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Proof step 1 from proof all_prime_divisors-in (conclusion)

⊦ j ∈ all_prime_divisors(i) → prime(j) ∧ j ≤ i

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ i0, j. i→n(i0) < i→n(i) → true → j ∈ all_prime_divisors(i0) → prime(j) ∧ j ≤ i0 ⊦ j ∈ all_prime_divisors(i) → prime(j) ∧ j ≤ i

Rule argument

indvar: i→n(i) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i)