1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/substitution/lift_eq.ma".
16 include "delayed_updating/syntax/path_update.ma".
17 include "delayed_updating/syntax/path_depth.ma".
18 include "ground/lib/stream_eq_eq.ma".
20 (* LIFT FOR PATH ***********************************************************)
22 (* Constructions with update ***********************************************)
24 axiom arith1 (p,q:pnat) (n:nat):
25 nrplus (pplus p q) n = pplus p (nrplus q n).
27 lemma pippo (f) (p) (m:pnat):
28 ⇂*[ninj (m+⧣p)]f ≗ ⇂*[ninj (m+❘p❘)]↑[p]f.
29 #f #p @(list_ind_rcons … p) -p [ // ]
31 [ <update_d_dx <depth_d_dx
32 <nplus_comm <nrplus_inj_sn <nrplus_inj_dx <arith1
33 @(stream_eq_trans … (lift_rmap_tls_d_dx …))
34 @(stream_eq_canc_dx … (IH …)) -IH //
36 | <update_L_dx <depth_L_dx
37 <nrplus_succ_dx >nsucc_inj //