matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma

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  14
  15 include "delayed_updating/substitution/fsubst.ma".
  16 include "delayed_updating/syntax/prototerm_constructors.ma".
  17 include "delayed_updating/syntax/prototerm_eq.ma".
  18 include "delayed_updating/syntax/path_closed.ma".
  19 include "delayed_updating/syntax/path_balanced.ma".
  20 include "delayed_updating/syntax/path_structure.ma".
  21 include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
  22 include "ground/xoa/ex_6_5.ma".
  23
  24 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
  25
  26 definition dbfr (r): relation2 prototerm prototerm ≝
  27            λt1,t2.
  28            ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
  29            ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓕ,m,𝟎❩ & q ϵ 𝐂❨Ⓕ,n,𝟎❩ & r◖𝗱↑n ϵ t1 &
  30            t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
  31 .
  32
  33 interpretation
  34   "balanced focused reduction with delayed updating (prototerm)"
  35   'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).
  36
  37 (* Constructions with subset_equivalence ************************************)
  38
  39 lemma dbfr_eq_trans (t) (t1) (t2) (r):
  40       t1 ➡𝐝𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐝𝐛𝐟[r] t2.
  41 #t #t1 #t2 #r
  42 * #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht #Ht2
  43 /3 width=13 by subset_eq_trans, ex6_5_intro/
  44 qed-.