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Proof step 32 from proof cast-mod-neg-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
# int2bits(j) = i→n(i) + 1, 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, 0 < j + 2 ^ i, j < ~1 ⊦ i = 1, j = ~1, j = j % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = i + i0 ↔ j = i0;% ⊦ i + 0 = i;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ n→i(m + n) = n→i(m) + n→i(n);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;