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Proof step 3 from proof append-toinf-ls (previous step)

⊦ σ + σ0 to∞ n∞ = σ to∞ n∞, # 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;%append-cancel-l-02: ⊦ σ0 + σ = σ0 ↔ σ = [] ∨ ¬ finp(σ0);%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%toinf-fin: ⊦ σ to∞ ⌜n⌝ = σ to n;%append-to-ls: ⊦ ¬ # σ < ⌜n⌝ → σ + σ0 to n = σ to n;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%natinf freely generated by ∞, ⌜ ⌝;;% ⊦ n∞ < ∞ ↔ n∞ ≠ ∞; (s)%stream-fin-forward: ⊦ finp(σ) → (∃ x. ⌜x⌝ = σ); (forward) from specification stream-basic% ⊦ ⌜m⌝ ≠ ∞; (s)