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Proof step 91 from proof cast-mod-neg-low (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
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

Rule argument

Additional information

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