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Proof step 6 from proof int2bits-2pot-04 (previous step)

j < 0, 0 ≤ i, j * 2 ^ i < 0, j * 2 ^ i < i ⊦ j = 0, int2bits(j * 2 ^ i) = int2bits(j) + mklist(false, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j < 2 ^ i, 0 < 2 ^ i, 0 ≤ i, j < 0, j * 2 ^ i < i, j < i, j + 1 < 2 ^ i ⊦ int2bits(j * 2 ^ i) = int2bits(j) + mklist(false, i→n(i)), j = 0

Rule argument

Additional information

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