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Proof step 21 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, ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦ ¬ dups(rmdup(ints)) ∧ (∀ i0. i0 ∈ rmdup(ints) → 1 < i0 ∧ i0 ≤ sqrt(2 * i)) ∧ rmdup(ints) ≠ [], ints = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
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)

Rule argument

Additional information

Used simplifier rules: rm-empty: ⊦ rmdup(ints) = [] ↔ ints = []; from specification list-dup[intlista]%rm-in-02: ⊦ i ∈ rmdup(ints) ↔ i ∈ ints; from specification list-dup[intlista]%rm-nodups: ⊦ ¬ dups(rmdup(ints)); from specification list-dup[intlista]