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Proof step 2 from proof max_prime_divisor-prime (previous step)

2 ≤ i, 0 ≤ i, 0 < i ⊦ prime(max_prime_divisor(i)), prime(i)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ prime(i) ∧ 2 ≤ i → (∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i))
Proof step 4:
¬ prime(i) ∧ 2 ≤ i → (∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i)), 2 ≤ i, 0 ≤ i, 0 < i ⊦ prime(max_prime_divisor(i)), prime(i)

Rule argument

spec: inst: name: prime-ex-max seq: ⊦ ¬ prime(i) ∧ 2 ≤ i → (∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i)) subst: [i] → [i] flags: current, []

Additional information

Used terms: i