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Proof step 17 from proof div-add1-negpos-neg-01 (previous step)

i1 * j + i2 * j + j0 = i0 * j + j1, i0 + 1 < j, j1 + 1 < j, 2 + i0 * j + j1 < j, i0 * j + j1 < j0, i0 * j + j1 < j, i0 * j + j1 < 0, i0 < j0, i0 < j, i0 ≤ 0, j1 < j0, j1 < j, j1 ≤ 0, 2 + i1 * j + i2 * j < j, i1 * j + i2 * j < 0, i1 + 1 < j0, j + i1 * j < j0, 0 ≤ i2 * j + j0, i1 * j + i2 * j < ~1, 0 < j0, j0 < j, i1 < j, i1 < 0, j + i1 * j ≤ 0, 1 < j, 0 < j, 0 ≤ i2, i1 < j0, 2 + i1 < j, (i1 * j + i2 * j) + 1 < j0, i1 * j + i2 * j < j0, i1 * j + i2 * j < j, i1 * j < j0, abs(j1) < j, (i0 * j + j1) + 1 < j0, j1 ≤ j0 ⊦ i0 = i1 + i2 + 1, j = 1, j0 = 0, j0 < j1 + j ∧ (i2 + i1) * j + j0 = i0 * j + j1, j * (i2 + i1) + j0 = i0 * j + j1 ∧ j1 + j ≤ j0 ∧ j0 < 2 * j + j1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, i1, i2] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i1, i2