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Proof step 37 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(i * i), mkDecimal(i * i, 2 * abs(i0)).scale / 2) = mkDecimal(i, i0), i = 0, i0 ≠ 0 ∧ i % 10 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: mod-square-10: ⊦ (i * i) % 10 = 0 ↔ i % 10 = 0; from specification int-gcd%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%two-zero: ⊦ 2 * i = 0 ↔ i = 0; from specification int-mult%abs-07: ⊦ abs(i) = 0 ↔ i = 0; from specification int-abs Used terms: 2 * abs(i0), i * i