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Proof step 88 from proof cast-mod-neg-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 89:
i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j % 2 ^ i < ~1, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < j % 2 ^ i, j + 2 ^ i ≤ 0, j + 2 ^ i < i, j % 2 ^ i < 0 ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest) = j % 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → n→i(i→n(i)) = i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;