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Proof step 22 from proof int2bits-rec-2pot-neg-02 (previous step)

# uint2bits(~(j % 2 ^ i)) ≤ i→n(i) + 1 ∧ uint2bits(~(j % 2 ^ i)) ≠ [], 0 ≤ i, j < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 < i, # uint2bits(~(j % 2 ^ i)) ≤ i→n(i) ⊦ j % 2 ^ i = 0, sgn ( bitsinvert(uint2bits(~(j / 2 ^ i))) +1 + (mklist(uint2bits(~(j % 2 ^ i)).first, i→n(i) + 1 - # uint2bits(~(j % 2 ^ i))) + uint2bits(~(j % 2 ^ i))).rest) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, true ∈ (mklist(uint2bits(~(j % 2 ^ i)).first, i→n(i) + 1 - # uint2bits(~(j % 2 ^ i))) + uint2bits(~(j % 2 ^ i))).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
# uint2bits(~(j % 2 ^ i)) ≤ i→n(i) + 1, 0 ≤ i, j < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 < i, # uint2bits(~(j % 2 ^ i)) ≤ i→n(i) ⊦ uint2bits(~(j % 2 ^ i)) = [], j % 2 ^ i = 0, sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) +1 + mklist(uint2bits(~(j % 2 ^ i)).first, i→n(i) - # uint2bits(~(j % 2 ^ i))) + uint2bits(~(j % 2 ^ i))) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, true ∈ uint2bits(~(j % 2 ^ i)), true ∈ mklist(uint2bits(~(j % 2 ^ i)).first, i→n(i) - # uint2bits(~(j % 2 ^ i)))

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ (boolvar ' + bits).rest = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ mklist(boolvar, 1) = boolvar ';% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;