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Proof step 16 from proof max_prime_divisor-nls-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 18:
j < i / j, 0 < i / j, 0 ≤ i / j, j0 < i / j, j0 | i / j, prime(j0), j < i, ∃ i0. j * i0 = i, prime(j), 0 < i, 0 ≤ i, 2 ≤ i, j < j0, 2 ≤ i / j, j + 1 < i / j, ∀ j1. j0 < j1 ∧ j1 < i / j ∧ prime(j1) → ¬ j1 | i / j, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i ⊦ prime(i / j), prime(i)

Rule argument

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

Additional information

Used terms: i, j