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Proof step 7 from proof middle-coef-max_exp (previous step)

i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | binom_coef(2 * j, j), 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)) ⊦ max_exp(i, binom_coef(2 * j, j)) ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i0 < max_exp(i, binom_coef(2 * j, j)), i ^ i0 < i ^ max_exp(i, binom_coef(2 * j, j)), i ^ i0 < i ^ (i0 + 1), 0 ≤ i0, 0 < j, 2 * j < i ^ max_exp(i, binom_coef(2 * j, j)), prime(i), i | binom_coef(2 * j, j), 2 * j < i ^ (i0 + 1), i ^ i0 ≤ 2 * j ⊦ max_exp(i, binom_coef(2 * j, j)) = 0

Rule argument

Additional information

Used simplifier rules: max_exp-pos-02: ⊦ 0 < max_exp(i, j) ↔ max_exp(i, j) ≠ 0;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs