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<tex> d_k \leq k \Leftrightarrow |\{ v \in VG | d_v \leq k \}| \geq k. </tex>
|proof=
<tex> \{ d_1, d_2, \ldots, d_k \} \subset \{ v \in VG | d_v \leq k \} \Rightarrow |\{ v \in VG | d_v \leq k \}| \geq k </tex>, q.e.d.
<tex> d_1 \leq d_2 \leq \ldots \leq d_k \leq \ldots \leq d_{k + p} \leq k \Rightarrow d_k \leq k </tex>, q.e.d.
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<tex>\ d_{n - k} \geq n - k \Leftrightarrow |\{ v \in VG | d_v \geq n - k \}| \geq k + 1. </tex>
|proof=
<tex> \{ d_{n - k}, d_{n - k + 1}, \ldots , d_n \} \subset \{ v \in VG | d_v \geq n - k \} \Rightarrow \{ v \in VG | d_v \geq n - k \} \geq k + 1 </tex>, q.e.d.
<tex> d_n \geq d_{n - 1} \ldots \geq d_{n - k} \geq \ldots \geq d_{n - k - p} \geq n - k \Rightarrow d_{n - k} \geq n - k </tex>, q.e.d.
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{{Лемма
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