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Proof step 11 from proof intshiftright-ls-02 (previous step)

(~1 * 2 ^ band(j, 31)) % 2 ^ band(j, 31) = 0 ∧ ~1 * 2 ^ band(j, 31) < 0 ∧ i + 1 < 0 ∧ 0 < 2 ^ band(j, 31), i < 0, band(j, 31) < 32, 0 < band(j, 31), 0 < (~1 * 2 ^ band(j, 31)) / 2 ^ band(j, 31) + (i + 1) / 2 ^ band(j, 31) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

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