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Proof step 19 from proof cast-law-mult-one (previous step)

0 ≤ j1 + 2 ^ i, 0 < i, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < 2 ^ i + j1, i0 ≤ 0, i0 < i, i0 < 2 ^ i + j1, 0 ≤ i, i0 * 2 ^ i < 2 ^ i ⊦ cast(i, j1 * j0) = cast(i, (j1 + 2 ^ i) * j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 21:
0 ≤ j1 + 2 ^ i, 0 < i, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < 2 ^ i + j1, i0 ≤ 0, i0 < i, i0 < 2 ^ i + j1, 0 ≤ i, i0 * 2 ^ i < 2 ^ i ⊦ cast(i, j1 * j0) = cast(i, j1 * j0 + 2 ^ i * j0)

Rule argument

seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j0, 2 ^ i, j1] rotate: F spec: int-mult inst: name: dist-lsplit

Additional information

Used terms: j0, 2 ^ i, j1