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Proof step 12 from proof bertrand-middle-primes (previous step)

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, 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 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 13:
2 ≤ 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, 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 ⊦

Rule argument

fma: 2 ≤ max_exp(i0, binom_coef(2 * i, i))

Additional information

Used simplifier rules: max_exp-primes-two: ⊦ max_exp(i, j) < 2 → all_prime_divisors(j) ≠ ints + i ' + ints0 + i ' + ints1;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista] Used formulas: 2 ≤ max_exp(i0, binom_coef(2 * i, i))