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Proof step 17 from proof fermat-pos (previous step)

1 ≤ j, prime(j), ≡mod(i1 ^ j, i1, j), 0 ≤ i1, 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 * binom_coef(j, j))'), i1, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%sum-one: ⊦ Σ i ' = i; from specification intlist%sum-app: ⊦ Σ(ints + ints0) = Σ ints + Σ ints0; from specification intlist%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%coef-same: ⊦ 0 ≤ j → binom_coef(j, j) = 1; from specification int-fac%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs