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Proof step 22 from proof fermat-pos (previous step)

¬ j | Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)), 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
0 < j, 0 ≤ j, 0 ≤ i1, ≡mod(i1 ^ j, i1, j), prime(j), ∀ i0, j. i→n(i0) < i→n(i1 + 1) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ j | Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)), ≡mod(Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)) + i1 ^ j, i1, j)

Proof step 22 from proof fermat-pos (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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