matita/matita/contribs/lambdadelta/delayed_updating/etc/balanced/ibfr.etc

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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_closed.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 definition ibfr (r): relation2 prototerm prototerm ≝
  29            λt1,t2.
  30            ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
  31            ⊗b ϵ 𝐁 & b ϵ 𝐂❨m❩ & q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
  32            t1[⋔r←↑[𝐮❨↑(m+n)❩](t1⋔(p◖𝗦))] ⇔ t2
  33 .
  34
  35 interpretation
  36   "balanced focused reduction with immediate updating (prototerm)"
  37   'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).