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Proof step 6 from proof max_prime_divisor-nls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ j | i ∧ prime(j) ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i) → max_prime_divisor(i) = j
Proof step 8:
1 < i / j, 0 < i / j, i < i / j, 2 < i / j, 0 < i, j < i, prime(j), j | i, 2 ≤ i, 0 ≤ i, ∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i ⊦ prime(i)

Rule argument

spec: <toplevel> 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] → [j, i] flags: <all paths>

Additional information

Used terms: j, i