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Proof step 2 from proof square-nls-02 (previous step)

i ≤ 0, 0 ≤ j, (j * (j + 1)) / 2 < i + j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ j ∧ i < 0 → ¬ (j * (j + 1)) / 2 < i + j

Rule argument

spec: int-div inst: name: square-nls-01 seq: ⊦ 0 ≤ j ∧ i < 0 → ¬ (j * (j + 1)) / 2 < i + j subst: [i, j] → [i, j] flags: rewrite, current

Additional information

Used simplifier rules: square-nls: ⊦ 0 ≤ j → ¬ (j * (j + 1)) / 2 < j;%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, j