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Proof step 22 from proof shiftright-neg-div (previous step)

2 * 0 ≤ 2 * (2 ^ (abs(j) - 2) + (i - 1) / 2), 2 * 2 ^ (abs(j) - 2) + i < 0, 1 < abs(j), 0 ≤ 2 ^ (abs(j) - 2) + (i - 1) / 2, i < 0, 2 ^ (abs(j) - 2) + i < (i - 1) / 2, ∀ i, j0. i→n(j0) < i→n(j) → i + 2 ^ (abs(j0) - 1) < 0 → j0 = 0 ∨ i >> abs(j0) = (i + 1 - 2 ^ abs(j0)) / 2 ^ abs(j0) ⊦ (i - 1) / 2 >> (abs(j) - 1) = (i + 1 - 2 ^ abs(j)) / 2 ^ abs(j), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ i * (j + j0) = i * j + i * j0
Proof step 24:
2 * 0 ≤ 2 * 2 ^ (abs(j) - 2) + 2 * (i - 1) / 2, 2 * 2 ^ (abs(j) - 2) + i < 0, 1 < abs(j), 0 ≤ 2 ^ (abs(j) - 2) + (i - 1) / 2, i < 0, 2 ^ (abs(j) - 2) + i < (i - 1) / 2, ∀ i, j0. i→n(j0) < i→n(j) → i + 2 ^ (abs(j0) - 1) < 0 → j0 = 0 ∨ i >> abs(j0) = (i + 1 - 2 ^ abs(j0)) / 2 ^ abs(j0) ⊦ (i - 1) / 2 >> (abs(j) - 1) = (i + 1 - 2 ^ abs(j)) / 2 ^ abs(j), j = 0

Rule argument

seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [(i - 1) / 2, 2 ^ (abs(j) - 2), 2] rotate: F spec: int-mult inst: name: dist-rsplit

Additional information

Used terms: (i - 1) / 2, 2 ^ (abs(j) - 2), 2