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Proof step 24 from proof square-le-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ i < j ∧ j ≤ j0 → i < j0

Rule argument

spec: int-abs name: forward-lsle seq: ⊦ i < j ∧ j ≤ j0 → i < j0 subst: [i, j, j0] → [j + j * j, i + i * i, i + j * j] 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%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss) Used terms: j + j * j, i + i * i, i + j * j