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/notation/relations/black_rightarrow_if_3.ma".
  20 include "ground/relocation/tr_uni.ma".
  21 include "ground/xoa/ex_4_3.ma".
  22
  23 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
  24
  25 (**) (* explicit ninj because we cannot declare the expectd type of k *)
  26 definition ifr (r): relation2 prototerm prototerm ≝
  27            λt1,t2.
  28            ∃∃p,q,k. p●𝗔◗𝗟◗q = r &
  29            (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
  30            t1[⋔r←↑[𝐮❨ninj k❩](t1⋔(p◖𝗦))] ⇔ t2
  31 .
  32
  33 interpretation
  34   "focused reduction with immediate updating (prototerm)"
  35   'BlackRightArrowIF t1 r t2 = (ifr r t1 t2).