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Proof step 11 from proof square-ls-02 (previous step)

i + i * i < i + j * j, i < j, 0 ≤ i, 0 ≤ j, j * j + j ≤ i * i + i, 0 < j ⊦ j + j * j < i + j * j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: forward-lels seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [i, j, j0] → [j + j * j, i + i * i, i + j * j] flags: rewrite

Additional information

Used simplifier rules: square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%absle: ⊦ 0 ≤ i → abs(i) = i; 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%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: j + j * j, i + i * i, i + j * j