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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
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 = []

Rule argument

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs