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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "delayed_updating/unwind0/unwind1_rmap_eq.ma".
16 include "delayed_updating/unwind0/unwind1_path.ma".
17 include "delayed_updating/substitution/lift_structure.ma".
19 (* BASIC UNWIND FOR PATH ****************************************************)
21 (* Constructions with structure *********************************************)
23 fact unwind1_path_d_dx_aux (k) (p) (n):
24 k = ❘p❘ → (⊗p)◖𝗱((▶p)@❨n❩) = ▼(p◖𝗱n).
25 #k @(nat_ind_succ … k) -k
26 [ #p #n #H0 >(list_length_inv_zero_sn … H0) -p //
28 [ #n #H0 elim (eq_inv_nsucc_zero … H0)
30 lapply (eq_inv_nsucc_bi … H0) -H0
31 [ cases p -p [ -IH | #l #p ] #H0 destruct <unwind1_path_d_lcons
32 [ <lift_path_d_sn <lift_path_empty <unwind1_path_d_empty
33 <list_cons_comm <(tr_pap_eq_repl … (unwind1_rmap_d_empty …)) //
34 | >list_cons_shift <lift_path_d_dx <IH -IH //
35 <structure_lift <structure_d_sn /3 width=1 by eq_f2/
37 | #H0 destruct <unwind1_path_m_sn <IH -IH //
38 | #H0 destruct <unwind1_path_L_sn <IH -IH //
39 | #H0 destruct <unwind1_path_A_sn <IH -IH //
40 | #H0 destruct <unwind1_path_S_sn <IH -IH //
46 lemma unwind1_path_d_dx (p) (n):
47 (⊗p)◖𝗱((▶p)@❨n❩) = ▼(p◖𝗱n).
48 /2 width=2 by unwind1_path_d_dx_aux/ qed.