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Proof step 6 from proof middle-coef-max_exp-stronger (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: ls-pos seq: ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0) subst: [j0, j, i] → [max_exp(i, binom_coef(2 * j, j)), i0, i] flags: rewrite

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: max_exp(i, binom_coef(2 * j, j)), i0, i