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Proof step 10 from proof cast-mult-add (previous step)

i0 < 0 ∧ j1 < 0 ∧ 0 < i, 0 ≤ i, i0 < 2 ^ i + j1, i0 < i, i0 ≤ 0, 0 < 2 ^ i + j1, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < i ⊦ cast(i, 2 ^ i * (i0 + j) + j1) = cast(i, j1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
0 ≤ i, i0 < 2 ^ i + j1, 0 < 2 ^ i + j1, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < i, i0 < 0 ⊦ cast(i, 2 ^ i * (i0 + j) + j1) = cast(i, j1)

Rule argument

Additional information

Used simplifier rules: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < 0 ∧ 0 ≤ j → i < j;