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Proof step 7 from proof cast-law-neg-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
0 ≤ j, 0 < i, j % 2 ^ i < 2 ^ (i - 1) ⊦ cast(i, ~ j) = cast(i, ~(j % 2 ^ i))

Rule argument

Additional information

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