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Proof step 10 from proof square-interval (previous step)

2 * (j + 1) ≤ 2 * j0, 0 ≤ j0, 0 ≤ j, 0 ≤ i, 2 * j + 2 ≤ 2 * j0, (j * j + j) + 2 * j0 < 3 * i + i * i + 2, i * i + i ≤ (j * j + j) + 2 * j0, j0 ≤ j, i * i < 2 * i + i * i + 2 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: le-pos seq: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0) subst: [i0, j, i] → [j0, j + 1, 2] flags: rewrite, current

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%succ-01: ⊦ i + 1 ≤ j ↔ i < j; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); 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 Used terms: j0, j + 1, 2