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Theorem bertrand-middle-primes

∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3, all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 2 < i ⊦ Π ints0 ≤ 4 ^ ((2 * i) / 3)

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