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Proof step 1 from proof ls-succ (conclusion)

⊦ n∞ < ⌜n + 1⌝ ↔ ¬ ⌜n⌝ < n∞

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: n∞

Additional information

Used simplifier rules: add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ;%less-inf1: ⊦ ¬ ∞ < n∞;%less-inf2: ⊦ ⌜m⌝ < ∞;%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ;%less-succ-leq: ⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝ ;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n;%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2;%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1;%natinf freely generated by ∞, ⌜ ⌝;;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2