matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/dbfr.etc

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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/arith/nat_rplus.ma".
  23 include "ground/xoa/ex_6_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            ⊗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).