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Proof step 1 from proof mult-def-any (conclusion)

⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))

User applied rule induction

And obtained the following new goals

Proof step 2:
true, ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → mkDecimal(i1, j) * mkDecimal(i2, j0) = mkDecimal(i1 * i2, abs(j) + abs(j0)) ⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))

Rule argument

indvar: i→n(i) + i→n(i0) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i) + i→n(i0)