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Proof step 8 from proof fermat-2 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ≡mod(i0, i2, j) → (≡mod(i * i0, i1, j) ↔ ≡mod(i * i2, i1, j))

Rule argument

spec: int-mod inst: name: cong-mult-rew seq: ⊦ ≡mod(i0, i2, j) → (≡mod(i * i0, i1, j) ↔ ≡mod(i * i2, i1, j)) subst: [i2, j, i1, i0, i] → [1, j, 1, i * i0, i ^ (j - 1)] flags: rewrite, current

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 1, j, 1, i * i0, i ^ (j - 1)