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Proof step 17 from proof uint2bits-2pot-neg-mone (previous step)

uint2bits(j * 2 ^ (i - 1) - 1) = uint2bits(j - 1) + mklist(true, i→n(i - 1)), 0 < j, 0 < i, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ 2 ^ (i - 1) * j = 1, uint2bits(2 ^ (i - 1) * j - 1) + true ' = uint2bits(j - 1) + mklist(true, i→n(i))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
uint2bits(j * 2 ^ (i - 1) - 1) = uint2bits(j - 1) + mklist(true, i→n(i - 1)), 0 < i, 0 < j, ∀ j, i0. i→n(i0) < i→n(i) → 0 < j ∧ 0 < i0 → uint2bits(j * 2 ^ i0 - 1) = uint2bits(j - 1) + mklist(true, i→n(i0)) ⊦ 2 ^ (i - 1) * j = 1, mklist(true, i→n(i - 1)) + true ' = mklist(true, i→n(i))

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ i * j = j * i;