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Proof step 5 from proof fermat-pos (previous step)

≡mod((i - 1) ^ j, i - 1, j), 0 < i, prime(j), ∀ i0, j. i→n(i0) < i→n(i) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ ≡mod(i ^ j, i, j)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
i = i1 + 1, ≡mod(i1 ^ j, i1, j), 0 < i, prime(j), ∀ i0, j. i→n(i0) < i→n(i) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ ≡mod(i ^ j, i, j)

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i, 1, i1] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i, 1, i1