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Proof step 3 from proof zero-ge-add-02 (previous step)

i * j0 + j * j0 < j0, i * j0 + j * j0 < i + j, i * j0 + j * j0 < 0, 0 < j0, (i * j0 + j * j0) + 1 < j0, 0 ≤ i + j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 5:
(i + j) * j0 + 1 < j0, 0 < j0, (i + j) * j0 < 0, (i + j) * j0 < i + j, (i + j) * j0 < j0, 0 ≤ i + j ⊦

Rule argument

spec: <toplevel> name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [i0, j, i] → [j, j0, i] flags: <rotated> <all paths>

Additional information

Used terms: j, j0, i