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Proof step 22 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, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ ints = [], 1 < i0 ∧ i0 ≤ sqrt(2 * i)

User applied rule all left

And obtained the following new goals

Proof step 23:
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 ∈ ints → i0 ≤ sqrt(2 * i), ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ ints = [], 1 < i0 ∧ i0 ≤ sqrt(2 * i)

Rule argument

pos: left 9 terms: i0 abort: F discard: F computed: T

Additional information

Used terms: i0