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Proof step 3 from proof square-nle-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1

Rule argument

spec: int-abs inst: name: forward-lele seq: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1 subst: [j, j0, j1] → [((j + 1) * (j + 2)) / 2, i + j, j] flags: rewrite

Additional information

Used simplifier rules: square-nle-01: ⊦ 0 ≤ j → ¬ ((j + 1) * (j + 2)) / 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%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: ((j + 1) * (j + 2)) / 2, i + j, j