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Proof step 13 from proof max_prime_divisor-nls-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ j | i ∧ prime(j) ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i) → max_prime_divisor(i) = j
Proof step 15:
j0 | i / j ∧ prime(j0) ∧ j0 < i / j ∧ (∀ j1. j0 < j1 ∧ j1 < i / j ∧ prime(j1) → ¬ j1 | i / j), 2 ≤ i / j, j < j0, 2 ≤ i, 0 ≤ i, 0 < i, prime(j), j | i, j < i, prime(j0), j0 | i / j, j0 < i / j, 0 ≤ i / j, 0 < i / j, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i, ∀ j1. j0 < j1 ∧ j1 < i / j ∧ prime(j1) → ¬ j1 | i / j ⊦ prime(i), prime(i / j)

Rule argument

spec: inst: name: max_prime_divisor-def seq: ⊦ j | i ∧ prime(j) ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i) → max_prime_divisor(i) = j subst: [j, i] → [j0, i / j] flags: rewrite, current

Additional information

Used terms: j0, i / j