| 0 < j - 1, 0 < i, 0 < j, isSquare((i ^ (j - 1)-1 * i) * i), ∀ j0, i. i→n(j0) < i→n(j) → isSquare(i ^ j0) ∧ 0 < i ∧ 0 < j0 → isSquare(i) ∨ even(j0) ⊦ isSquare(i), even(j) |
0 < i, isSquare(i ^ (j - 2) * i * i), 1 < j, 0 < j, ∀ j0, i. i→n(j0) < i→n(j) → isSquare(i ^ j0) ∧ 0 < i ∧ 0 < j0 → isSquare(i) ∨ even(j0) ⊦ isSquare(i), even(j)
Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs%sub-pred: ⊦ i -1 = i - 1; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs