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Proof step 5 from proof uint2bits-2pot-01 (previous step)

0 < j * 2 ^ i ∧ j * 2 ^ i ≠ 1, 0 < j, 0 ≤ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ uint2bits((j * 2 ^ i) / 2) + ((j * 2 ^ i) % 2 = 1) = uint2bits(j) + mklist(false, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < j, 0 ≤ i, 0 < 2 ^ i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 < j → uint2bits(j * 2 ^ i0) = uint2bits(j) + mklist(false, i→n(i0)) ⊦ j * 2 ^ i = 1, uint2bits((j * 2 ^ i) / 2) + ((j * 2 ^ i) % 2 = 1)' = uint2bits(j) + mklist(false, i→n(i))

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ bits + boolvar = bits + boolvar ';