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Proof step 39 from proof mult-def-any (previous step)

i % 10 = 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)) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 41:
10 ≠ 0, ∃ j0. i = j0 * 10, ∀ 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)) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))

Rule argument

spec: int-div inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [10, i] flags: rewrite

Additional information

Used terms: 10, i