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

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
primes(ints), max(ints) ≤ i, ¬ dups(ints) ⊦ Π ints ≤ 4 ^ i
Proof step 4:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ primes(ints0) ∧ max(ints0) ≤ (2 * i) / 3 ∧ ¬ dups(ints0)

Rule argument

spec: inst: name: prime-product seq: primes(ints), max(ints) ≤ i, ¬ dups(ints) ⊦ Π ints ≤ 4 ^ i subst: [ints, i] → [ints0, (2 * i) / 3] flags: current, []

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: ints0, (2 * i) / 3