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Proof step 11 from proof cast-if (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 < i, j % 2 ^ i + 2 ^ (i - 1) < 0, j < 0 ⊦ cast(i, j) = j % 2 ^ i + 2 ^ i

Rule argument

Additional information

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