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Proof step 1 from proof square-le (conclusion)

⊦ m * (m + 1) ≤ n * (n + 1) ↔ m ≤ n

User applied rule insert lemma

And obtained the following new goals

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

Rule argument

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

Additional information

Used terms: n, m