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Proof step 1 from proof square-nle-01 (conclusion)

⊦ (n * (n + 1)) / 2 ≤ n ↔ n < 2

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ (m * (m + 1)) / 2 < (n * (n + 1)) / 2 ↔ m < n
Proof step 3:
(1 * (1 + 1)) / 2 < (n * (n + 1)) / 2 ↔ 1 < n ⊦ (n * (n + 1)) / 2 ≤ n ↔ n < 2

Rule argument

spec: nat-div inst: name: square-ls-02 seq: ⊦ (m * (m + 1)) / 2 < (n * (n + 1)) / 2 ↔ m < n subst: [m, n] → [1, n] flags: current, []

Additional information

Used terms: 1, n