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Proof step 17 from proof dec2int-def-any (previous step)

i % 10 = 0, dec2int(mkDecimal(i / 10, abs(j) - 1)) = (i / 10) / 10 ^ (abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, (i / 10) / 10 ^ (abs(j) - 1) = i / 10 ^ abs(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 19:
10 ≠ 0, ∃ j0. i = j0 * 10, dec2int(mkDecimal(i / 10, abs(j) - 1)) = (i / 10) / 10 ^ (abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, (i / 10) / 10 ^ (abs(j) - 1) = i / 10 ^ abs(j)

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