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Proof step 1 from proof square-two (conclusion)

⊦ m ≤ n → (n * n + n = m * 2 ↔ ¬ ¬(n = m ∧ n < 2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
n * n + n = m * 2, m ≤ n ⊦ n = m ∧ m < 2

Rule argument

Additional information

Used simplifier rules: coef-17: ⊦ m * n + n = m1 * n ↔ ¬ ¬(m + 1 = m1 ∨ n = 0);%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;%twols-02: ⊦ m ≠ 0 → (m < 2 ↔ m = 1); from specification nat-basic1%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-num-04: n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0; from specification nat