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Proof step 19 from proof max_prime_divisor-nls-02 (previous step)

1 < j0, 0 < j0, 0 < j, j + 1 < i0, 2 ≤ i0, j < j0, 2 ≤ j * i0, prime(j), prime(j0), j0 | i0, j0 < i0, 0 ≤ i0, j < i0, 0 < i0, 2 < i0, ∀ j1. j0 < j1 ∧ j1 < i0 ∧ prime(j1) → ¬ j1 | i0, ∀ j0. j < j0 ∧ j0 < j * i0 ∧ prime(j0) → ¬ j0 | j * i0 ⊦ prime(i0), prime(j * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 21:
1 < j0, 0 < j0, 0 < j, j + 1 < i0, 2 ≤ i0, j < j0, 2 ≤ j * i0, prime(j), prime(j0), ∃ i1. j0 * i1 = i0, j0 < i0, 0 ≤ i0, j < i0, 0 < i0, 2 < i0, ∀ j1. j0 < j1 ∧ j1 < i0 ∧ prime(j1) → ¬ j1 | i0, ∀ j0. j < j0 ∧ j0 < j * i0 ∧ prime(j0) → ¬ j0 | j * i0 ⊦ prime(i0), prime(j * i0)

Rule argument

spec: inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i0, j0] flags: rewrite, current

Additional information

Used terms: i0, j0