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Proof step 10 from proof bertrand-small-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, i0 ^ max_exp(i0, binom_coef(2 * i, i)) ≤ 2 * i, 2 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, 0 < i, i0 ∈ ints, prime(i0), i0 | binom_coef(2 * i, i), 2 ≤ binom_coef(2 * i, i), 2 * i < i0 ^ n→i(#oc(i0, ints)), 0 < binom_coef(2 * i, i), 0 ≤ binom_coef(2 * i, i), 0 < i0, i0 ^ max_exp(i0, binom_coef(2 * i, i)) < i0 ^ n→i(#oc(i0, ints)), ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: ls-pos seq: ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0) subst: [j0, j, i] → [n→i(#oc(i0, ints)), max_exp(i0, binom_coef(2 * i, i)), i0] flags: rewrite

Additional information

Used simplifier rules: max_exp-pos: ⊦ 0 ≤ max_exp(i, j);%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ 1 ^ j = 1; from specification int-pot Used terms: n→i(#oc(i0, ints)), max_exp(i0, binom_coef(2 * i, i)), i0