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Proof step 10 from proof square-inject (previous step)

((m0 + n0) * (m0 + n0 + 1)) % 2 = 0 ∧ 2 ≠ 0, ((m + n) * (m + n + 1)) % 2 = 0 ∧ 2 ≠ 0, (m + n) * (m + n + 1) + 2 * n = (m0 + n0) * (m0 + n0 + 1) + 2 * n0 ⊦ ((m + n) * (m + n + 1)) / 2 + n = ((m0 + n0) * (m0 + n0 + 1)) / 2 + n0 ↔ m = m0 ∧ n = n0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: nat-mult inst: name: square-inject seq: m * (m + 1) + 2 * m0 = n * (n + 1) + 2 * n0, m0 ≤ m, n0 ≤ n ⊦ m = n ∧ m0 = n0 subst: [m, m0, n, n0] → [n + m, n, n0 + m0, n0] flags:

Additional information

Used simplifier rules: square-even-02: ⊦ (m * m + m) % 2 = 0;%square-even-02: ⊦ (m * m + m) % 2 = 0;%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%rsucc-02: ⊦ m * (n + 1) = m * n + m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%succ: ⊦ (* m0) * m + m = (m0 + 1) * m; from specification nat-mult%lep: ⊦ m ≤ m + n; from specification nat Used terms: n + m, n, n0 + m0, n0