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Proof step 7 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, i0 * 2 ^ i + j1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j1 < 0, 0 < i, 0 < 2 ^ i + j1 ⊦ 0 = i, cast(i, j * 2 ^ i + j1) = cast(i, j1)

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i * 0 = 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + 0 = i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 1 * i = i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ ¬ i < j ↔ j ≤ i;