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Proof step 25 from proof bertrand-prime-factors (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints0 + ints2 + ints3 + ints, 0 < i, 1 < i, ordered≤(ints0 + ints2 + ints3 + ints), j1 ∈ ints3, (2 * i) / 3 < j1, i < j1, 0 < j1, 1 < j1, ∀ i0. i0 ∈ ints3 ∨ i0 ∈ ints → (2 * i) / 3 < i0, ∀ i1. i1 ∈ ints0 → i1 < sqrt(2 * i) ∨ i1 = sqrt(2 * i), ∀ i1. i1 ∈ ints2 → i1 < (2 * i) / 3 ∨ i1 = (2 * i) / 3, ∀ i1. i1 ∈ ints → i < i1, ∀ i1. i1 ∈ ints3 → i1 < i ∨ i1 = i, ∀ i0. i0 ∈ ints2 ∨ i0 ∈ ints3 ∨ i0 ∈ ints → sqrt(2 * i) < i0 ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 14 terms: j1

Additional information

Used simplifier rules: ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista] Used terms: j1