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Proof step 17 from proof fermat-2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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)

Rule argument

Additional information

Used simplifier rules: eq-nonzero: ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%neq-not-zero: ⊦ i * j ≠ i * j0 → i ≠ 0; (forward) from specification int-mult