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

0 < j0, prime(i), 0 < j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → prime(i) ∧ 0 < j1 → (i | j ^ j1 ↔ i | j) ∨ j = 0 ⊦ i | j ^ j0 -1 * j ↔ i | j, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
prime(i), 0 < j0, i | j ^ (j0 - 1), ∀ j1, i, j. i→n(j1) < i→n(j0) → prime(i) ∧ 0 < j1 → (i | j ^ j1 ↔ i | j) ∨ j = 0 ⊦ j = 0, i | j

Rule argument

Additional information

Used simplifier rules: prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0);%divides-mult-01: ⊦ i | j → i | j * j0;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%sub-pred: ⊦ i -1 = i - 1; from specification int-abs