+++ /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/arith/nat_le_pred.ma".
-include "ground/relocation/rtmap_after_uni.ma".
-include "ground/relocation/rtmap_basic.ma".
-
-(* RELOCATION MAP ***********************************************************)
-
-(* Properties with composition **********************************************)
-
-lemma after_basic_rc (m2,m1):
- m1 ≤ m2 → ∀n2,n1.m2 ≤ n1+m1 → 𝐁❨m2,n2❩ ⊚ 𝐁❨m1,n1❩ ≘ 𝐁❨m1,n1+n2❩.
-#m2 #m1 @(nat_ind_2_succ … m2 m1) -m2 -m1
-[ #m1 #H #n2 #n1 #_
- <(nle_inv_zero_dx … H) -m1 //
-| #m2 #IH #_ #n2 #n1 <nplus_zero_dx #H
- elim (nle_inv_succ_sn … H) -H #Hm2 #Hn1
- >Hn1 -Hn1 <nplus_succ_sn
- /3 width=7 by after_push/
-| #m2 #m1 #IH #H1 #n2 #n1 <nplus_succ_dx #H2
- lapply (nle_inv_succ_bi … H1) -H1 #H1
- lapply (nle_inv_succ_bi … H2) -H2 #H2
- /3 width=7 by after_refl/
-]
-qed.