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Proof step 15 from proof divmod2-2pot-neg (previous step)

(i0 * 2 ^ i) % 2 = 0, 0 < i, abs(j0) < 2 ^ i, 1 < i, i0 * 2 ^ i + j0 < 0, i0 < i, j0 < i, j0 - 1 < 0, i0 * 2 ^ i < 0, 0 < 2, i0 ≤ 0, j0 ≤ 0, 0 ≤ i ⊦ ((j0 - 1) / 2) % 2 = ((j0 - 1) / 2 + i0 * 2 ^ (i - 1)) % 2, (i0 * 2 ^ (i - 1)) % 2 = 0 ∧ (j0 - 1) / 2 < 0 ∧ i0 * 2 ^ (i - 1) < 0 ∧ 0 < 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
i0 < 0, 0 < i, abs(j0) < 2 ^ i, 1 < i, i0 * 2 ^ i + j0 < 0, j0 < i, j0 ≤ 0, 0 ≤ i ⊦ ((j0 - 1) / 2) % 2 = ((j0 - 1) / 2 + i0 * 2 ^ (i - 1)) % 2, i0 = 0, (i0 * 2 ^ (i - 1)) % 2 = 0 ∧ j0 < 0

Rule argument

Additional information

Used simplifier rules: mod-2pot: ⊦ 0 < i → (j * 2 ^ i) % 2 = 0;%pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; (s)% ⊦ i < 0 → (i * j < 0 ↔ 0 < j); (s)% ⊦ i ≤ ~1 ↔ i < 0; (s)% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; (s)% ⊦ (* i) + i0 - (* j) = (i - j) + i0; (s)% ⊦ i + (j - i0) = i + j - i0; (s)%0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0; (s)% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < 1 ↔ i ≤ 0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i - j < i0 ↔ i < j + i0; (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)% ⊦ i ≤ 0 → (i * j < 0 ↔ 0 < j ∧ i ≠ 0); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult