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Proof step 8 from proof cast-mult-add-h (previous step)

j0 = i0 + 2 ^ i, 0 ≤ j0, j0 < 2 ^ i, 0 < i ⊦ 0 = i, cast(i, i0) = cast(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
i0 < 0, 0 ≤ i0 + 2 ^ i, 0 < i ⊦ cast(i, i0) = cast(i, i0 + 2 ^ i), 0 = i

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j < j ↔ i < 0;