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Proof step 15 from proof cast-if (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
j < 0, 0 ≤ 2 ^ (i - 1) + j % 2 ^ i, 0 < i ⊦ cast(i, j) = j % 2 ^ i

Rule argument

Additional information

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