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Proof step 1 from proof bertrand-small-primes (conclusion)

∀ j. j ∈ ints → j ≤ sqrt(2 * i), all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 2 < i ⊦ Π ints ≤ (2 * i) ^ (sqrt(2 * i) - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 0 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, 2 < i, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs