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Proof step 14 from proof intshiftrsign-2pot-neg (previous step)

j0 * 2 ^ j < 0 ∧ (j0 * 2 ^ j) % 2 = 0, 0 < j, j < 32, j0 * 2 ^ j < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ i % 2 ^ j0 = 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = i / 2 ^ j0 ⊦ (j0 * 2 ^ j) / 2 i>> (j - 1) = j0, ((j0 * 2 ^ j) / 2) % 2 ^ (j - 1) = 0, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 < j, j < 32, j0 * 2 ^ j < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ i % 2 ^ j0 = 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = i / 2 ^ j0 ⊦ j = 1, j0 * 2 ^ (j - 1) i>> (j - 1) = j0, (j0 * 2 ^ (j - 1)) % 2 ^ (j - 1) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (j * 2 ^ i) % 2 = 0;