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Proof step 22 from proof BertrandsPostulate (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints2 + ints1 + ints0, 4 ^ i ≤ 4 ^ ((2 * i) / 3) * (2 * i) ^ sqrt(2 * i), 0 < i, 2 < i, binom_coef(2 * i, i) ≤ (2 * i) ^ (sqrt(2 * i) - 1) * 4 ^ ((2 * i) / 3), 4 ^ i ≤ binom_coef(2 * i, i) * 2 * i, i < 1024, ∀ j. j ∈ ints0 → (2 * i) / 3 < j ∧ j ≤ i, ∀ j. j ∈ ints1 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3, ∀ j. j ∈ ints2 → j ≤ sqrt(2 * i), ∀ i0. 0 < i0 ∧ i0 ≤ 1024 → (∃ j. prime(j) ∧ i0 < j ∧ j ≤ 2 * i0) ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 11 terms: i

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i