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Proof step 71 from proof cast-mod-neg-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 72:
i→n(i) = # fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest, j + 2 ^ i < i, j + 2 ^ i ≤ 0, 2 ^ (i - 1) + j < 0, j < 2 ^ (i - 1), j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0, 0 < i, # int2bits(j % 2 ^ i) ≤ i→n(i), j + 2 ^ i < j % 2 ^ i, 0 < j % 2 ^ i ⊦ bits2int(fillsgn(i→n(i) + 1, int2bits(j % 2 ^ i)).rest) = j % 2 ^ i + 2 ^ i, j = ~1, i = 1, j % 2 ^ i = 0, ~1 = j % 2 ^ i

Rule argument

Additional information

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