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Proof step 1 from proof cast-mult-add-h (conclusion)

⊦ j < 0 ∧ 0 ≤ j0 ∧ j0 < 2 ^ i ∧ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)