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Proof step 14 from proof pot-isSquare (previous step)

1 < abs(j - 2), 0 < i, isSquare(i ^ (j - 2) * i * i), 1 < j, 0 < j, j ≤ abs(j - 2), ∀ j0, i. i→n(j0) < i→n(j) → isSquare(i ^ j0) ∧ 0 < i ∧ 0 < j0 → isSquare(i) ∨ even(j0) ⊦ j = 2, isSquare(i), even(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [j - 2] flags: rewrite

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1 Used terms: j - 2