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Proof step 2 from proof add-less-fin-01 (previous step)

⊦ n∞ = ⌜0⌝ , ⌜n⌝ < n∞ + ⌜n⌝

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: n∞

Additional information

Used simplifier rules: gen: ⊦ ;%disj: ⊦ ⌜m⌝ ≠ ∞;%add-inf2: ⊦ ⌜m⌝ + ∞ = ∞;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%less-inf2: ⊦ ⌜m⌝ < ∞;%inj: ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0;%ls-natinf-to-nat-1-2: ⊦ ⌜n⌝ < ⌜m⌝ + ⌜n0⌝ ↔ n < m + n0;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic