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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c1">G1</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> implies <font color="Maroon" title="c2">G2</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> )</span><br/>

<b>assume </b><a NAME="E1:73"/><i><font color="Green" title="E58">A1</font></i>: 
<font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">G1</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> or <font color="Maroon" title="c2">G2</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a> )</span><br/>

<b>assume </b><a NAME="E2:73"/><i><font color="Green" title="E59">A2</font></i>: 
<font color="Maroon" title="c1">G1</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">u</font>, <font color="Maroon" title="c4">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v</font> implies <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/><b>assume </b><a NAME="E1:73_1"/><i><font color="Green" title="E60">A3</font></i>: 
<font color="Maroon" title="c3">u</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span><br/><b>reconsider </b><font color="Maroon" title="c5">u2</font> = <font color="Maroon" title="c3">u</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="chord.html#E1:73"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c6">v2</font> = <font color="Maroon" title="c4">v</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <b>by </b><i><a class="txt" href="chord.html#E1:73"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="glib_000.html#D36" title="GLIB_000:def.36">GLIB_000:def 36</a></i>;<br/><a NAME="E4:73_1"/>
<font color="Maroon" title="c5">u2</font>,<font color="Maroon" title="c6">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="chord.html#E2:73"><i><font color="Green" title="E59">A2</font></i></a>, <a class="txt" href="chord.html#E1:73_1"><i><font color="Green" title="E60">A3</font></i></a>, <a class="ref" href="chord.html#D6" target="_self" title="CHORD:def.6">Def6</a></i>;<br/><b>hence </b><a NAME="E5:73_1"/>
<font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c4">v</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <b>by </b><i><a class="txt" href="chord.html#E1:73"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="chord.html#T44" target="_self" title="CHORD:th.44">Th44</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:73"/>
<font color="Maroon" title="c2">G2</font> is <a href="chord.html#V2" title="CHORD:attr.2">complete</a>
 <b>by </b><i><a class="ref" href="chord.html#D6" target="_self" title="CHORD:def.6">Def6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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