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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "delayed_updating/unwind1/unwind_prototerm.ma".
16 include "delayed_updating/substitution/fsubst.ma".
17 include "delayed_updating/substitution/lift_prototerm.ma".
18 include "delayed_updating/syntax/prototerm_equivalence.ma".
19 include "delayed_updating/syntax/path_depth.ma".
20 include "delayed_updating/syntax/path_structure.ma".
21 include "delayed_updating/syntax/path_balanced.ma".
22 include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
23 include "ground/xoa/ex_1_2.ma".
24 include "ground/xoa/and_4.ma".
26 (* IMMEDIATE FOCUSED REDUCTION ************************************************)
28 definition ifr (p) (q): relation2 prototerm prototerm ≝
31 ∧∧ (⊗b ϵ 𝐁 ∧ 𝟎 = ❘b❘) & ↑❘q❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
32 t1[⋔r←↑[𝐮❨❘b●𝗟◗q❘❩](t1⋔(p◖𝗦))] ⇔ t2
36 "focused balanced reduction with immediate updating (prototerm)"
37 'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).