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Proof step 5 from proof square-ls-02 (previous step)

⊦ 0 ≤ i ∧ 0 ≤ j → (((i + 1) * ((i + 1) + 1)) / 2 < ((j + 1) * ((j + 1) + 1)) / 2 ↔ i < j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: nls: ⊦ ¬ i < j ∧ ¬ i0 < j0 → ¬ i + i0 < j + j0; 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%ls-add-both: ⊦ i < j → i1 + i < i1 + j; from specification int-basic2%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs Used terms: j + 1, i + 1