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Proof step 16 from proof middle-coef-max_exp (previous step)

i ^ i0 < i ^ max_exp(i, fac(2 * j) / (fac(j) * fac(j))), 0 ≤ j, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), i | fac(2 * j) / (fac(j) * fac(j)), prime(i), 2 * j < i ^ max_exp(i, fac(2 * j) / (fac(j) * fac(j))), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), i0 < max_exp(i, fac(2 * j) / (fac(j) * fac(j))), fac(j) * fac(j) | fac(2 * j) ⊦ max_exp(i, fac(2 * j) / (fac(j) * fac(j))) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: max_exp-div seq: ⊦ 0 < j ∧ 0 < j0 ∧ prime(i) ∧ j0 | j → max_exp(i, j / j0) = max_exp(i, j) - max_exp(i, j0) subst: [j0, j, i] → [fac(j) * fac(j), fac(2 * j), i] flags: rewrite, current

Additional information

Used simplifier rules: fac-pos-01: ⊦ ¬ fac(i) ≤ 0;%fac-le-zero: ⊦ i * fac(j) ≤ 0 ↔ i ≤ 0;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: fac(j) * fac(j), fac(2 * j), i