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Proof step 13 from proof square-le-04 (previous step)

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