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Proof step 1 from proof le-plus (conclusion)

⊦ 0 ≤ i ∧ 0 < j → i ^2 < (i + j)^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: Square-def: ⊦ i ^2 = i * i;%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j); from specification int-mult