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Theorem lim-exists

mon(σσ), σσ ≠ [] ⊦ ∃ σ. (∀ n. ⌜n⌝ < # σσ → σσ[n] ⊑ σ) ∧ (∀ m. ¬ # σ < ⌜m⌝ → (∃ n. ⌜n⌝ < # σσ ∧ ⌜σ to m⌝ ⊑ σσ[n]))

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