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Proof step 3 from proof middle-coef-max_exp-stronger (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), prime(i), 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)) ⊦

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