Used simplifier rules: append-inf: ⊦ ⌜nf⌝ + σ = ⌜nf⌝ ;%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2;%size-inf: ⊦ # ⌜nf⌝ = ∞;% ⊦ ⌜m⌝ ≠ ∞; (s)% ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0; (s)