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Proof step 15 from proof bertrand-small-primes (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0, Π ints ≤ (2 * i) ^ n→i(# rmdup(ints)), 0 < i, (2 * i) ^ (sqrt(2 * i) - 1) < Π ints, 2 < i, (2 * i) ^ (sqrt(2 * i) - 1) < (2 * i) ^ n→i(# rmdup(ints)), ∀ j. j ∈ ints → j ≤ sqrt(2 * i) ⊦

Rule argument

Additional information

Used simplifier rules: forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs