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Proof step 55 from proof cast-mod-neg-high (previous step)

fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) ≠ [], 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→n(i) ≤ # int2bits(j / 2 ^ i - 1) + (# fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)))-1, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ i→n(i) = (# fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)))-1, j % 2 ^ i = 0, i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j / 2 ^ i - 1) + 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 56:
j + 2 ^ i ≤ 0, j + 2 ^ i < i, 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→n(i) ≤ (# fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1) + # int2bits(j / 2 ^ i - 1) ⊦ j % 2 ^ i = 0, i = 1, j = ~1, bits2int(lastn(i→n(i), int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest)) = j % 2 ^ i, fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) = [], i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)) - 1

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ n -1 = n - 1;