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Proof step 24 from proof bertrand-small-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, 0 < sqrt(2 * i), sqrt(2 * i) ≤ n→i(# rmdup(ints)), 2 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, Π ints ≤ (2 * i) ^ n→i(# rmdup(ints)), 0 < i, i0 ∈ ints, i0 ≤ sqrt(2 * i), i0 ≤ 1, i0 ≤ n→i(# rmdup(ints)), ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ ints = []

User applied rule cut formula

And closed the goal!

Rule argument

fma: i0 ∈ all_prime_divisors(binom_coef(2 * i, i))

Additional information

Used simplifier rules: in-11: ⊦ i ∈ ints → i ∈ ints + ints0; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used formulas: i0 ∈ all_prime_divisors(binom_coef(2 * i, i))