❪f❫ ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
-      ∃∃n1. 𝐂❪f1❫ ≘ n1 & n1 ≤ n.
-#f #n #H elim H -f -n
-[ /4 width=4 by gr_sor_des_isi_sn, gr_fcla_isi, ex2_intro/
-| #f #n #_ #IH #f1 #f2 #H
-  elim (gr_sor_inv_push … H) -H [ |*: // ] #g1 #g2 #Hf #H1 #H2 destruct
-  elim (IH … Hf) -f /3 width=3 by gr_fcla_push, ex2_intro/
-| #f #n #_ #IH #f1 #f2 #H
-  elim (gr_sor_inv_next … H) -H [1,3,4: * |*: // ] #g1 #g2 #Hf #H1 #H2 destruct
-  elim (IH … Hf) -f /3 width=3 by gr_fcla_push, gr_fcla_next, nle_succ_bi, nle_succ_dx, ex2_intro/
-]
-qed-.
-
-(*** sor_fwd_fcla_dx_ex *)
-lemma gr_sor_des_fcla_dx:
-      ∀f,n. 𝐂❪f❫ ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
-      ∃∃n2. 𝐂❪f2❫ ≘ n2 & n2 ≤ n.
-/3 width=4 by gr_sor_des_fcla_sn, gr_sor_comm/ qed-.