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Proof step 2 from proof n2s-length-03 (previous step)

100 ≤ m, m < 1000 ⊦ # n→s(m) = 3, m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 10 ≤ n → n→s(n) = n→s(n / 10) + n→s(n % 10)
Proof step 4:
10 ≤ m, 100 ≤ m, m < 1000 ⊦ #(n→s(m / 10) + n→s(m % 10)) = 3, m = 0

Rule argument

spec: inst: name: n2s-rec seq: ⊦ 10 ≤ n → n→s(n) = n→s(n / 10) + n→s(n % 10) subst: [n] → [m] flags: rewrite, current

Additional information

Used simplifier rules: n2s-length: ⊦ m < 10 → # n→s(m) = 1;%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat Used terms: m