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Proof step 22 from proof div-div-pred-01 (previous step)

j0 ≤ 0, i1 * 4 + j1 ≤ ~3, i1 * 4 + j1 < 0, abs(j0) < 2, abs(j1) < 4, i1 ≤ 0, j1 ≤ 0, j0 + (i1 * 4 + j1) * 2 < ~7, j0 + (i1 * 4 + j1) * 2 < 0 ⊦ i1 = (j0 + (i1 * 4 + j1) * 2) / 8

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 24:
j0 ≤ 0, i1 * 4 + j1 ≤ ~3, i1 * 4 + j1 < 0, abs(j0) < 2, abs(j1) < 4, i1 ≤ 0, j1 ≤ 0, j0 + (i1 * 4) * 2 + j1 * 2 < ~7, j0 + (i1 * 4) * 2 + j1 * 2 < 0 ⊦ i1 = (j0 + (i1 * 4) * 2 + j1 * 2) / 8

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [2, j1, i1 * 4] flags: rewrite

Additional information

Used terms: 2, j1, i1 * 4