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Proof step 2 from proof get-toinf (previous step)

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

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;%get-to: m < n, ¬ # σ < ⌜n⌝ ⊦ (σ to n)[m] = σ[m];%natinf freely generated by ∞, ⌜ ⌝;;%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat