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

<span class="kw">let </span><font color="Maroon" title="c1">G</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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V3" title="GLIB_014:attr.3">loopless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V3" title="GLIB_014:attr.3">loopless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V4" title="GLIB_014:attr.4">non-multi</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V4" title="GLIB_014:attr.4">non-multi</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<a NAME="E1:251"/><span class="lab"><font color="Green" title="E150">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is    <a href="glib_014.html#M1" title="GLIB_014:mode.1">GraphUnion</a> of <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glenum00.html#T198" target="_self" onmouseover="rs('glenum00/T198')" onmouseout="rh()">Th198</a></span>;<br/>
<span class="kw">thus </span><a NAME="E2:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V3" title="GLIB_000:attr.3">loopless</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V3" title="GLIB_014:attr.3">loopless</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V4" title="GLIB_014:attr.4">non-multi</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V4" title="GLIB_014:attr.4">non-multi</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E3:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V5" title="GLIB_000:attr.5">non-multi</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V4" title="GLIB_014:attr.4">non-multi</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E4:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V6" title="GLIB_000:attr.6">non-Dmulti</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V5" title="GLIB_014:attr.5">non-Dmulti</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E5:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V6" title="GLIB_014:attr.6">simple</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E6:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V7" title="GLIB_014:attr.7">Dsimple</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E7:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V8" title="GLIB_014:attr.8">acyclic</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E8:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_008.html#V1" title="GLIB_008:attr.1">edgeless</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V12" title="GLIB_014:attr.12">edgeless</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></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"> ( ( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  implies <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  ) &amp; ( <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  ) )</span><br/>

<span class="kw">thus </span><a NAME="E9:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="chord.html#V6" title="CHORD:attr.6">chordal</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V11" title="GLIB_014:attr.11">chordal</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></a>, <a class="ref" href="glib_015.html#T63" onmouseover="rs('glib_015/T63')" onmouseout="rh()">GLIB_015:63</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"> ( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E10:251"/>
( <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V1" title="GLIB_012:attr.1">loopfull</a>  iff <font color="Maroon" title="c1">G</font> <a href="glenum00.html#K15" title="GLENUM00:func.15">.allComponents()</a>  is  <a href="glib_014.html#V13" title="GLIB_014:attr.13">loopfull</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:251"><span class="lab"><font color="Green" title="E150">A1</font></span></a>, <a class="ref" href="glib_015.html#T63" onmouseover="rs('glib_015/T63')" onmouseout="rh()">GLIB_015:63</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>
