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Proof step 20 from proof fermat-pos (previous step)

prime(j), ≡mod(i1 ^ j, i1, j), 0 ≤ i1, 0 ≤ j, 0 < j, ∀ i0, j. i→n(i0) < i→n(i1 + 1) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ ≡mod(Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)) + i1 ^ j, i1, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mod inst: name: cong-add seq: ⊦ j | j0 → (≡mod(j0 + i, i0, j) ↔ ≡mod(i, i0, j)) subst: [j, i0, i, j0] → [j, i1, i1 ^ j, Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0))] flags: rewrite, current

Additional information

Used terms: j, i1, i1 ^ j, Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0))