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Proof step 6 from proof bertrand-middle-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, dups(ints0), 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 rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ dups(ints) ↔ (∃ i, ints0, ints1, ints2. ints = ints0 + (i + (ints1 + (i + ints2))))
Proof step 8:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, ∃ i, ints3, ints1, ints2. ints0 = ints3 + (i + (ints1 + (i + ints2))), 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦

Rule argument

spec: list-dup inst: intlista name: dups seq: ⊦ dups(ints) ↔ (∃ i, ints0, ints1, ints2. ints = ints0 + (i + (ints1 + (i + ints2)))) subst: [ints] → [ints0] flags: rewrite

Additional information

Used terms: ints0