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Proof step 10 from proof fermat-1 (previous step)

prime(j), i < 0 ⊦ i = 0, ≡mod(i ^ j, i, j)

User applied rule insert lemma

And obtained the following new goals

Proof step 11:
⊦ prime(j) ∧ 0 < i → ≡mod(i ^ j, i, j)
Proof step 12:
prime(j) ∧ 0 < ~ i → ≡mod(~ i ^ j, ~ i, j), prime(j), i < 0 ⊦ i = 0, ≡mod(i ^ j, i, j)

Rule argument

spec: int-mod inst: name: fermat-pos seq: ⊦ prime(j) ∧ 0 < i → ≡mod(i ^ j, i, j) subst: [j, i] → [j, ~ i] flags: current, []

Additional information

Used terms: j, ~ i