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Proof step 6 from proof prime-divides-pot-01 (previous step)

0 < j, 0 < j, prime(i), ∀ j0, i, i0. i→n(j0) < i→n(j) → prime(i) ∧ 0 < j0 → (i | i0 ^ j0 ↔ i | i0) ⊦ i | i0 ^ j -1 * i0 ↔ i | i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j, prime(i), i | i0 ^ (j - 1), ∀ j0, i, i0. i→n(j0) < i→n(j) → prime(i) ∧ 0 < j0 → (i | i0 ^ j0 ↔ i | i0) ⊦ i | i0

Rule argument

Additional information

Used simplifier rules: divides-mult-01: ⊦ i | j → i | j * j0; from specification int-gcd%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%sub-pred: ⊦ i -1 = i - 1; from specification int-abs