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Proof step 18 from proof div-div-rec (previous step)

i1 * 2 + j1 < 0, 2 ^ i * ((i1 * 2 + j1) + 1) + j0 < 0, (i1 * 2 + j1) + 1 < i, 0 ≤ i, 2 ^ i * (2 * (i1 + 1) + j1) + (j0 - 1) < 0, 0 < i, abs(j0) < 2 ^ i, j1 ≤ 0, j1 < i, i1 ≤ 0, i1 < i, abs(j1) < 2, j0 ≤ 0, j0 < i ⊦ i1 = (2 ^ i * (2 * (i1 + 1) + j1) + j0 - 2 ^ i * 2) / (2 ^ i * 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ i * (j + j0) = i * j + i * j0
Proof step 20:
i1 * 2 + j1 < 0, 2 ^ i * ((i1 * 2 + j1) + 1) + j0 < 0, (i1 * 2 + j1) + 1 < i, 0 ≤ i, (2 ^ i * 2 * (i1 + 1) + 2 ^ i * j1) + (j0 - 1) < 0, 0 < i, abs(j0) < 2 ^ i, j1 ≤ 0, j1 < i, i1 ≤ 0, i1 < i, abs(j1) < 2, j0 ≤ 0, j0 < i ⊦ i1 = ((2 ^ i * 2 * (i1 + 1) + 2 ^ i * j1) + j0 - 2 ^ i * 2) / (2 ^ i * 2)

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [j1, 2 * (i1 + 1), 2 ^ i] flags: rewrite

Additional information

Used terms: j1, 2 * (i1 + 1), 2 ^ i