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Proof step 9 from proof square-ls-03 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 10:
(m * (m + 1) + 2 * m0) / 2 < ((m + 1) * (m + 2)) / 2, m0 ≤ m, m ≤ n, ((m + 1) * (m + 2)) / 2 ≤ ((n + 1) * (n + 2)) / 2 ⊦ (m * (m + 1) + 2 * m0) / 2 < ((n + 1) * (n + 2)) / 2, n < m
Proof step 13:
m0 ≤ m, m ≤ n, ((m + 1) * (m + 2)) / 2 ≤ ((n + 1) * (n + 2)) / 2 ⊦ (m * (m + 1) + 2 * m0) / 2 < ((n + 1) * (n + 2)) / 2, n < m, (m * (m + 1) + 2 * m0) / 2 < ((m + 1) * (m + 2)) / 2

Rule argument

fma: (m * (m + 1) + 2 * m0) / 2 < ((m + 1) * (m + 2)) / 2

Additional information

Used formulas: (m * (m + 1) + 2 * m0) / 2 < ((m + 1) * (m + 2)) / 2