+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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/relocation/gr_isi_eq.ma".
-include "ground/relocation/gr_sor_eq.ma".
-include "ground/relocation/gr_sor_sor.ma".
-
-(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
-
-(* Constructions with gr_isi ************************************************)
-
-(*** sor_isid_sn *)
-corec lemma gr_sor_isi_sn:
- โf1. ๐โชf1โซ โ โf2. f1 โ f2 โ f2.
-#f1 * -f1
-#f1 #g1 #Hf1 #H1 #f2 cases (gr_map_split_tl f2)
-/3 width=7 by gr_sor_push_bi, gr_sor_push_next/
-qed.
-
-(*** sor_isid_dx *)
-corec lemma gr_sor_isi_dx:
- โf2. ๐โชf2โซ โ โf1. f1 โ f2 โ f1.
-#f2 * -f2
-#f2 #g2 #Hf2 #H2 #f1 cases (gr_map_split_tl f1)
-/3 width=7 by gr_sor_push_bi, gr_sor_next_push/
-qed.
-
-(*** sor_isid *)
-lemma gr_sor_isi_bi_isi:
- โf1,f2,f. ๐โชf1โซ โ ๐โชf2โซ โ ๐โชfโซ โ f1 โ f2 โ f.
-/4 width=3 by gr_sor_eq_repl_back_dx, gr_sor_eq_repl_back_sn, gr_isi_inv_eq_repl/ qed.
-
-
-(* Destructions with gr_isi *************************************************)
-
-(*** sor_fwd_isid1 *)
-corec lemma gr_sor_des_isi_sn:
- โf1,f2,f. f1 โ f2 โ f โ ๐โชfโซ โ ๐โชf1โซ.
-#f1 #f2 #f * -f1 -f2 -f
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
-[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
-cases (gr_isi_inv_next โฆ Hg โฆ H)
-qed-.
-
-(*** sor_fwd_isid2 *)
-corec lemma gr_sor_des_isi_dx:
- โf1,f2,f. f1 โ f2 โ f โ ๐โชfโซ โ ๐โชf2โซ.
-#f1 #f2 #f * -f1 -f2 -f
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
-[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
-cases (gr_isi_inv_next โฆ Hg โฆ H)
-qed-.
-
-(* Inversions with gr_isi ***************************************************)
-
-(*** sor_isid_inv_sn *)
-lemma gr_sor_inv_isi_sn:
- โf1,f2,f. f1 โ f2 โ f โ ๐โชf1โซ โ f2 โก f.
-/3 width=4 by gr_sor_isi_sn, gr_sor_mono/
-qed-.
-
-(*** sor_isid_inv_dx *)
-lemma gr_sor_inv_isi_dx:
- โf1,f2,f. f1 โ f2 โ f โ ๐โชf2โซ โ f1 โก f.
-/3 width=4 by gr_sor_isi_dx, gr_sor_mono/
-qed-.
-
-(*** sor_inv_isid3 *)
-lemma gr_sor_inv_isi:
- โf1,f2,f. f1 โ f2 โ f โ ๐โชfโซ โ
- โงโง ๐โชf1โซ & ๐โชf2โซ.
-/3 width=4 by gr_sor_des_isi_dx, gr_sor_des_isi_sn, conj/ qed-.