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Proof step 77 from proof cast-mod-neg-low (previous step)

¬ j % 2 ^ i < ~1, i→n(i) = # int2bits(j % 2 ^ i).rest, i→n(i) < # int2bits(j % 2 ^ i), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(int2bits(j % 2 ^ i).rest) = j % 2 ^ i + 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
i→n(i) = # int2bits(j % 2 ^ i).rest, i→n(i) < # int2bits(j % 2 ^ i), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, j + 2 ^ i ≤ 0, j + 2 ^ i < i, ~1 ≤ j % 2 ^ i ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(int2bits(j % 2 ^ i).rest) = j % 2 ^ i + 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;