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Proof step 10 from proof fermat-2 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 11:
i0 * i * i ^ (j - 1) = i0 * i ^ j, gcd(j, i) = 1, prime(j), ≡mod(i * i0, 1, j) ⊦ ≡mod(i0 * i * i ^ (j - 1), 1, j), ≡mod(i ^ (j - 1), 1, j)
Proof step 17:
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)

Rule argument

fma: i0 * i * i ^ (j - 1) = i0 * i ^ j

Additional information

Used formulas: i0 * i * i ^ (j - 1) = i0 * i ^ j