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Proof step 4 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) ∧ max(ints0) ≤ (2 * i) / 3 ∧ ¬ dups(ints0)

User applied rule cut formula

And obtained the following new goals

Proof step 5:
dups(ints0), 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)
Proof step 24:
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 ⊦ dups(ints0), primes(ints0) ∧ max(ints0) ≤ (2 * i) / 3 ∧ ¬ dups(ints0)

Rule argument

fma: dups(ints0)

Additional information

Used formulas: dups(ints0)