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Proof step 5 from proof cast-law-mult-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 7:
0 ≤ j1, 0 < j1, j1 < 2 ^ i, 0 ≤ i, 0 ≤ i0, 0 < i ⊦ cast(i, (i0 * 2 ^ i) * j0 + j1 * j0) = cast(i, cast(i, j1) * j0)

Rule argument

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

Additional information

Used terms: j0, j1, i0 * 2 ^ i