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Proof step 9 from proof cast-law-neg-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
0 ≤ j, 0 < i, 2 ^ (i - 1) ≤ j % 2 ^ i ⊦ cast(i, ~ j) = cast(i, 2 ^ i - j % 2 ^ i)

Rule argument

Additional information

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