-(**************************************************************************)
-(* ___ *)
-(* ||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.ma".
-include "ground/relocation/gr_after_after.ma".
-
-(* RELATIONAL COMPOSITION FOR GENERIC RELOCATION MAPS ***********************)
-
-(* Constructions with gr_isi ************************************************)
-
-(*** after_isid_sn *)
-corec lemma gr_after_isi_sn:
- âf1. đâŞf1⍠â âf2. f1 â f2 â f2.
-#f1 * -f1
-#f1 #g1 #Hf1 #H1 #f2 cases (gr_map_split_tl f2) #H2
-/3 width=7 by gr_after_push, gr_after_refl/
-qed.
-
-(*** after_isid_dx *)
-corec lemma gr_after_isi_dx:
- âf2. đâŞf2⍠â âf1. f1 â f2 â f1.
-#f2 * -f2
-#f2 #g2 #Hf2 #H2 #f1 cases (gr_map_split_tl f1) #H1
-[ /3 width=7 by gr_after_refl/
-| @(gr_after_next ⌠H1 H1) /3 width=3 by gr_isi_push/
-]
-qed.
-
-(* Destructions with gr_isi *************************************************)
-
-(*** after_isid_inv_sn *)
-lemma gr_after_isi_inv_sn:
- âf1,f2,f. f1 â f2 â f â đâŞf1⍠â f2 ⥠f.
-/3 width=6 by gr_after_isi_sn, gr_after_mono/ qed-.
-
-(*** after_isid_inv_dx *)
-lemma gr_after_isi_inv_dx:
- âf1,f2,f. f1 â f2 â f â đâŞf2⍠â f1 ⥠f.
-/3 width=6 by gr_after_isi_dx, gr_after_mono/ qed-.
-
-(*** after_fwd_isid1 *)
-corec lemma gr_after_des_isi_sn:
- âf1,f2,f. f1 â f2 â f â đâŞf⍠â đâŞf1âŤ.
-#f1 #f2 #f * -f1 -f2 -f
-#f1 #f2 #f #g1 [1,2: #g2 ] #g #Hf #H1 [1,2: #H2 ] #H0 #H
-[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
-cases (gr_isi_inv_next ⌠H ⌠H0)
-qed-.
-
-(*** after_fwd_isid2 *)
-corec lemma gr_after_des_isi_dx:
- âf1,f2,f. f1 â f2 â f â đâŞf⍠â đâŞf2âŤ.
-#f1 #f2 #f * -f1 -f2 -f
-#f1 #f2 #f #g1 [1,2: #g2 ] #g #Hf #H1 [1,2: #H2 ] #H0 #H
-[ /4 width=6 by gr_isi_inv_push, gr_isi_push/ ]
-cases (gr_isi_inv_next ⌠H ⌠H0)
-qed-.
-
-(*** after_inv_isid3 *)
-lemma gr_after_inv_isi:
- âf1,f2,f. f1 â f2 â f â đâŞf⍠â đâŞf1⍠⧠đâŞf2âŤ.
-/3 width=4 by gr_after_des_isi_dx, gr_after_des_isi_sn, conj/ qed-.