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Proof step 4 from proof middle-coef-max_exp-big-primes (previous step)

∃ i0. 0 ≤ i0 ∧ j ^ i0 ≤ 2 * i ∧ 2 * i < j ^ (i0 + 1), 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j ⊦ max_exp(j, binom_coef(2 * i, i)) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j ^ i0 ≤ 2 * i, 2 * i < j ^ (i0 + 1), 0 < i, 2 < i, prime(j), j ≤ i, (2 * i) / 3 < j, 0 ≤ i0, j ^ i0 < j ^ (i0 + 1) ⊦ max_exp(j, binom_coef(2 * i, i)) = 0

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs