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Proof step 5 from proof square-ls-03 (previous step)

m0 ≤ m, m ≤ n ⊦ (m * (m + 1)) / 2 + m0 < ((n + 1) * (n + 2)) / 2, n < m, ((n + 1) * (n + 2)) / 2 < ((m + 1) * (m + 2)) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m < n ↔ ¬ n ≤ m
Proof step 7:
((m + 1) * (m + 2)) / 2 ≤ ((n + 1) * (n + 2)) / 2, m ≤ n, m0 ≤ m ⊦ n < m, (m * (m + 1)) / 2 + m0 < ((n + 1) * (n + 2)) / 2

Rule argument

spec: nat name: lels seq: ⊦ m < n ↔ ¬ n ≤ m subst: [n, m] → [((m + 1) * (m + 2)) / 2, ((n + 1) * (n + 2)) / 2] flags: <all paths>

Additional information

Used terms: ((m + 1) * (m + 2)) / 2, ((n + 1) * (n + 2)) / 2