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

0 < i / j, 0 < i, j < j0, j < i, j0 < i / j, prime(j), prime(j0), j | i, j0 | i / j, 0 ≤ i / j, 0 ≤ i, 2 ≤ i, 2 ≤ 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
j0 < i / j, j < i, j < j0, 0 < i, 0 < i / j, prime(j0), prime(j), j0 | i / j, j | i, 2 ≤ i / j, 2 ≤ i, 0 ≤ i, 0 ≤ 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)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information