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Proof step 11 from proof square-isSquare (previous step)

(i * i) % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → isSquare(mkDecimal(i1 * i1, 2 * abs(i0)).int) ⊦ i = 0, i0 = 0, isSquare(mkDecimal(i * i, 2 * abs(i0)).int)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int
Proof step 13:
(i * i) % 10 = 0 ∧ 2 * abs(i0) ≠ 0 ∧ i * i ≠ 0, (i * i) % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → isSquare(mkDecimal(i1 * i1, 2 * abs(i0)).int) ⊦ i = 0, i0 = 0, isSquare(mkDecimal((i * i) / 10, abs(2 * abs(i0)) - 1).int)

Rule argument

spec: decimal inst: name: intvalue-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int subst: [j, i] → [2 * abs(i0), i * i] flags: rewrite

Additional information

Used simplifier rules: two-zero: ⊦ 2 * i = 0 ↔ i = 0; from specification int-mult%abs-07: ⊦ abs(i) = 0 ↔ i = 0; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%square-zero: ⊦ i * i = 0 ↔ i = 0; from specification int-mult Used terms: 2 * abs(i0), i * i