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Proof step 11 from proof cast-mult-add-h (previous step)

¬(~(2 ^ i) < i0 ∧ i0 < 0 ∧ 0 < i), i0 < 0, 0 ≤ i0 + 2 ^ i, 0 < i ⊦ cast(i, i0) = cast(i, i0 + 2 ^ i), 0 = i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
0 = i0 + 2 ^ i, 0 < i, i0 < 0 ⊦ 0 = i, cast(i, i0) = 0

Rule argument

Additional information

Used simplifier rules: cast-zero: ⊦ 0 < i → cast(i, 0) = 0;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i + j = j + i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ~ i < j ↔ 0 < j + i;