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Proof step 46 from proof middle-coef-max_exp (previous step)

¬(0 ≤ 1 ∧ 1 ≤ i0), i0 < n→i(# countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0)), 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), 0 < Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 ≤ Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < fac(j), 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 ^ Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0), 0 < j, 0 ≤ i0, Σ countFun(1, i0, λ j0. 2 * j / i ^ j0) + i0 < Σ countFun(1, i0, λ j0. (2 * j) / i ^ j0), 0 < fac(2 * j), 1 < i ^ (i0 + 1), 0 < i ^ (i0 + 1), 1 < i, 0 < i ⊦ Σ countFun(1, i0, λ j0. (2 * j) / i ^ j0) = Σ countFun(1, i0, λ j0. 2 * j / i ^ j0), 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: nat2int: ⊦ 0 ≤ n→i(n); from specification intnat%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%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%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%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%ax-04: ⊦ i + 0 = i; from specification int-basic2%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%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