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<b>let </b><font color="Maroon" title="c1">G1</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/><b>let </b><font color="Maroon" title="c2">G2</font> be    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c3">v1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>;<br/><b>let </b><font color="Maroon" title="c4">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>;<br/>







<b>assume </b><a NAME="E1:174"/><i><font color="Green" title="E72">A1</font></i>: 
<font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font>
 ;<br/>

<a NAME="E2:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#T82" target="_self" title="GLIB_000:th.82">Th82</a></i>;<br/>
<a NAME="E3:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E4:174"/><b>then </b>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T80" title="CARD_1:th.80">CARD_1:80</a></i>;<br/>
<a NAME="E5:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:174"/><i><font color="Green" title="E73">A2</font></i>: 
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a> 
 ;<br/>

<a NAME="E7:174"/>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a> </span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c2">G2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="glib_000.html#E1:174"><i><font color="Green" title="E72">A1</font></i></a>, <a class="ref" href="glib_000.html#T82" target="_self" title="GLIB_000:th.82">Th82</a></i>;<br/>
<a NAME="E8:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E9:174"/><b>then </b>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="card_1.html#T80" title="CARD_1:th.80">CARD_1:80</a></i>;<br/>
<a NAME="E10:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E11:174"/>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a> 
 ;<br/>

<a NAME="E12:174"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="glib_000.html#E6:174"><i><font color="Green" title="E73">A2</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E13:174"/><b>then </b>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a> </span>)</span>
 
;<br/>
<b>hence </b><a NAME="E14:174"/>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a> 
 ;<br/>


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