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Proof step 41 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
j < 0, 0 < i, 0 < j + 2 ^ i, 0 < 2 ^ i + j, j + 2 ^ (i - 1) < 0, 2 ^ (i - 1) ≤ (2 ^ i + j) % 2 ^ i ⊦ cast(i, j + 2 ^ i) = j + 2 ^ i

Rule argument

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + 1 ≤ j ↔ i < j;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;