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<b>let </b><font color="Maroon">G1</font> be  <a href="glib_000.html#V2" target="_self">finite</a> <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>;<br/>







<b>assume </b><a NAME="E1:174"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font>
 ;<br/>

<a NAME="E2:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E3:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E4:174"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T80">CARD_1:80</a></i>;<br/>
<a NAME="E5:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:174"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">v2</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a> 
 ;<br/>

<a NAME="E7:174"/>
<font color="Maroon">v2</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">G2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#D29" target="_self">Def29</a>, </i>;<br/>
<a NAME="E8:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E9:174"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T80">CARD_1:80</a></i>;<br/>
<a NAME="E10:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a>  <a href="xxreal_0.html#R1">&lt;=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E11:174"/>
<font color="Maroon">v2</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a> 
 ;<br/>

<a NAME="E12:174"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">v2</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#D32" target="_self">Def32</a>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E13:174"/><b>then </b>
<font color="Maroon">v2</font> <a href="glib_000.html#K36" target="_self">.degree()</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E14:174"/>
<font color="Maroon">v2</font> <a href="glib_000.html#K36" target="_self">.degree()</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K36" target="_self">.degree()</a> 
 ;<br/>


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