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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>













<b>assume </b><a NAME="E1:181"/>
<font color="Maroon">G1</font> <a href="glib_000.html#R5" target="_self">==</a> <font color="Maroon">G2</font>
 ;<br/>

<a NAME="E2:181"/><b>then </b>
<font color="Maroon">G1</font> is    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G2</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#D33" target="_self">Def33</a></i>;<br/>
<b>hence </b><a NAME="E3:181"/>
( ( <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font> implies <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font> ) &amp; ( <font color="Maroon">e</font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G1</font> implies <font color="Maroon">e</font> <a href="glib_000.html#R2" target="_self">DJoins</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">G2</font> ) &amp; ( <font color="Maroon">e</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G1</font> implies <font color="Maroon">e</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G2</font> ) &amp; ( <font color="Maroon">e</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G1</font> implies <font color="Maroon">e</font> <a href="glib_000.html#R4" target="_self">DSJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G2</font> ) )
 <b>by </b><i/>;<br/>


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