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Proof step 2 from proof all_prime_divisors-in (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i;%div-not-ls: ⊦ i < j ∧ 0 < i → ¬ j | i; from specification int-gcd%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs