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Proof step 2 from proof pot-add-min (previous step)

0 ≤ j, 0 ≤ j0 ⊦ i * 10 ^ j + i0 * 10 ^ j0 = (i * 10 ^ (j - min(j, j0)) + i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 4:
0 ≤ j, 0 ≤ j0 ⊦ i * 10 ^ j + i0 * 10 ^ j0 = (i * 10 ^ (j - min(j, j0))) * 10 ^ min(j, j0) + (i0 * 10 ^ (j0 - min(j, j0))) * 10 ^ min(j, j0)

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [10 ^ min(j, j0), i0 * 10 ^ (j0 - min(j, j0)), i * 10 ^ (j - min(j, j0))] flags: rewrite

Additional information

Used terms: 10 ^ min(j, j0), i0 * 10 ^ (j0 - min(j, j0)), i * 10 ^ (j - min(j, j0))