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Proof step 7 from proof cast-law-mult-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
0 < i ⊦ cast(i, j + j0) = cast(i, cast(i, j) + cast(i, j0))
Proof step 9:
0 < i, 0 ≤ i, i0 < 2 ^ i + j1, i0 < i, i0 ≤ 0, 0 < 2 ^ i + j1, i0 * 2 ^ i + j1 < 0, j1 < 0, 0 < i ⊦ cast(i, (i0 * 2 ^ i + j1) * j0) = cast(i, cast(i, cast(i, i0 * 2 ^ i) + cast(i, j1)) * j0)

Rule argument

name: cast-law-add rotate: F subst: [j0, j, i] → [j1, i0 * 2 ^ i, i]

Additional information

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