| 10 ≠ 0, ∃ j0. i = j0 * 10, ∀ i1, i0. i→n(i1) < i→n(i) → true → even(mkDecimal(i1 * i1, 2 * abs(i0)).scale) ⊦ i = 0, i0 = 0, even(mkDecimal((i * i) / 10, 2 * abs(i0) - 1).scale) |
∀ i1, i0. i→n(i1) < i→n(j * 10) → true → even(mkDecimal(i1 * i1, 2 * abs(i0)).scale) ⊦ i0 = 0, j = 0, even(mkDecimal((j * j) * 10, 2 * abs(i0) - 1).scale)
Used simplifier rules: div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j; from specification int-div%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult