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Proof step 94 from proof cast-mod-neg-low (previous step)

¬ abs(j) < 2 ^ i, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0, 0 < i, j < 2 ^ (i - 1), 0 ≤ 2 ^ (i - 1) + j, j % 2 ^ i < j ⊦ j = j % 2 ^ i + 2 ^ i

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → ¬ 2 ^ i ≤ 2 ^ (i - 1);% ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;