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Proof step 27 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: 0 ≤ i, 0 < j ⊦ (2 * i + 1) / (2 * j) = i / j subst: [j, i] → [2 ^ (j - 1), 2 ^ (j - 1) - i0 + 1] rotate: F spec: int-div inst: name: div-twoodd

Additional information

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