+++ /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_tl_eq.ma".
-include "ground/relocation/gr_coafter.ma".
-
-(* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
-
-(* Constructions with gr_eq *************************************************)
-
-(*** coafter_eq_repl_back2 *)
-corec lemma gr_coafter_eq_repl_back_sn:
- ∀f1,f. gr_eq_repl_back (λf2. f2 ~⊚ f1 ≘ f).
-#f1 #f #f2 * -f2 -f1 -f
-#f21 #f1 #f #g21 [1,2: #g1 ] #g #Hf #H21 [1,2: #H1 ] #H #g22 #H0
-[ cases (gr_eq_inv_push_sn … H0 … H21) -g21 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_push_sn … H0 … H21) -g21 /3 width=7 by gr_coafter_push/
-| cases (gr_eq_inv_next_sn … H0 … H21) -g21 /3 width=5 by gr_coafter_next/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd2 *)
-lemma gr_coafter_eq_repl_fwd_sn:
- ∀f1,f. gr_eq_repl_fwd (λf2. f2 ~⊚ f1 ≘ f).
-#f1 #f @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back_sn/
-qed-.
-
-(*** coafter_eq_repl_back1 *)
-corec lemma gr_coafter_eq_repl_back_dx:
- ∀f2,f. gr_eq_repl_back (λf1. f2 ~⊚ f1 ≘ f).
-#f2 #f #f1 * -f2 -f1 -f
-#f2 #f11 #f #g2 [1,2: #g11 ] #g #Hf #H2 [1,2: #H11 ] #H #g2 #H0
-[ cases (gr_eq_inv_push_sn … H0 … H11) -g11 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_next_sn … H0 … H11) -g11 /3 width=7 by gr_coafter_push/
-| @(gr_coafter_next … H2 H) /2 width=5 by/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd1 *)
-lemma gr_coafter_eq_repl_fwd_dx:
- ∀f2,f. gr_eq_repl_fwd (λf1. f2 ~⊚ f1 ≘ f).
-#f2 #f @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back_dx/
-qed-.
-
-(*** coafter_eq_repl_back0 *)
-corec lemma gr_coafter_eq_repl_back:
- ∀f1,f2. gr_eq_repl_back (λf. f2 ~⊚ f1 ≘ f).
-#f2 #f1 #f * -f2 -f1 -f
-#f2 #f1 #f01 #g2 [1,2: #g1 ] #g01 #Hf01 #H2 [1,2: #H1 ] #H01 #g02 #H0
-[ cases (gr_eq_inv_push_sn … H0 … H01) -g01 /3 width=7 by gr_coafter_refl/
-| cases (gr_eq_inv_next_sn … H0 … H01) -g01 /3 width=7 by gr_coafter_push/
-| cases (gr_eq_inv_push_sn … H0 … H01) -g01 /3 width=5 by gr_coafter_next/
-]
-qed-.
-
-(*** coafter_eq_repl_fwd0 *)
-lemma gr_coafter_eq_repl_fwd:
- ∀f2,f1. gr_eq_repl_fwd (λf. f2 ~⊚ f1 ≘ f).
-#f2 #f1 @gr_eq_repl_sym /2 width=3 by gr_coafter_eq_repl_back/
-qed-.