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<span class="kw">let </span><font color="Maroon" title="c1">G1</font> be   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">e</font> being   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c1">G1</font>  ex <font color="Olive" title="b3">G2</font> being   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <font color="Maroon" title="c1">G1</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Olive" title="b3">G2</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">e</font>,<font color="Olive" title="b1">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">e</font> being   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c1">G1</font>  ex <font color="Olive" title="b2">G2</font> being   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <font color="Maroon" title="c1">G1</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Olive" title="b2">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c2">v</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">e</font> be   <a href="glib_008.html#NM1" title="GLIB_008:NM.1">Edge</a> of <font color="Maroon" title="c1">G1</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">G2</font> being   <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>   <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> st <font color="Maroon" title="c1">G1</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Olive" title="b1">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">v</font></span><br/>





<span class="kw">take </span><font color="Maroon" title="c4">G2</font> =  the   <a href="glib_000.html#NM8" title="GLIB_000:NM.8">removeEdge</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c3">e</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">G1</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Maroon" title="c4">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">v</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">u</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">e</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">w</font> = <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">e</font>;<br/>
<a NAME="E1:95"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D10" onmouseover="rs('zfmisc_1/D10')" onmouseout="rh()">ZFMISC_1:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:95"/>
<font color="Maroon" title="c1">G1</font> is    <a href="glib_006.html#M3" title="GLIB_006:mode.3">addEdge</a> of <font color="Maroon" title="c4">G2</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_008.html#T37" onmouseover="rs('glib_008/T37')" onmouseout="rh()">GLIB_008:37</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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