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Proof step 7 from proof cast-mult-neg (previous step)

j0 < 0 ∧ j0 % 2 ^ i < ~(2 ^ (i - 1)) ∧ 0 < i, j < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 % 2 ^ i < 0 ⊦ cast(i, j * 2 ^ i + j0) = j0 % 2 ^ i + 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j < 0, j0 < 0, 0 < i, 2 ^ (i - 1) + j0 % 2 ^ i < 0 ⊦ cast(i, j * 2 ^ i + j0) = j0 % 2 ^ i + 2 ^ i

Rule argument

Additional information

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