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Proof step 24 from proof intshiftrsign-2pot-neg-01 (previous step)

¬ 2 * 2 ^ (j - 1) ≠ 0, ¬(0 < i0 + 1 - 2 ^ (j - 1) ∧ 0 < 2 ^ (j - 1)), 0 < j, j < 32, 0 ≤ j, i0 < 0, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = (i - (2 ^ j0 - 1)) / 2 ^ j0 ⊦ j = 1, (i0 + 1 - 2 ^ (j - 1)) / 2 ^ (j - 1) = ~(2 * (2 ^ (j - 1) - i0 + 1) + 1) / (2 * 2 ^ (j - 1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
2 ^ (j - 1) = 0, i0 < 0, 0 ≤ j, j < 32, 0 < j, ∀ i, j0. i→n(j0) < i→n(j) → true → i < 0 ∧ 0 < j0 ∧ j0 < 32 → i i>> j0 = (i - (2 ^ j0 - 1)) / 2 ^ j0 ⊦ j = 1, (1 + i0) / 0 = ((i0 + 1) * 2 - 1) / 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ ~(i - j) = j - i;% ⊦ i + ~ j = i - j;% ⊦ ~ i * j = ~(i * j);% ⊦ 0 - i = ~ i;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ ¬ 2 ^ i < 0;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 2 * i = 0 ↔ i = 0;