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Proof step 5 from proof bertrand-small-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 2 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, 0 < i, i0 ∈ ints, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ 0 < i0 ∧ i0 ^ n→i(#oc(i0, ints)) ≤ 2 * i

User applied rule cut formula

And obtained the following new goals

Proof step 6:
i0 ∈ all_prime_divisors(binom_coef(2 * i, i)), all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 2 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, 0 < i, i0 ∈ ints, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ 0 < i0 ∧ i0 ^ n→i(#oc(i0, ints)) ≤ 2 * i

Rule argument

fma: i0 ∈ all_prime_divisors(binom_coef(2 * i, i))

Additional information

Used simplifier rules: in-11: ⊦ i ∈ ints → i ∈ ints + ints0; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista] Used formulas: i0 ∈ all_prime_divisors(binom_coef(2 * i, i))