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Proof step 17 from proof square-sqrt (previous step)

i % 10 = 0, 0 < i, ∀ i1, i0. i→n(i1) < i→n(i) → 0 ≤ i1 → mkDecimal(sqrt(mkDecimal(i1 * i1, 2 * abs(i0)).int), mkDecimal(i1 * i1, 2 * abs(i0)).scale / 2) = mkDecimal(i1, i0) ⊦ i = 0, i0 = 0, mkDecimal(sqrt(mkDecimal((i * i) / 10, 2 * abs(i0) - 1).int), mkDecimal((i * i) / 10, 2 * abs(i0) - 1).scale / 2) = mkDecimal(i, i0)

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, 0 < i, ∀ i1, i0. i→n(i1) < i→n(i) → 0 ≤ i1 → mkDecimal(sqrt(mkDecimal(i1 * i1, 2 * abs(i0)).int), mkDecimal(i1 * i1, 2 * abs(i0)).scale / 2) = mkDecimal(i1, i0) ⊦ i = 0, i0 = 0, mkDecimal(sqrt(mkDecimal((i * i) / 10, 2 * abs(i0) - 1).int), mkDecimal((i * i) / 10, 2 * abs(i0) - 1).scale / 2) = mkDecimal(i, i0)

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