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Proof step 6 from proof cast-mult-add-h-01 (previous step)

0 ≤ j - 1 ∧ 0 ≤ j0 + 2 ^ i ∧ 0 < i, 0 < 2 ^ i + j0, j0 < 0, 0 ≤ j, 0 < i ⊦ cast(i, j0 + 2 ^ i) = cast(i, j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j, 0 ≤ j0 + 2 ^ i, 0 < i, 0 ≤ j, j0 < 0, 0 < 2 ^ i + j0 ⊦ cast(i, j0 + 2 ^ i) = cast(i, j0)

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;