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

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  10 (*       \ /        This file is distributed under the terms of the       *)
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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_head.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 (**) (* explicit ninj because we cannot declare the expectd type of k *)
  28 definition dbfr (r): relation2 prototerm prototerm ≝
  29            λt1,t2.
  30            ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
  31            ⊗b ϵ 𝐁 & b = ↳[h]b &
  32            (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
  33            t1[⋔r←𝛕(k+h).(t1⋔(p◖𝗦))] ⇔ t2
  34 .
  35
  36 interpretation
  37   "balanced focused reduction with delayed updating (prototerm)"
  38   'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).