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Proof step 30 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 ⊦ max(ints0) ≤ (2 * i) / 3, dups(ints0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, (2 * i) / 3 < max(ints0), ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ dups(ints0)

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs