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

⊦ m * (m + 1) ≤ (n + 1) * (n + 2) ↔ m ≤ n + 1

User applied rule apply lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: square-le seq: ⊦ m * (m + 1) ≤ n * (n + 1) ↔ m ≤ n subst: [m, n] → [m, n + 1]

Additional information

Used terms: m, n + 1