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Proof step 5 from proof max_exp-fac-gen-stronger (previous step)

1 < i ^ i0, 0 ≤ i0, 0 < i ^ i0, 0 < j, j < i ^ i0, prime(i) ⊦ Σ countFun(1, i0, λ j0. j / i ^ j0) = Σ countFun(1, i0 - 1, λ j0. j / i ^ j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: countFun-last seq: ⊦ i ≤ j → countFun(i, j, intfun) = countFun(i, j - 1, intfun) + intfun(j) ' subst: [intfun, j, i] → [λ j0. j / i ^ j0, i0, 1] flags: rewrite

Additional information

Used simplifier rules: div-zero-06: ⊦ i < j ∧ 0 < j ∧ 0 < i → i / j = 0; from specification int-div%sum-app: ⊦ Σ(ints + ints0) = Σ ints + Σ ints0; from specification intlist%sum-one: ⊦ Σ i ' = i; from specification intlist%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%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: λ j0. j / i ^ j0, i0, 1