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Proof step 5 from proof fermat-2-mod (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j)
Proof step 7:
0 < j, gcd(j, i) = 1, prime(j), i ^ (j - 1) |%| j = 1 |%| j ⊦ i ^ (j - 1) |%| j = 1

Rule argument

spec: int-mod inst: name: congmod-def-mod seq: ⊦ 0 < j → (≡mod(i, i0, j) ↔ i |%| j = i0 |%| j) subst: [j, i0, i] → [j, 1, i ^ (j - 1)] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: j, 1, i ^ (j - 1)