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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K17" title="GLIB_000:func.17">.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#K17" title="GLIB_000:func.17">.size()</a> </span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#K17" title="GLIB_000:func.17">.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#K17" title="GLIB_000:func.17">.size()</a> </span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G2</font> <a href="glib_000.html#K17" title="GLIB_000:func.17">.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#K17" title="GLIB_000:func.17">.size()</a> </span><br/>





<a NAME="E1:154"/><span class="lab"><font color="Green" title="E60">A1</font></span>: 
 <a href="glib_000.html#K25" title="GLIB_000:func.25">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T56" target="_self" title="GLIB_000:th.56">Th56</a></span>;<br/>
<a NAME="E2:154"/><span class="kw">then </span>
 <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#K25" title="GLIB_000:func.25">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T45" title="XBOOLE_1:th.45">XBOOLE_1:45</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:154"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">G2</font> <a href="glib_000.html#K17" title="GLIB_000:func.17">.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#K17" title="GLIB_000:func.17">.size()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:154"><span class="lab"><font color="Green" title="E60">A1</font></span></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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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