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Proof step 11 from proof cast-law-neg-pos (previous step)

j = i0 * 2 ^ i + j0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 ≤ i0 ∧ 0 < 2 ^ i, 0 ≤ j, 0 < i, 2 ^ (i - 1) ≤ j0 ⊦ cast(i, ~ j) = cast(i, 2 ^ i - j0)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: cast-mult-neg-02: ⊦ 0 < i → cast(i, ~(j * 2 ^ i + j0)) = cast(i, ~ j0);%cast-sub-2pot: ⊦ 0 < i → cast(i, 2 ^ i - j0) = cast(i, ~ j0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;