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<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_012.html#V6" title="GLIB_012:attr.6">self-complementary</a>  iff  ex <font color="Olive" title="b1">H</font> being    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</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"> (  ex <font color="Olive" title="b1">H</font> being    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a>  implies <font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V6" title="GLIB_012:attr.6">self-complementary</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:191_1"/><span class="lab"><font color="Green" title="E89">A1</font></span>: 
<font color="Maroon" title="c1">G</font> is  <a href="glib_012.html#V6" title="GLIB_012:attr.6">self-complementary</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">  ex <font color="Olive" title="b1">H</font> being    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font> st <font color="Olive" title="b1">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> </span><br/><span class="kw">reconsider </span><font color="Maroon" title="c2">H</font> =  the    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font> as    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font> ;<br/><span class="kw">take </span><font color="Maroon" title="c3">H</font> = <font color="Maroon" title="c2">H</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="c3">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> </span><br/><span class="kw">thus </span><a NAME="E3:191_1"/>
<font color="Maroon" title="c3">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:191_1"><span class="lab"><font color="Green" title="E89">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"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">given </span><font color="Maroon" title="c2">H0</font> being    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font><span class="kw"> such that </span><a NAME="E3:191"/><span class="lab"><font color="Green" title="E89">A2</font></span>: 
<font color="Maroon" title="c2">H0</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</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_012.html#V6" title="GLIB_012:attr.6">self-complementary</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">H</font> be    <a href="glib_012.html#M5" title="GLIB_012:mode.5">GraphComplement</a> of <font color="Maroon" title="c1">G</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glib_012.html#D13" target="_self" onmouseover="rs('glib_012/D13')" onmouseout="rh()">GLIB_012:def 13</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="c3">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> </span><br/>

<a NAME="E4:191"/>
<font color="Maroon" title="c3">H</font> is <font color="Maroon" title="c2">H0</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_012.html#T104" target="_self" onmouseover="rs('glib_012/T104')" onmouseout="rh()">Th104</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:191"/>
<font color="Maroon" title="c3">H</font> is <font color="Maroon" title="c1">G</font> <a href="glib_010.html#V19" title="GLIB_010:attr.19">-isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:191"><span class="lab"><font color="Green" title="E89">A2</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"> verum</span><br/>


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