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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
16 include "delayed_updating/syntax/path_closed_height.ma".
18 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
20 (* Destructions with cpp and height *****************************************)
22 lemma nap_depth_unwind2_rmap_closed (o) (f) (q) (n):
24 f@§❨♯q❩+♭q = ▶[f]q@§❨♭q❩.
26 <(path_closed_des_depth … Hq) in ⊢ (???%);
27 /2 width=2 by nap_plus_unwind2_rmap_closed_depth/
30 lemma tls_depth_unwind2_rmap_closed (o) (f) (q) (n):
32 ⇂*[♯q]f ≗ ⇂*[♭q]▶[f]q.
33 #o #f #q #n #Hq elim Hq -q -n //
35 >(npsucc_pred k) in ⊢ (%→?); <nplus_succ_dx #Hq #IH
36 <height_d_dx <depth_d_dx
37 >(path_closed_des_succ_depth … Hq)
38 @(stream_eq_trans … (tls_unwind2_rmap_d_dx …))
39 >nrplus_inj_dx >nrplus_inj_sn >nsucc_unfold
40 <(path_closed_des_succ_depth … Hq) -Hq
41 <nplus_comm <stream_tls_plus
42 <nplus_comm <stream_tls_plus
43 /2 width=1 by stream_tls_eq_repl/