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Proof step 7 from proof cast-if (previous step)

¬ 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 8:
0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i, 0 ≤ j ⊦ j % 2 ^ i = cast(i, j) + 2 ^ i

Rule argument

Additional information

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