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Proof step 4 from proof bertrand-big-primes (previous step)

(2 * i) / 3 < j ∧ j ≤ i ∧ prime(j) ∧ 2 < i → max_exp(j, binom_coef(2 * i, i)) = 0, 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j, j | binom_coef(2 * i, i) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
max_exp(j, binom_coef(2 * i, i)) = 0, j | binom_coef(2 * i, i), (2 * i) / 3 < j, j ≤ i, prime(j), 2 < i, 0 < i ⊦

Rule argument

Additional information

Used simplifier rules: lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs