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Proof step 25 from proof int2bits-rec-2pot-neg-02 (previous step)

¬ j % 2 ^ i < 0, # 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)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
# 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), j + 2 ^ i < j % 2 ^ i, 0 < j % 2 ^ i ⊦ 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, uint2bits(~(j % 2 ^ i)) = [], 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: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j → ¬ j < i;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);