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Proof step 21 from proof cast-law-add-one (previous step)

2 ^ i ≠ 0, ∃ j0. j = j0 * 2 ^ i, 0 < i, j < 0 ⊦ cast(i, j + j0) = cast(i, cast(i, j) + j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
0 < i, j1 * 2 ^ i < 0 ⊦ cast(i, j1 * 2 ^ i + j0) = cast(i, j0)

Rule argument

Additional information

Used simplifier rules: cast-mult-2pot: ⊦ 0 < i → cast(i, j * 2 ^ i) = 0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;