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Proof step 7 from proof bertrand-small-primes (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
prime(i), 0 < j ⊦ i ^ max_exp(i, binom_coef(2 * j, j)) ≤ 2 * j
Proof step 9:
i0 ^ max_exp(i0, binom_coef(2 * i, i)) ≤ 2 * i, all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 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, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦

Rule argument

spec: inst: name: middle-coef-max_exp-stronger seq: prime(i), 0 < j ⊦ i ^ max_exp(i, binom_coef(2 * j, j)) ≤ 2 * j subst: [i, j] → [i0, i] flags: current, []

Additional information

Used terms: i0, i