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Theorem toinftoinf-append-add

⊦ ¬ # σ < n∞ ∧ ¬ # σ0 < n∞1 → (σ to∞ n∞) + σ0 to∞ n∞1 + n∞ = (σ to∞ n∞) + (σ0 to∞ n∞1)

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