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

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  14
  15 include "delayed_updating/substitution/fsubst.ma".
  16 include "delayed_updating/substitution/lift_prototerm.ma".
  17 include "delayed_updating/syntax/prototerm_equivalence.ma".
  18 include "delayed_updating/syntax/path_depth.ma".
  19 include "delayed_updating/syntax/path_structure.ma".
  20 include "delayed_updating/syntax/path_balanced.ma".
  21 include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
  22 include "ground/xoa/ex_1_2.ma".
  23 include "ground/xoa/and_4.ma".
  24
  25 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
  26
  27 definition ifr (p) (q): relation2 prototerm prototerm ≝
  28            λt1,t2. ∃∃b,n.
  29            let r ≝ p●𝗔◗b●𝗟◗q in
  30            ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
  31               t1[⋔r←↑[𝐮❨❘b●𝗟◗q❘❩](t1⋔(p◖𝗦))] ⇔ t2
  32 .
  33
  34 interpretation
  35   "focused balanced reduction with immediate updating (prototerm)"
  36   'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).