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Proof step 5 from proof modeven-neg (previous step)

i = i0 * 2 + j0, j0 = 0, i < 0, abs(j0) < 2, 0 < 2, j0 ≤ 0 ⊦ (i + 1) % 2 = ~1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i0 < 0 ⊦ (1 + i0 * 2) % 2 = ~1

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)% ⊦ i + 0 = i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2