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Proof step 18 from proof fermat-2 (previous step)

gcd(j, i) = 1, ≡mod(i * i0, 1, j), prime(j) ⊦ i0 = 0, i * i ^ (j - 1) = i ^ j, ≡mod(i ^ (j - 1), 1, j), ≡mod(i0 * i * i ^ (j - 1), 1, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ 0 < i → j ^ i = j ^ i -1 * j

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j, i] flags: rewrite

Additional information

Used simplifier rules: sub-pred: ⊦ i -1 = i - 1; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: j, i