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Proof step 2 from proof append-to-ls (previous step)

⊦ σ + σ0 to n = σ to n, # σ < ⌜n⌝

Heuristic structural induction applied rule structural induction

And closed the goal!

Rule argument

term: σ

Additional information

Used simplifier rules: to-fin: ⊦ ⌜x⌝ to n = ⌜x to n⌝ ;%size-fin: ⊦ # ⌜x⌝ = ⌜# x⌝ ;%append-to-le-01: ⊦ m ≤ # x → ⌜x⌝ + σ to m = ⌜x to m⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%to-inf: ⊦ ⌜nf⌝ to n = ⌜nf to n⌝ ;%stream freely generated by ⌜ ⌝, ⌜ ⌝;;%inj-02: ⊦ ⌜x⌝ = ⌜x0⌝ ↔ x = x0; from specification stream-basic%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat