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Proof step 7 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i + j = j + i;% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;