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Proof step 4 from proof cast-mult-add-h (previous step)

0 ≤ i, 0 < i, j0 < 2 ^ i, j < 0, 0 ≤ j0 ⊦ cast(i, (j + 1) * 2 ^ i + (j0 - 2 ^ i)) = cast(i, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ j < 0 ∧ j0 < 0 ∧ 0 < i → cast(i, j * 2 ^ i + j0) = cast(i, j0)
Proof step 6:
¬(j + 1 < 0 ∧ j0 - 2 ^ i < 0 ∧ 0 < i), 0 ≤ i, 0 < i, j0 < 2 ^ i, j < 0, 0 ≤ j0 ⊦ cast(i, (j + 1) * 2 ^ i + (j0 - 2 ^ i)) = cast(i, j0)
Proof step 16:
j + 1 < 0 ∧ j0 - 2 ^ i < 0 ∧ 0 < i, 0 ≤ i, 0 < i, j0 < 2 ^ i, j < 0, 0 ≤ j0 ⊦ cast(i, j0 - 2 ^ i) = cast(i, j0)

Rule argument

name: cast-mult-neg rotate: F subst: [j0, j, i] → [j0 - 2 ^ i, j + 1, i]

Additional information

Used terms: j0 - 2 ^ i, j + 1, i