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Proof step 32 from proof fermat-pos (previous step)

prime(j), ≡mod(i1 ^ j, i1, j), 0 ≤ i1, 0 ≤ j, j1 < j, 0 < j1, 1 < j, 0 < j, j1 ≤ j, 0 ≤ j1, ∀ i0, j. i→n(i0) < i→n(i1 + 1) → prime(j) ∧ 0 < i0 → ≡mod(i0 ^ j, i0, j) ⊦ gcd(j, j1) = 1, ≡mod(Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)) + i1 ^ j, i1, j), j | Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)), j | i1, j | binom_coef(j, j1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

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

Additional information

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