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Proof step 35 from proof cast-mod-neg-low (previous step)

j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i ≠ 0, i→n(i) ≤ #(int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest), 0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 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 + 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
0 < i, j < 0, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 2 ^ (i - 1), 2 ^ (i - 1) + j < 0, i→n(i) ≤ # int2bits(j / 2 ^ i - 1) + # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i ≤ 0, j + 2 ^ i < i ⊦ 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 + 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → i→n(i + 1) = i→n(i) + 1;