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Proof step 7 from proof intshiftleft-is-mult-01 (previous step)

band(j, 31) ≠ 0 ⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31), band(j, 31) ≠ 0 ∧ ¬ i < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
i < 0 ⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31), band(j, 31) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)