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Proof step 15 from proof fermat-1 (previous step)

¬(odd(j) ∧ 0 < j), prime(j), i < 0, ≡mod(~ i ^ j, ~ i, j) ⊦ i = 0, ≡mod(i ^ j, i, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
i < 0, ≡mod(i ^ 2, ~ i, 2) ⊦ i = 0, ≡mod(i ^ 2, i, 2)

Rule argument

Additional information

Used simplifier rules: odd-two: ⊦ ¬ odd(2); from specification int-min%minus-square-01: ⊦ ~ i ^ 2 = i ^ 2; from specification int-pot%numlslsdel: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); from specification int-basic1%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%prime-not-odd: ⊦ ¬ odd(j) → (prime(j) ↔ j = 2); from specification int-gcd%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs