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Proof step 2 from proof toinf-to-leq (previous step)

⊦ (σ to∞ n∞) to m = σ to m, n∞ < ⌜m⌝ , # σ < n∞, # σ < ⌜m⌝

User applied rule constructor cut

And closed the goal!

Rule argument

var: n∞

Additional information

Used simplifier rules: toinf-inf: ⊦ σ to∞ ∞ = σ;%toinf-fin: ⊦ σ to∞ ⌜n⌝ = σ to n;%to-to-leq: ¬ # σ < ⌜n⌝ ⊦ m ≤ n → σ to n to m = σ to m;%natinf freely generated by ∞, ⌜ ⌝;;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat