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Proof step 3 from proof square-nle-01 (previous step)

(1 * (1 + 1)) / 2 < (n * (n + 1)) / 2 ↔ 1 < n ⊦ (n * (n + 1)) / 2 ≤ n ↔ n < 2

User applied rule simplifier

And obtained the following new goals

Proof step 4:
(n * n + n) / 2 ≠ 0 ∧ (n * n + n) / 2 ≠ 1 ↔ n ≠ 0 ∧ n ≠ 1 ⊦ (n * n + n) / 2 ≤ n ↔ n < 2

Rule argument

Additional information

Used simplifier rules: one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1%rsucc-02: ⊦ m * (n + 1) = m * n + m; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2