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Proof step 31 from proof cast-mod-neg-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
i→n(i) ≤ # int2bits(j), 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, 0 < j + 2 ^ i ⊦ i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j))) = j % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;