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Proof step 24 from proof middle-coef-max_exp (previous step)

prime(i) ∧ 0 < j ∧ 0 ≤ i0 + 1 ∧ j < i ^ (i0 + 1), 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 * Σ countFun(1, i0 + 1 - 1, λ j0. j / i ^ j0)), 0 < j, 0 ≤ i0, i ^ i0 < i ^ (i0 + 1), 2 * Σ countFun(1, i0 + 1 - 1, λ j0. j / i ^ j0) + i0 < max_exp(i, fac(2 * j)), 0 < fac(2 * j), i ^ i0 < i ^ (max_exp(i, fac(2 * j)) - 2 * Σ countFun(1, i0 + 1 - 1, λ j0. j / i ^ j0)), 0 < fac(j) ⊦ max_exp(i, fac(2 * j)) = 2 * Σ countFun(1, i0 + 1 - 1, λ j0. j / i ^ j0)

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, 2 * j, i] flags: rewrite, current

Additional information

Used simplifier rules: numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); 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, 2 * j, i