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Theorem partitionRefinement-def

⊦ partitionRefinement(P, A, P0, A0, X) ↔ (∀ p. p ∈ P → (∃ p0. p0 ∈ P0 ∧ (⟦p⟧ (A) = ⟦p0⟧ (A0) ∩ list2set(X) ∨ ⟦p⟧ (A) = ⟦p0⟧ (A0) \ list2set(X))))