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Proof step 6 from proof prime-fac-divides (previous step)

0 < j, 0 < j, i < j, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ i | j * fac(j - 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j, i < j, prime(i), ∀ j0, i. i→n(j0) < i→n(j) → prime(i) ∧ i < j0 ∧ 0 < j0 → i | fac(j0) ⊦ i | j, i | fac(j - 1)

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0); from specification int-gcd