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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> implies for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  holds <br/>for <font color="Olive" title="b3">u2</font>, <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="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">u2</font> &amp; <font color="Olive" title="b2">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">u2</font>,<font color="Olive" title="b4">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/>

<b>assume </b><a NAME="E1:50"/><i><font color="Green" title="E42">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"> for <font color="Olive" title="b1">u1</font>, <font color="Olive" title="b2">v1</font> being  <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font>  st <font color="Olive" title="b1">u1</font>,<font color="Olive" title="b2">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  holds <br/>for <font color="Olive" title="b3">u2</font>, <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="c2">G2</font>  st <font color="Olive" title="b1">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">u2</font> &amp; <font color="Olive" title="b2">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">u2</font>,<font color="Olive" title="b4">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span><br/>

<b>let </b><font color="Maroon" title="c3">u1</font>, <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="c1">G1</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">u1</font>,<font color="Maroon" title="c4">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  implies for <font color="Olive" title="b1">u2</font>, <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="c2">G2</font>  st <font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u2</font> &amp; <font color="Maroon" title="c4">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">u2</font>,<font color="Olive" title="b2">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/>

<b>assume </b><a NAME="E2:50"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">u2</font>, <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="c2">G2</font>  st <font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">u2</font> &amp; <font color="Maroon" title="c4">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">u2</font>,<font color="Olive" title="b2">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span><br/>

<b>let </b><font color="Maroon" title="c5">u2</font>, <font color="Maroon" title="c6">v2</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">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v2</font> implies <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>  )</span><br/>

<b>assume </b><a NAME="E3:50"/><i><font color="Green" title="E44">A3</font></i>: 
( <font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">v2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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> </span><br/>

<b>consider </b><font color="Maroon" title="c7">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:50"/><i><font color="Green" title="E45">A4</font></i>: 
<font color="Maroon" title="c7">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c1">G1</font>
 <b>by </b><i><a class="txt" href="#E2:50"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="chord.html#D3" target="_self" title="CHORD:def.3">Def3</a></i>;<br/>
<a NAME="E6:50"/>
<font color="Maroon" title="c7">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c5">u2</font>,<font color="Maroon" title="c6">v2</font>,<font color="Maroon" title="c2">G2</font>
 
<b>by </b><i><a class="txt" href="#E1:50"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="#E3:50"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="#E5:50"><i><font color="Green" title="E45">A4</font></i></a>, <a class="ref" href="glib_000.html#T91" title="GLIB_000:th.91">GLIB_000:91</a></i>;<br/>
<b>hence </b><a NAME="E7:50"/>
<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="ref" href="chord.html#D3" target="_self" title="CHORD:def.3">Def3</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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