(**************************************************************************)
include "delayed_updating/substitution/lift_rmap.ma".
-include "ground/relocation/tr_pn_eq.ma".
+include "delayed_updating/substitution/prelift_rmap_eq.ma".
include "ground/lib/stream_tls_plus.ma".
-include "ground/lib/stream_tls_eq.ma".
include "ground/arith/nat_plus_rplus.ma".
include "ground/arith/nat_rplus_pplus.ma".
(* Constructions with lift_eq ***********************************************)
lemma lift_rmap_eq_repl (p):
- stream_eq_repl … (λf1,f2. ↑[p]f1 ≗ ↑[p]f2).
+ stream_eq_repl … (λf1,f2. 🠢[f1]p ≗ 🠢[f2]p).
#p elim p -p //
-* [ #k ] #p #IH #f1 #f2 #Hf
-[ /3 width=1 by stream_tls_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 prelift_rmap_eq_repl/
qed.
lemma tls_lift_rmap_d_dx (f) (p) (n) (k):
- ⇂*[n+k]↑[p]f ≗ ⇂*[n]↑[p◖𝗱k]f.
+ ⇂*[n+k]🠢[f]p ≗ ⇂*[n]🠢[f](p◖𝗱k).
#f #p #n #k
<lift_rmap_d_dx >nrplus_inj_dx >nrplus_inj_sn //
qed.