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Proof step 7 from proof cast-law-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

name: cast-mult-add rotate: F subst: [j0, j, i] → [j0, i0, i]

Additional information

Used terms: j0, i0, i