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Proof step 5 from proof snd-def (previous step)

⊦ ((m + n) * (m + n + 1)) / 2 + n - (maxenc(((m + n) * (m + n + 1)) / 2 + n) * (maxenc(((m + n) * (m + n + 1)) / 2 + n) + 1)) / 2 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ maxenc(((m + n) * (m + n + 1)) / 2 + n) = m + n

Rule argument

spec: nat-pair inst: name: max-square seq: ⊦ maxenc(((m + n) * (m + n + 1)) / 2 + n) = m + n subst: [n, m] → [n, m] flags: rewrite, current

Additional information

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