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Proof step 8 from proof intshiftrsign-abs-le (previous step)

abs(i) < abs(i i>> band(j, 31)) ⊦ band(j, 31) = 0, ¬ i < 0 ∧ ¬ band(j, 31) ≤ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i < 0, 0 < abs(i i>> band(j, 31)) + i ⊦ band(j, 31) = 0

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%band-notneg: ⊦ 0 ≤ i → ¬ band(i, j) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);