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Proof step 28 from proof bertrand-middle-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ ∀ i. i ∈ ints0 → prime(i), dups(ints0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 2 < i, 4 ^ ((2 * i) / 3) < Π ints0, 0 < i, i0 ∈ ints0, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ dups(ints0), prime(i0)

Proof step 28 from proof bertrand-middle-primes (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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