--- /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/notation/relations/rfun_c_2.ma".
+include "ground/arith/nat_succ.ma".
+include "ground/relocation/gr_isi.ma".
+
+(* FINITE COLENGTH ASSIGNMENT FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(*** fcla *)
+inductive gr_fcla: relation2 gr_map nat ā
+(*** fcla_isid *)
+| gr_fcla_isi (f): šāŖfā« ā gr_fcla f (š)
+(*** fcla_push *)
+| gr_fcla_push (f) (n): gr_fcla f n ā gr_fcla (ā«Æf) n
+(*** fcla_next *)
+| gr_fcla_next (f) (n): gr_fcla f n ā gr_fcla (āf) (ān)
+.
+
+interpretation
+ "finite colength assignment (generic relocation maps)"
+ 'RFunC f n = (gr_fcla f n).
+
+(* Basic inversion lemmas ***************************************************)
+
+(*** fcla_inv_px *)
+lemma gr_fcla_inv_push (g) (m): šāŖgā« ā m ā āf. ā«Æf = g ā šāŖfā« ā m.
+#g #m * -g -m
+[ /3 width=3 by gr_fcla_isi, gr_isi_inv_push/
+| #g #m #Hg #f #H >(eq_inv_gr_push_bi ā¦ H) -f //
+| #g #m #_ #f #H elim (eq_inv_gr_push_next ā¦ H)
+]
+qed-.
+
+(*** fcla_inv_nx *)
+lemma gr_fcla_inv_next (g) (m): šāŖgā« ā m ā āf. āf = g ā āān. šāŖfā« ā n & ān = m.
+#g #m * -g -m
+[ #g #Hg #f #H destruct
+ elim (gr_isi_inv_next ā¦ Hg) -Hg //
+| #g #m #_ #f #H elim (eq_inv_gr_next_push ā¦ H)
+| #g #m #Hg #f #H >(eq_inv_gr_next_bi ā¦ H) -f
+ /2 width=3 by ex2_intro/
+]
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(*** cla_inv_nn *)
+lemma gr_cla_inv_next_succ (g) (m): šāŖgā« ā m ā āf,n. āf = g ā ān = m ā šāŖfā« ā n.
+#g #m #H #f #n #H1 #H2 elim (gr_fcla_inv_next ā¦ H ā¦ H1) -g
+#x #Hf #H destruct <(eq_inv_nsucc_bi ā¦ H) -n //
+qed-.
+
+(*** cla_inv_np *)
+lemma gr_cla_inv_next_zero (g) (m): šāŖgā« ā m ā āf. āf = g ā š = m ā ā„.
+#g #m #H #f #H1 elim (gr_fcla_inv_next ā¦ H ā¦ H1) -g
+#x #_ #H1 #H2 destruct /2 width=2 by eq_inv_zero_nsucc/
+qed-.
+
+(*** fcla_inv_xp *)
+lemma gr_fcla_inv_zero (g) (m): šāŖgā« ā m ā š = m ā šāŖgā«.
+#g #m #H elim H -g -m /3 width=3 by gr_isi_push/
+#g #m #_ #_ #H destruct elim (eq_inv_zero_nsucc ā¦ H)
+qed-.
+
+(*** fcla_inv_isid *)
+lemma gr_fcla_inv_isi (g) (m): šāŖgā« ā m ā šāŖgā« ā š = m.
+#f #n #H elim H -f -n /3 width=3 by gr_isi_inv_push/
+#f #n #_ #_ #H elim (gr_isi_inv_next ā¦ H) -H //
+qed-.