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Proof step 8 from proof all_prime_divisors-in-01 (previous step)

2 ≤ i ∧ ¬ prime(i), ∀ i0, j. i→n(i0) < i→n(i) → true → (j ∈ all_prime_divisors(i0) ↔ prime(j) ∧ j | i0 ∧ 2 ≤ i0) ⊦ j ∈ all_prime_divisors(i / max_prime_divisor(i)) + max_prime_divisor(i) ' ↔ prime(j) ∧ j | i ∧ 2 ≤ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
2 ≤ i, 0 < i, 0 ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → true → (j ∈ all_prime_divisors(i0) ↔ prime(j) ∧ j | i0 ∧ 2 ≤ i0) ⊦ j ∈ all_prime_divisors(i / max_prime_divisor(i)) ∨ j = max_prime_divisor(i) ↔ prime(j) ∧ j | i, prime(i)

Rule argument

Additional information

Used simplifier rules: 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%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]