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Proof step 37 from proof cast-mod-neg-high (previous step)

# int2bits(j) = i→n(i) + 1, 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(int2bits(j).rest) = j % 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
# int2bits(j) = i→n(i) + 1, 0 < j + 2 ^ i, j < j % 2 ^ i, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < 0, 0 < i, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0 ⊦ bits2int(int2bits(j).rest) = j % 2 ^ i, j = ~1, i = 1

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;