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Proof step 51 from proof div-div-rec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 52:
⊦ i + j + i0 = (i + j) + i0
Proof step 53:
2 ^ i * (j1 + 2 * (i1 + 1)) + j0 < i, 2 ^ i * (j1 + 2 * (i1 + 1)) + j0 ≤ 0, 0 ≤ i, (2 * i1 + j1) + 1 < i, 2 ^ i * ((2 * i1 + j1) + 1) + j0 < 0, 2 * i1 + j1 < 0, j0 < i, j0 ≤ 0, abs(j1) < 2, i1 < i, i1 ≤ 0, j1 < i, j1 ≤ 0, abs(j0) < 2 ^ i, 0 < i ⊦ i1 = (2 ^ i * 2 * i1 + 2 ^ i * j1 + j0) / (2 * 2 ^ i)

Rule argument

spec: int-basic2 inst: name: add-a seq: ⊦ i + j + i0 = (i + j) + i0 subst: [i0, j, i] → [j0, 2 ^ i * j1, 2 ^ i * 2 * i1] flags: rewrite

Additional information

Used terms: j0, 2 ^ i * j1, 2 ^ i * 2 * i1