<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">G2</font> be   <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">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G1</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">E</font><br/>  for <font color="Olive" title="b3">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b2">G1</font><br/>  for <font color="Olive" title="b4">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v2</font> holds <br/>( ( <font color="Olive" title="b3">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Olive" title="b4">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Olive" title="b3">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Olive" title="b4">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Olive" title="b3">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Olive" title="b4">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">G1</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">E</font><br/>  for <font color="Olive" title="b2">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b3">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> holds <br/>( ( <font color="Olive" title="b2">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Olive" title="b3">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Olive" title="b2">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Olive" title="b3">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Olive" title="b2">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Olive" title="b3">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G1</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">G1</font><br/>  for <font color="Olive" title="b2">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v2</font> holds <br/>( ( <font color="Olive" title="b1">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Olive" title="b2">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Olive" title="b1">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Olive" title="b2">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Olive" title="b1">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Olive" title="b2">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v1</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c3">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">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</font>  st <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> holds <br/>( ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Olive" title="b1">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Olive" title="b1">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Olive" title="b1">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G2</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="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v2</font> implies ( ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:30"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v2</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="c4">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span><br/>

<div><span class="kw">hereby </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"> ( ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) &amp; ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  ) )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:30_1"/>
<font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</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"> <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> </span><br/><a NAME="E2:30_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D49" onmouseover="rs('glib_000/D49')" onmouseout="rh()">GLIB_000:def 49</a></span>;<br/><a NAME="E3:30_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="glib_007.html#T13" target="_self" onmouseover="rs('glib_007/T13')" onmouseout="rh()">Th13</a></span>;<br/><span class="kw">hence </span><a NAME="E4:30_1"/>
<font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D49" onmouseover="rs('glib_000/D49')" onmouseout="rh()">GLIB_000:def 49</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/></div>
<span class="kw">end;</span></div>

<div><span class="kw">hereby </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"> ( <font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  implies <font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:30_2"/>
<font color="Maroon" title="c4">v1</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</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"> <font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a> </span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:30_2"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
( <font color="Maroon" title="c4">v1</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  not <font color="Maroon" title="c6">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c3">G1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D51" onmouseover="rs('glib_000/D51')" onmouseout="rh()">GLIB_000:def 51</a></span>;<br/><a NAME="E4:30_2"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
 not <font color="Maroon" title="c6">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">v2</font>,<font color="Maroon" title="c5">v2</font>,<font color="Maroon" title="c1">G2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E3:30_2"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="glib_007.html#T9" target="_self" onmouseover="rs('glib_007/T9')" onmouseout="rh()">Th9</a></span>;<br/><a NAME="E5:30_2"/>
<font color="Maroon" title="c5">v2</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E3:30_2"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="glib_007.html#T13" target="_self" onmouseover="rs('glib_007/T13')" onmouseout="rh()">Th13</a></span>;<br/><span class="kw">hence </span><a NAME="E6:30_2"/>
<font color="Maroon" title="c5">v2</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:30_2"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="glib_000.html#D51" onmouseover="rs('glib_000/D51')" onmouseout="rh()">GLIB_000:def 51</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/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E4:30"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<font color="Maroon" title="c4">v1</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</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"> <font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a> </span><br/>

<a NAME="E5:30"/>
 for <font color="Olive" title="b1">G4</font> being   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c5">v2</font> holds  <font color="Maroon" title="c1">G2</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">G4</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a> 
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="30_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">G4</font> be   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c5">v2</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">G2</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">G4</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">G3</font> =  the   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c4">v1</font>;<br/>
<a NAME="E1:30_3"/>
<font color="Maroon" title="c6">G4</font> is    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of  the   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c2">E</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">G1</font> <a href="glib_000.html#K20" title="GLIB_000:func.20">.edgesInOut</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">v2</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="glib_007.html#T22" target="_self" onmouseover="rs('glib_007/T22')" onmouseout="rh()">Th22</a></span>;<br/>
<a NAME="E2:30_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<font color="Maroon" title="c6">G4</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c4">v1</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T21" target="_self" onmouseover="rs('glib_007/T21')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E3:30_3"/>
<font color="Maroon" title="c3">G1</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c3">G1</font>,<font color="Maroon" title="c4">v1</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:30"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="glib_002.html#D10" onmouseover="rs('glib_002/D10')" onmouseout="rh()">GLIB_002:def 10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:30_3"/>
<font color="Maroon" title="c1">G2</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c6">G4</font> <a href="glib_002.html#K4" title="GLIB_002:func.4">.numComponents()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_3"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="glib_007.html#T21" target="_self" onmouseover="rs('glib_007/T21')" onmouseout="rh()">Th21</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:30"/>
<font color="Maroon" title="c5">v2</font> is  <a href="glib_002.html#V5" title="GLIB_002:attr.5">cut-vertex</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#D10" onmouseover="rs('glib_002/D10')" onmouseout="rh()">GLIB_002:def 10</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/>


</div>
