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Proof step 1 from proof encode-zero (conclusion)

⊦ encode(m, n) = 0 ↔ m = 0 ∧ n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n

Rule argument

spec: <toplevel> name: encode-def seq: ⊦ encode(m, n) = ((m + n) * (m + n + 1)) / 2 + n subst: [n, m] → [n, m] flags: <all paths>

Additional information

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