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Proof step 6 from proof mult-def-any (previous step)

∀ 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)), i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1)
Proof step 8:
¬(i0 % 10 = 0 ∧ j0 ≠ 0), ∀ 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)), i % 10 = 0 ∧ j ≠ 0
Proof step 22:
i0 % 10 = 0 ∧ j0 ≠ 0, ∀ 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 / 10, abs(j0) - 1) = mkDecimal(i * i0, abs(j) + abs(j0)), i % 10 = 0 ∧ j ≠ 0

Rule argument

spec: decimal inst: name: mkDecimal-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1) subst: [j, i] → [j0, i0] flags: rewrite

Additional information

Used terms: j0, i0