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Proof step 13 from proof cast-add-2pot-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
0 ≤ j + 2 ^ (i - 1), 0 < 2 ^ i + j, j < 0, 0 < i, 0 < j + 2 ^ i, (j + 2 ^ i) % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, j + 2 ^ i) = j

Rule argument

Additional information

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