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Proof step 16 from proof mult-dist (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ mkDecimal(i, j) + mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) + i0 * 10 ^ abs(j), abs(j) + abs(j0))
Proof step 18:
⊦ mkDecimal(i * (i1 * 10 ^ abs(i4) + i3 * 10 ^ abs(i2)), abs(i0) + abs(i2) + abs(i4)) = mkDecimal((i * i1) * 10 ^ abs(abs(i0) + abs(i4)) + (i * i3) * 10 ^ abs(abs(i0) + abs(i2)), abs(abs(i0) + abs(i2)) + abs(abs(i0) + abs(i4)))

Rule argument

spec: inst: name: add-def-any seq: ⊦ mkDecimal(i, j) + mkDecimal(i0, j0) = mkDecimal (i * 10 ^ abs(j0) + i0 * 10 ^ abs(j), abs(j) + abs(j0)) subst: [j0, i0, j, i] → [abs(i0) + abs(i4), i * i3, abs(i0) + abs(i2), i * i1] flags: rewrite, current

Additional information

Used terms: abs(i0) + abs(i4), i * i3, abs(i0) + abs(i2), i * i1