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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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11 (* v GNU General Public License Version 2 *)
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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/notation/relations/black_rightarrow_if_3.ma".
20 include "ground/relocation/tr_uni.ma".
21 include "ground/xoa/ex_4_3.ma".
23 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
25 definition ifr (r): relation2 prototerm prototerm ≝
27 ∃∃p,q,n. p●𝗔◗𝗟◗q = r &
28 q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
29 t1[⋔r←↑[𝐮❨↑n❩](t1⋔(p◖𝗦))] ⇔ t2
33 "focused reduction with immediate updating (prototerm)"
34 'BlackRightArrowIF t1 r t2 = (ifr r t1 t2).