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Proof step 20 from proof add-a (previous step)

⊦ mkDecimal(i * 10 ^ abs(i2) * 10 ^ abs(i4) + (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2)) * 10 ^ abs(i0), abs(i0) + abs(i2) + abs(i4)) = mkDecimal((i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0)) * 10 ^ abs(i4) + i3 * 10 ^ (abs(i0) + abs(i2)), (abs(i0) + abs(i2)) + abs(i4))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 22:
⊦ mkDecimal(i * 10 ^ abs(i2) * 10 ^ abs(i4) + (i1 * 10 ^ abs(i4)) * 10 ^ abs(i0) + (i3 * 10 ^ abs(i2)) * 10 ^ abs(i0), abs(i0) + abs(i2) + abs(i4)) = mkDecimal((i * 10 ^ abs(i2) + i1 * 10 ^ abs(i0)) * 10 ^ abs(i4) + i3 * 10 ^ (abs(i0) + abs(i2)), (abs(i0) + abs(i2)) + abs(i4))

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [10 ^ abs(i0), i3 * 10 ^ abs(i2), i1 * 10 ^ abs(i4)] flags: rewrite

Additional information

Used terms: 10 ^ abs(i0), i3 * 10 ^ abs(i2), i1 * 10 ^ abs(i4)