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Proof step 10 from proof middle-coef-max_exp-big-primes (previous step)

i0 ≤ 2, j ^ i0 < j ^ (i0 + 1), 0 ≤ i0, (2 * i) / 3 < j, j ≤ i, prime(j), 2 < i, 0 < i, 2 * i < j ^ (i0 + 1), j ^ i0 ≤ 2 * i, i0 < i ⊦ Σ countFun(1, i0, λ i0. (2 * i) / j ^ i0 - 2 * i / j ^ i0) = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i0 = 0

Additional information

Used simplifier rules: Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%one: ⊦ i ^ 1 = i; from specification int-pot%leone: ⊦ 1 ≤ i ↔ 0 < i; 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%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ 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%ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1); from specification int-mult Used formulas: i0 = 0