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

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

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ gcd(i, j) = 1 → (∃ i0. ≡mod(i * i0, 1, j))
Proof step 4:
gcd(i, j) = 1 → (∃ i0. ≡mod(i * i0, 1, j)), gcd(j, i) = 1, prime(j) ⊦ ≡mod(i ^ (j - 1), 1, j)

Rule argument

spec: int-mod inst: name: congmod-inverse seq: ⊦ gcd(i, j) = 1 → (∃ i0. ≡mod(i * i0, 1, j)) subst: [i, j] → [i, j] flags: current, []

Additional information

Used terms: i, j