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Proof step 10 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 ≤ j + 2 ^ (i - 1), 0 < 2 ^ i + j, j < 0, 0 < i, 0 < j + 2 ^ i ⊦ cast(i, j + 2 ^ i) = j

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;