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Proof step 15 from proof div-div-rec (previous step)

j + 1 = 2 ^ i * (2 * (i1 + 1) + j1) + j0, i1 * 2 + j1 < 0, 2 ^ i * ((i1 * 2 + j1) + 1) + j0 < 0, (i1 * 2 + j1) + 1 < i, 0 ≤ i, j < 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 16:
⊦ i + (* j) = i0 + (* j0) ↔ i = i0 + (j0 - j)
Proof step 17:
j = 2 ^ i * (2 * (i1 + 1) + j1) + (j0 - 1), i1 * 2 + j1 < 0, 2 ^ i * ((i1 * 2 + j1) + 1) + j0 < 0, (i1 * 2 + j1) + 1 < i, 0 ≤ i, j < 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)

Rule argument

spec: int-abs inst: name: numadd seq: ⊦ i + (* j) = i0 + (* j0) ↔ i = i0 + (j0 - j) subst: [j0, i0, j, i] → [j0, 2 ^ i * (2 * (i1 + 1) + j1), 1, j] flags: rewrite

Additional information

Used terms: j0, 2 ^ i * (2 * (i1 + 1) + j1), 1, j