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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">S</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Olive" title="b1">S</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:56"/><span class="lab"><font color="Green" title="E49">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">S</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Olive" title="b1">S</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">S</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font></span><br/>

<div><span class="lab"><font color="Green" title="E50">A2</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_1"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> )</span><br/><span class="kw">assume </span><a NAME="E1:56_1"/><span class="lab"><font color="Green" title="E51">A3</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c5">t2</font> = <font color="Maroon" title="c4">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E51">A3</font></span></a></span>;<br/><a NAME="E3:56_1"/><span class="lab"><font color="Green" title="E52">A4</font></span>: 
 not <font color="Maroon" title="c5">t2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="chord.html#T50" target="_self" onmouseover="rs('chord/T50')" onmouseout="rh()">Th49</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c6">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font><span class="kw"> such that </span><br/><a NAME="E5:56_1"/><span class="lab"><font color="Green" title="E53">A5</font></span>: 
<font color="Maroon" title="c6">v2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">and </span><br/><a NAME="E6:56_1"/><span class="lab"><font color="Green" title="E54">A6</font></span>: 
<font color="Maroon" title="c5">t2</font>,<font color="Maroon" title="c6">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_1"><span class="lab"><font color="Green" title="E51">A3</font></span></a>, <a class="ref" href="chord.html#T50" target="_self" onmouseover="rs('chord/T50')" onmouseout="rh()">Th49</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">t1</font> = <font color="Maroon" title="c5">t2</font>, <font color="Maroon" title="c8">v1</font> = <font color="Maroon" title="c6">v2</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E49">A1</font></span></a></span>;<br/><a NAME="E8:56_1"/>
<font color="Maroon" title="c7">t1</font>,<font color="Maroon" title="c8">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E6:56_1"><span class="lab"><font color="Green" title="E54">A6</font></span></a>, <a class="ref" href="chord.html#T44" target="_self" onmouseover="rs('chord/T44')" onmouseout="rh()">Th43</a></span>;<br/><span class="kw">hence </span><a NAME="E9:56_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_1"><span class="lab"><font color="Green" title="E52">A4</font></span></a>, <a class="txt" href="#E5:56_1"><span class="lab"><font color="Green" title="E53">A5</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>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="56_2"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> holds <br/><font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> implies <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> )</span><br/><span class="kw">assume </span><a NAME="E1:56_2"/><span class="lab"><font color="Green" title="E51">A7</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c5">t1</font> = <font color="Maroon" title="c4">x</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E51">A7</font></span></a></span>;<br/><a NAME="E3:56_2"/><span class="lab"><font color="Green" title="E52">A8</font></span>: 
 not <font color="Maroon" title="c5">t1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E51">A7</font></span></a>, <a class="ref" href="chord.html#T50" target="_self" onmouseover="rs('chord/T50')" onmouseout="rh()">Th49</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c6">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><span class="kw"> such that </span><br/><a NAME="E5:56_2"/><span class="lab"><font color="Green" title="E53">A9</font></span>: 
<font color="Maroon" title="c6">v1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">and </span><br/><a NAME="E6:56_2"/><span class="lab"><font color="Green" title="E54">A10</font></span>: 
<font color="Maroon" title="c5">t1</font>,<font color="Maroon" title="c6">v1</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_2"><span class="lab"><font color="Green" title="E51">A7</font></span></a>, <a class="ref" href="chord.html#T50" target="_self" onmouseover="rs('chord/T50')" onmouseout="rh()">Th49</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c7">t2</font> = <font color="Maroon" title="c5">t1</font>, <font color="Maroon" title="c8">v2</font> = <font color="Maroon" title="c6">v1</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E49">A1</font></span></a></span>;<br/><a NAME="E8:56_2"/>
<font color="Maroon" title="c7">t2</font>,<font color="Maroon" title="c8">v2</font> <a href="chord.html#R1" title="CHORD:pred.1">are_adjacent</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E49">A1</font></span></a>, <a class="txt" href="#E6:56_2"><span class="lab"><font color="Green" title="E54">A10</font></span></a>, <a class="ref" href="chord.html#T44" target="_self" onmouseover="rs('chord/T44')" onmouseout="rh()">Th43</a></span>;<br/><span class="kw">hence </span><a NAME="E9:56_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:56_2"><span class="lab"><font color="Green" title="E52">A8</font></span></a>, <a class="txt" href="#E5:56_2"><span class="lab"><font color="Green" title="E53">A9</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">hence </span><a NAME="E4:56"/>
<font color="Maroon" title="c1">G1</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G2</font> <a href="chord.html#K2" title="CHORD:func.2">.AdjacentSet</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:56"><span class="lab"><font color="Green" title="E50">A2</font></span></a>, <a class="ref" href="tarski.html#T2" onmouseover="rs('tarski/T2')" onmouseout="rh()">TARSKI:2</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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