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Proof step 77 from proof int2bits-add-low (previous step)

0 ≤ 2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0, j * 2 ^ i + j0 < 0, 0 < i, j < 0, j0 < 0, 0 < 2 ^ (i - 1) + j0 ⊦ i < n→i(# int2bits(~(j * 2 ^ i + j0))), sgn(uint2bits(2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0).rest) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
0 < i, j < 0, j0 < 0, 0 < 2 ^ (i - 1) + j0, n→i(# int2bits(~(j * 2 ^ i + j0))) ≤ i, 0 ≤ 2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0, j * 2 ^ i + j0 < 0 ⊦ sgn(uint2bits(2 ^ n→i(# int2bits(~(j * 2 ^ i + j0))) + j * 2 ^ i + j0).rest) = int2bits(j - 1) + fillsgn(i→n(i), int2bits(j0))

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;