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Proof step 5 from proof cast-mult-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j < 0 ∧ j0 < 0 ∧ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)
Proof step 7:
¬(i0 < 0 ∧ j1 < 0 ∧ 0 < i), 0 ≤ i, i0 < 2 ^ i + j1, i0 < i, i0 ≤ 0, 0 < 2 ^ i + j1, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < i ⊦ cast(i, 2 ^ i * (i0 + j) + j1) = cast(i, i0 * 2 ^ i + j1)
Proof step 10:
i0 < 0 ∧ j1 < 0 ∧ 0 < i, 0 ≤ i, i0 < 2 ^ i + j1, i0 < i, i0 ≤ 0, 0 < 2 ^ i + j1, j1 < 0, i0 * 2 ^ i + j1 < 0, 0 < i ⊦ cast(i, 2 ^ i * (i0 + j) + j1) = cast(i, j1)

Rule argument

name: cast-mult-neg rotate: F subst: [j0, j, i] → [j1, i0, i]

Additional information

Used terms: j1, i0, i