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Proof step 7 from proof square-ls-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs name: forward-lsle seq: ⊦ i < j ∧ j ≤ j0 → i < j0 subst: [i, j, j0] → [i + i * i, j + j * j, j + i * i] flags: <all paths>

Additional information

Used simplifier rules: square-le: ⊦ i * i ≤ j * j ↔ abs(i) ≤ abs(j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i + j ≤ i + j0 ↔ j ≤ j0; (s)% ⊦ 0 ≤ i → abs(i) = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i + j < i + i0 ↔ j < i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i + i * i, j + j * j, j + i * i