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Theorem partititions-def

⊦ partitions(P, n0) ↔ (∀ n. n < n0 → (∃ m. m < # P ∧ n ∈ P[m] ∧ (∀ m0. m0 < # P ∧ m0 ≠ m → ¬ n ∈ P[m0])))