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<span class="kw">let </span><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" 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">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/>

<span class="kw">assume </span><a NAME="E1:48"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<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" 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">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/>

<span class="kw">let </span><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" 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">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/>

<span class="kw">assume </span><a NAME="E2:48"/>
<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" 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">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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E4:48"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
<font color="Maroon" title="c5">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>
 ;<br/>
<span class="kw">let </span><font color="Maroon" title="c6">u2</font>, <font color="Maroon" title="c7">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" 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">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font> &amp; <font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v2</font> implies <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E5:48"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
<font color="Maroon" title="c3">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u2</font>
 <span class="kw">and </span><br/><a NAME="E6:48"/><span class="lab"><font color="Green" title="E46">A4</font></span>: 
<font color="Maroon" title="c4">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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="c6">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> </span><br/>

<a NAME="E7:48"/>
<font color="Maroon" title="c5">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font>,<font color="Maroon" title="c2">G2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="txt" href="#E5:48"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="txt" href="#E6:48"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="txt" href="#E4:48"><span class="lab"><font color="Green" title="E44">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:48"/>
<font color="Maroon" title="c6">u2</font>,<font color="Maroon" title="c7">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</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"> verum</span><br/>


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