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Proof step 11 from proof bertrand-middle-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints4 + (i0 ' + ints3 + i0 ' + ints2) + ints1, 2 < i, 0 < i, 4 ^ ((2 * i) / 3) < Π ints4 * i0 * Π ints3 * i0 * Π ints2, ∀ j. j ∈ ints4 ∨ j = i0 ∨ j ∈ ints3 ∨ j ∈ ints2 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ prime(i0)

User applied rule cut formula

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: neq: ⊦ ¬ i ∈ ints → ints ≠ ints0 + i ' + ints1; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist Used formulas: i0 ∈ all_prime_divisors(binom_coef(2 * i, i))