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Proof step 12 from proof intshiftrsign-2pot-neg-01 (previous step)

j1 = ~1, 0 < j, abs(j1) < 2, i0 < j, i0 ≤ 0, j1 < j, j1 ≤ 0, j < 32, i0 * 2 + j1 < ~1, i0 * 2 + j1 < 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 * (i0 + 1) + j1 - 2 ^ j) / 2 ^ j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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 * (i0 + 1) - 1 + 2 ^ j) / 2 ^ j

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i - i1 - j = i - i1 + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i < 0 ⊦ (* i) + j = j - ~ i;