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Proof step 8 from proof bertrand-middle-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, ∃ i, ints3, ints1, ints2. ints0 = ints3 + (i + (ints1 + (i + ints2))), 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
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

Additional information

Used simplifier rules: in-01: ⊦ i ≠ i0 → (i ∈ i0 ' + ints ↔ i ∈ ints); from specification list[intlista]%in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]%prod-rec: ⊦ Π(i ' + ints) = i * Π ints; from specification intlist%product-app: ⊦ Π(ints + ints0) = Π ints * Π ints0; from specification intlist%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]