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Proof step 17 from proof middle-coef-max_exp-le (previous step)

¬(0 ≤ 1 ∧ 1 ≤ i0), i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), prime(i), Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) ≤ n→i(# countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0)), i0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), i ^ i0 < i ^ (i0 + 1), 0 ≤ i0, 0 < j, 0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), i0 < n→i(# countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0)) ⊦ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%one: ⊦ i ^ 1 = i; from specification int-pot%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%l: ⊦ # ints = 0 ↔ ints = []; from specification list-data[intlista]%zero: ⊦ 0 < m ↔ m ≠ 0; from specification nat-basic1%num-n2i-ls-02: 0 ≤ i ⊦ (* i) < n→i(n) ↔ i→n(i) < n; from specification intnat%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs