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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">E</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span><br/> for <font color="Olive" title="b2">G2</font> being  <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G1</font>,<font color="Olive" title="b1">E</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">G2</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span><br/><b>let </b><font color="Maroon" title="c2">E</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">G2</font> being  <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">E</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">G2</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span><br/><b>let </b><font color="Maroon" title="c3">G2</font> be   <a href="glib_000.html#NM9" title="GLIB_000:NM.9">removeEdges</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G2</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span><br/>





<a NAME="E1:150"/><i><font color="Green" title="E61">A1</font></i>: 
 <a href="glib_000.html#K26" title="GLIB_000:func.26">the_Edges_of</a> <font color="Maroon" title="c3">G2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Maroon" title="c2">E</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T56" target="_self" title="GLIB_000:th.56">Th56</a></i>;<br/>
<a NAME="E2:150"/><b>then </b>
 <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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="c3">G2</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">E</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></i>;<br/>
<b>hence </b><a NAME="E3:150"/>
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G2</font> <a href="glib_000.html#K18" title="GLIB_000:func.18">.size()</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon" title="c2">E</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:150"><i><font color="Green" title="E61">A1</font></i></a>, <a class="ref" href="card_2.html#T53" title="CARD_2:th.53">CARD_2:53</a>, <a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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