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Proof step 4 from proof max_exp-zero (previous step)

prime(i), j0 < i, 0 < j0, 0 < i, 1 < i ⊦ n→i(#oc(i, all_prime_divisors(i + j0))) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ i + j0, 2 ≤ i + j0, i | i + j0, 1 < i, 0 < i, 0 < j0, j0 < i, prime(i) ⊦

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%zero-02: ⊦ 0 < i ∧ 0 < j → 0 < i + j; from specification int-basic2%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist%oc-zero: ⊦ #oc(i, ints) = 0 ↔ ¬ i ∈ ints; from specification list-perm[intlista]%nat2int-02: ⊦ n→i(n) = 0 ↔ n = 0; from specification intnat