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Proof step 9 from proof square-nle-01 (previous step)

n * n + n = m0 * 2 + n0, n0 < 2, m0 ≤ n ⊦ m0 = 0, m0 = 1, n = 0, n = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-basic name: twols-02 seq: ⊦ m ≠ 0 → (m < 2 ↔ m = 1) subst: [m] → [n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m * m + m ≠ 2 * n + 1; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ m ≤ n → (n * n + n = m * 2 ↔ n = m ∧ n < 2); (s)% ⊦ m ≠ 0 → (m < 2 ↔ m = 1); (s) Used terms: n0