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Proof step 13 from proof max_exp-fac-gen (previous step)

0 ≤ i0, 1 < i ^ i0, j2 < i, 0 < i ^ i0, 0 ≤ j2, prime(i), j2 < i ^ i0, 1 < i, 0 < i, 0 < j2, ∀ j0, i2, i0. i→n(j0) < i→n(0 * i + j2) → prime(i2) ∧ j0 < i2 ^ i0 ∧ 0 < j0 ∧ 0 < i2 ^ i0 ∧ 0 ≤ i0 ∧ 1 < i2 ^ i0 → max_exp(i2, fac(j0)) = Σ countFun(1, i0, λ j1. j0 / i2 ^ j1) ⊦ 0 = Σ countFun(1, i0, λ j. j2 / i ^ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: sum-constant-countFun seq: ∀ i1. i ≤ i1 ∧ i1 ≤ j → intfun(i1) = i0, i ≤ j, 0 ≤ i ⊦ Σ countFun(i, j, intfun) = (1 + j - i) * i0 subst: [i0, intfun, j, i] → [0, λ j. j2 / i ^ j, i0, 1] flags: rewrite

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%Mult-zero: ⊦ i * 0 = 0; 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: 0, λ j. j2 / i ^ j, i0, 1