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Proof step 117 from proof cast-mod-neg-high (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 118:
0 ≤ 2 ^ (i - 1) + j, 0 < i, j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, j < 2 ^ (i - 1) ⊦ j = j % 2 ^ i

Rule argument

Additional information

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