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Proof step 2 from proof bertrand-small-primes (previous step)

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) ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
∀ i. i ∈ ints → 0 < i ∧ i ^ n→i(#oc(i, ints)) ≤ j ⊦ Π ints ≤ j ^ n→i(# rmdup(ints))
Proof step 4:
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) ⊦ ∀ i0. i0 ∈ ints → 0 < i0 ∧ i0 ^ n→i(#oc(i0, ints)) ≤ 2 * i
Proof step 15:
Π ints ≤ (2 * i) ^ n→i(# rmdup(ints)), 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

spec: inst: name: product-pot-no-dups seq: ∀ i. i ∈ ints → 0 < i ∧ i ^ n→i(#oc(i, ints)) ≤ j ⊦ Π ints ≤ j ^ n→i(# rmdup(ints)) subst: [ints, j] → [ints, 2 * i] flags: current, []

Additional information

Used terms: ints, 2 * i