matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_crux.ma

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  14
  15 include "delayed_updating/unwind/unwind2_rmap_closed.ma".
  16
  17 (* TAILED UNWIND FOR RELOCATION MAP *****************************************)
  18
  19 (* Crucial constructions with tr_uni ****************************************)
  20
  21 (* Note: crux of the commutation between unwind and balanced focused reduction *)
  22 lemma unwind2_rmap_uni_crux (f) (p) (b) (q) (m) (n):
  23       b ϵ 𝐂❨Ⓕ,m❩ → q ϵ 𝐂❨Ⓕ,n❩ →
  24       (𝐮❨↑(♭b+♭q)❩ ∘ ▶[f]p ≗ ▶[f](p●𝗔◗b●𝗟◗q) ∘ 𝐮❨↑(m+n)❩).
  25 #f #p #b #q #m #n #Hm #Hn
  26 <list_append_rcons_sn <list_append_rcons_sn >list_append_assoc
  27 >list_append_rcons_sn >(list_append_rcons_sn … b)
  28 @(stream_eq_trans … (tr_compose_uni_dx_pap …)) <tr_pap_succ_nap
  29 @(stream_eq_trans ????? (tr_compose_eq_repl …))
  30 [| @tls_succ_plus_unwind2_rmap_append_closed_Lq_dx // | skip
  31 |  <nap_plus_unwind2_rmap_append_closed_Lq_dx // | skip
  32 ] -Hn
  33 @tr_eq_inv_nap_zero_tl_bi
  34 [ <tr_compose_nap <tr_compose_nap <tr_uni_nap <tr_uni_nap
  35   >nsucc_unfold >nplus_succ_dx >nplus_succ_dx <nplus_assoc <nplus_assoc
  36   >tr_nap_plus_dx <unwind2_rmap_append <nap_plus_unwind2_rmap_closed
  37   /2 width=2 by pcc_A_sn/
  38 | @(stream_eq_canc_sn … (tr_tl_compose_uni_sn …))
  39   @(stream_eq_trans ????? (tr_tl_compose_uni_sn …))
  40   >stream_tls_succ <unwind2_rmap_append
  41   /3 width=2 by tls_succ_unwind2_rmap_closed, pcc_A_sn/
  42 ]
  43 qed-.