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Proof step 18 from proof bertrand-middle-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints4 + (i0 ' + ints3 + i0 ' + ints2) + ints1, 4 ^ ((2 * i) / 3) < Π ints4 * i0 * Π ints3 * i0 * Π ints2, 0 < i, 2 < i, i0 ^ max_exp(i0, binom_coef(2 * i, i)) ≤ 2 * i, 2 ≤ max_exp(i0, binom_coef(2 * i, i)), 2 * i < i0 ^ 2, i0 ^ max_exp(i0, binom_coef(2 * i, i)) < i0 ^ 2, ∀ j. j ∈ ints4 ∨ j = i0 ∨ j ∈ ints3 ∨ j ∈ ints2 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ max_exp(i0, binom_coef(2 * i, i)) = 0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs