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Proof step 5 from proof middle-coef-max_exp-le (previous step)

i ^ i0 ≤ 2 * j ∧ 2 * j < i ^ (i0 + 1) ∧ 0 ≤ i0 ∧ prime(i) ∧ 0 < j, i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), 0 ≤ i0, prime(i), 0 < j ⊦ ∀ i1. i1 ∈ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) → i1 ≤ 1, Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0) ≤ i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%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%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs