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Proof step 12 from proof mult-dist (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Proof step 14:
⊦ 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, i0) * mkDecimal(i3, i4)

Rule argument

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

Additional information

Used terms: i2, i1, i0, i