matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.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_balanced.ma".
  20 include "delayed_updating/syntax/path_structure.ma".
  21 include "delayed_updating/notation/relations/black_rightarrow_ibf_3.ma".
  22 include "ground/relocation/tr_uni.ma".
  23 include "ground/arith/nat_rplus.ma".
  24 include "ground/xoa/ex_6_5.ma".
  25
  26 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
  27
  28 (**) (* explicit ninj because we cannot declare the expectd type of k *)
  29 definition ibfr (r): relation2 prototerm prototerm ≝
  30            λt1,t2.
  31            ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
  32            ⊗b ϵ 𝐁 & b = ↳[h]b &
  33            (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
  34            t1[⋔r←↑[𝐮❨k+h❩](t1⋔(p◖𝗦))] ⇔ t2
  35 .
  36
  37 interpretation
  38   "balanced focused reduction with immediate updating (prototerm)"
  39   'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).