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Proof step 22 from proof middle-coef-max_exp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: max_exp-fac-gen-stronger seq: ⊦ prime(i) ∧ 0 < j ∧ 0 ≤ i0 ∧ j < i ^ i0 → max_exp(i, fac(j)) = Σ countFun(1, i0 - 1, λ j0. j / i ^ j0) subst: [i0, j, i] → [i0 + 1, j, i] flags: rewrite, current

Additional information

Used simplifier rules: numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0 + 1, j, i