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Proof step 11 from proof intshiftrsign-abs-le (previous step)

i < 0 ∧ 0 < band(j, 31) ∧ band(j, 31) < 32, i < 0, 0 < abs((i - (2 ^ band(j, 31) - 1)) / 2 ^ band(j, 31)) + i ⊦ band(j, 31) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
band(j, 31) < 32, i < 0, 0 < band(j, 31), 0 < abs(i + 1 - 2 ^ band(j, 31)) / 2 ^ band(j, 31) + i ⊦ band(j, 31) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ abs(2 ^ i) = 2 ^ i;%j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j);% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);% ⊦ i - (j - j0) = i + j0 - j;