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Proof step 39 from proof int2bits-rec-2pot-neg-02 (previous step)

j / 2 ^ i - 1 < 0, true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest, 0 ≤ i, j < 0, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 0 < i ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = sgn(bitsinvert(uint2bits(abs(j / 2 ^ i - 1))) +1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
j / 2 ^ i < i, j / 2 ^ i ≤ 0, 0 < i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j < 0, 0 ≤ i, true ∈ fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest ⊦ sgn(bitsinvert(uint2bits(~(j / 2 ^ i))) + bitsinvert(fillsgn(i→n(i) + 1, uint2bits(~(j % 2 ^ i))).rest) +1) = sgn(bitsinvert(uint2bits(1 - j / 2 ^ i)) +1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + ~ j = i - j;% ⊦ ~(i - 1) = ~ i + 1;% ⊦ i < 0 → abs(i) = ~ i;