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(*       ___                                                              *)
(*      ||M||                                                             *)
(*      ||A||       A project by Andrea Asperti                           *)
(*      ||T||                                                             *)
(*      ||I||       Developers:                                           *)
(*      ||T||         The HELM team.                                      *)
(*      ||A||         http://helm.cs.unibo.it                             *)
(*      \   /                                                             *)
(*       \ /        This file is distributed under the terms of the       *)
(*        v         GNU General Public License Version 2                  *)
(*                                                                        *)
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include "delayed_updating/syntax/prototerm.ma".
include "delayed_updating/notation/functions/pitchforkleftarrow_3.ma".

(* FOCALIZED SUBSTITUTION ***************************************************)

definition fsubst (p) (u): prototerm → prototerm ≝
           λt,q.
           ∨∨ ∃∃r. r ϵ u & p●r = q
            | ∧∧ q ϵ t & (∀r. p●r = q → ⊥)
.

interpretation
  "focalized substitution (prototerm)"
  'PitchforkLeftArrow t p u = (fsubst p u t).