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Proof step 9 from proof mult-a (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Proof step 11:
⊦ mkDecimal(i * i1 * i3, abs(i0) + abs(abs(i2) + abs(i4))) = (mkDecimal(i, i0) * mkDecimal(i1, i2)) * 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] → [abs(i2) + abs(i4), i1 * i3, i0, i] flags: rewrite, current

Additional information

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