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Proof step 31 from proof fermat-pos (previous step)

¬(gcd(j, j1) = 1 ∧ j1 ≤ j ∧ 0 ≤ j1), prime(j), ≡mod(i1 ^ j, i1, j), 0 ≤ i1, 0 ≤ j, j1 < j, 0 < j1, 1 < 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), j | Σ countFun(1, j - 1, λ j0. i1 ^ j0 * binom_coef(j, j0)), j | i1, j | binom_coef(j, j1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs