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Proof step 2 from proof to-empty2 (previous step)

σ to n = [] ⊦ n = 0, # σ < ⌜n⌝

User applied rule constructor cut

And closed the goal!

Rule argument

var: σ

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%to-empty-fin2: ⊦ n ≤ # x → (x to n = [] ↔ n = 0);%to-inf: ⊦ ⌜nf⌝ to n = ⌜nf to n⌝ ;%fin-empty: ⊦ ⌜x⌝ = [] ↔ x = [];%to-empty-inf: ⊦ nf to n = [] ↔ n = 0;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat