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Proof step 6 from proof square-interval (previous step)

n * (n + 1) < (m + 1) * ((m + 1) + 1), m < n + 1, n * (n + 1) + 2 * n0 < (n + 1) * (n + 2), m * (m + 1) ≤ n * (n + 1) + 2 * n0, n * (n + 1) + 2 * n0 < (m + 1) * (m + 2), n0 ≤ n ⊦ m = n

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: neq-01: ⊦ m ≠ n → (m < n + 1 ↔ m < n); from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%ls-02: ⊦ m < n → ¬ n < m; from specification nat-basic1 Used terms: m + 1, n