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Proof step 7 from proof uint2bits-div2pot-01 (previous step)

j = i0 * 2 ^ i + j0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 < 2 ^ i ∧ 0 ≤ j, j0 = 0, 0 < j, 0 ≤ i, 2 ^ i ≤ j ⊦ uint2bits(j) = butlastn(i→n(i), uint2bits(j)) + mklist(false, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 < 2 ^ i, 0 ≤ i0, 0 ≤ i, 0 < i0 ⊦ uint2bits(i0 * 2 ^ i) = butlastn(i→n(i), uint2bits(i0 * 2 ^ i)) + mklist(false, i→n(i))

Rule argument

Additional information

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