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Proof step 3 from proof square-nls-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic1 inst: name: trans seq: ⊦ i < j ∧ j < j0 → i < j0 subst: [i, j, j0] → [(j * (j + 1)) / 2, i + j, j] flags: rewrite

Additional information

Used simplifier rules: square-nls: ⊦ 0 ≤ j → ¬ (j * (j + 1)) / 2 < j;%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%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs Used terms: (j * (j + 1)) / 2, i + j, j