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Proof step 8 from proof square-sqrt (previous step)

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) ⊦ mkDecimal(sqrt(mkDecimal(i * i, 2 * abs(i0)).int), mkDecimal(i * i, 2 * abs(i0)).scale / 2) = mkDecimal(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 10:
¬ ¬((i * i) % 10 = 0 ∧ 2 * abs(i0) ≠ 0 ∧ i * i ≠ 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) ⊦ mkDecimal(sqrt(mkDecimal(i * i, 2 * abs(i0)).int), mkDecimal(i * i, 2 * abs(i0)).scale / 2) = mkDecimal(i, i0)
Proof step 36:
¬((i * i) % 10 = 0 ∧ 2 * abs(i0) ≠ 0 ∧ i * i ≠ 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) ⊦ mkDecimal(sqrt(i * i), mkDecimal(i * i, 2 * abs(i0)).scale / 2) = mkDecimal(i, i0)

Rule argument

spec: decimal inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i subst: [j, i] → [2 * abs(i0), i * i] flags: rewrite

Additional information

Used terms: 2 * abs(i0), i * i