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

gcd(j, i) = 1, prime(j) ⊦ i ^ (j - 1) |%| j = 1

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ prime(j) ∧ gcd(j, i) = 1 → ≡mod(i ^ (j - 1), 1, j)
Proof step 4:
prime(j) ∧ gcd(j, i) = 1 → ≡mod(i ^ (j - 1), 1, j), gcd(j, i) = 1, prime(j) ⊦ i ^ (j - 1) |%| j = 1

Rule argument

spec: int-mod inst: name: fermat-2 seq: ⊦ prime(j) ∧ gcd(j, i) = 1 → ≡mod(i ^ (j - 1), 1, j) subst: [j, i] → [j, i] flags: current, []

Additional information

Used terms: j, i