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Proof step 34 from proof mult-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(0 * 10) → true → mkDecimal(i1, j) * mkDecimal(i2, j0) = mkDecimal(i1 * i2, abs(j) + abs(j0)) ⊦ j0 = 0, abs(j) + abs(j0) = 0, mkDecimal(0, mkDecimal(i, j).scale) = mkDecimal(0, abs(j) + abs(j0) - 1), i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal inst: name: mkDecimal-zero seq: ⊦ mkDecimal(0, j) = mkDecimal(0, 0) subst: [j] → [mkDecimal(i, j).scale] flags: rewrite

Additional information

Used terms: mkDecimal(i, j).scale