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def definition def or abbrev

PeelingWitness

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formal statement (Lean)

  88def PeelingWitness {n}
  89  (inputs : InputSet n) (aRef : Assignment n) (φ : CNF n) (H : XORSystem n) : Prop :=

proof body

Definition body.

  90  Nonempty (PeelingData inputs aRef φ H)
  91
  92/-- Forced-implication reachability (abstract): there is a directed arborescence
  93    of locally-determining constraints from OUTPUT to every input.
  94
  95    **Definition**: We define ForcedArborescence as equivalent to PeelingWitness.
  96    The peeling order (v₁, v₂, ..., vₙ) with determining constraints (K₁, K₂, ..., Kₙ)
  97    implicitly defines an arborescence where each variable's parent is determined
  98    by the constraint that determines it.
  99
 100    **Graph interpretation**: The arborescence edges are:
 101    - v → K_i for each variable v mentioned in K_i's "known" portion
 102    - K_i → v_i for the variable determined by K_i
 103
 104    This forms a directed tree rooted at OUTPUT reaching all input variables. -/

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