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Proof step 11 from proof cast-mult-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j subst: [j, i] → [j0, j * 2 ^ i] rotate: F spec: int-abs inst: name: zero-ge-01

Additional information

Used simplifier rules: ⊦ i < 0 → (i * j < 0 ↔ 0 < j);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j0, j * 2 ^ i