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Proof step 10 from proof divmod2-2pot-neg (previous step)

(i0 * 2 ^ i) % 2 = 0 ∧ j0 - 1 < 0 ∧ i0 * 2 ^ i < 0 ∧ 0 < 2, 0 ≤ i, i0 < i, i0 ≤ 0, j0 < i, j0 ≤ 0, i0 * 2 ^ i + j0 < 0, abs(j0) < 2 ^ i, 1 < i, 0 < i ⊦ ((j0 - 1) / 2) % 2 = ((j0 - 1) / 2 + (i0 * 2 ^ i) / 2) % 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1)
Proof step 12:
0 < i, (i0 * 2 ^ i) % 2 = 0 ∧ j0 - 1 < 0 ∧ i0 * 2 ^ i < 0 ∧ 0 < 2, 0 ≤ i, i0 < i, i0 ≤ 0, j0 < i, j0 ≤ 0, i0 * 2 ^ i + j0 < 0, abs(j0) < 2 ^ i, 1 < i, 0 < i ⊦ ((j0 - 1) / 2) % 2 = ((j0 - 1) / 2 + i0 * 2 ^ (i - 1)) % 2

Rule argument

spec: int-pot inst: name: div2-2pot-04 seq: ⊦ 0 < j → (i * 2 ^ j) / 2 = i * 2 ^ (j - 1) subst: [j, i] → [i, i0] flags: rewrite, current

Additional information

Used terms: i, i0