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_guard.ma".
  21 include "delayed_updating/syntax/path_structure.ma".
  22 include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
  23 include "ground/xoa/ex_7_5.ma".
  24
  25 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
  26
  27 definition dbfr (r): relation2 prototerm prototerm ≝
  28            λt1,t2.
  29            ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
  30            p ϵ 𝐆 & ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓕ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
  31            t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
  32 .
  33
  34 interpretation
  35   "balanced focused reduction with delayed updating (prototerm)"
  36   'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).
  37
  38 (* Constructions with subset_equivalence ************************************)
  39
  40 lemma dbfr_eq_trans (t) (t1) (t2) (r):
  41       t1 ➡𝐝𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐝𝐛𝐟[r] t2.
  42 #t #t1 #t2 #r
  43 * #p #b #q #m #n #Hr #Hp #Hb #Hm #Hn #Ht1 #Ht #Ht2
  44 /3 width=14 by subset_eq_trans, ex7_5_intro/
  45 qed-.