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Proof step 35 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
j < 0, 0 < i, 0 < j + 2 ^ i, j % 2 ^ i + 2 ^ (i - 1) < 0 ⊦ cast(i, j + 2 ^ i) = j % 2 ^ i + 2 ^ i

Rule argument

Additional information

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