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Proof step 14 from proof cast-law-add-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
0 ≤ j, 0 ≤ j0, 0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i ⊦ cast(i, j + j0) = cast(i, j0 + j % 2 ^ i - 2 ^ i)

Rule argument

Additional information

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