(**************************************************************************)
include "delayed_updating/unwind/unwind2_rmap.ma".
-include "ground/relocation/tr_compose_eq.ma".
-include "ground/relocation/tr_pn_eq.ma".
+include "delayed_updating/unwind/preunwind2_rmap_eq.ma".
+include "ground/relocation/tr_uni_compose.ma".
+include "ground/arith/nat_rplus_pplus.ma".
-(* UNWIND MAP FOR PATH ******************************************************)
+(* TAILED UNWIND FOR RELOCATION MAP *****************************************)
-(* Constructions with stream_eq *********************************************)
+(* Constructions with tr_map_eq *********************************************)
lemma unwind2_rmap_eq_repl (p):
stream_eq_repl … (λf1,f2. ▶[f1]p ≗ ▶[f2]p).
#p elim p -p //
-* [ #n ] #p #IH #f1 #f2 #Hf
-[ /3 width=1 by tr_compose_eq_repl/
-| /2 width=1 by/
-| /3 width=1 by tr_push_eq_repl/
-| /2 width=1 by/
-| /2 width=1 by/
-]
+#l #p #IH #f1 #f2 #Hf
+/3 width=1 by preunwind2_rmap_eq_repl/
qed-.
+
+lemma tls_unwind2_rmap_d_dx (f) (p) (h) (k):
+ ⇂*[h+k]▶[f]p ≗ ⇂*[h]▶[f](p◖𝗱k).
+#f #p #h #k
+<unwind2_rmap_d_dx >nrplus_inj_dx
+/2 width=1 by tr_tls_compose_uni_dx/
+qed.