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_eq.ma".
  18 include "delayed_updating/syntax/path_head.ma".
  19 include "delayed_updating/syntax/path_reverse.ma".
  20 include "delayed_updating/notation/relations/black_rightarrow_if_4.ma".
  21
  22 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
  23
  24 definition ifr (p) (q): relation2 prototerm prototerm ≝
  25            λt1,t2. ∃n:pnat.
  26            let r ≝ p●𝗔◗𝗟◗q in
  27            ∧∧ (𝗟◗q)ᴿ = ↳[n](rᴿ) & r◖𝗱n ϵ t1 &
  28               t1[⋔r←↑[𝐮❨n❩](t1⋔(p◖𝗦))] ⇔ t2
  29 .
  30
  31 interpretation
  32   "focused reduction with immediate updating (prototerm)"
  33   'BlackRightArrowIF t1 p q t2 = (ifr p q t1 t2).