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Proof step 26 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 ⊦ primes(ints0), dups(ints0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ primes(ints) ↔ (∀ i. i ∈ ints → prime(i))
Proof step 28:
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 ⊦ ∀ i. i ∈ ints0 → prime(i), dups(ints0)

Rule argument

spec: intlist inst: name: primes-def seq: ⊦ primes(ints) ↔ (∀ i. i ∈ ints → prime(i)) subst: [ints] → [ints0] flags: rewrite

Additional information

Used terms: ints0