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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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font>, <font color="Olive" title="b5">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b4">y</font> &amp; <font color="Olive" title="b2">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b4">y</font>,<font color="Olive" title="b5">z</font> holds <br/><font color="Olive" title="b1">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Olive" title="b2">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b3">x</font>,<font color="Olive" title="b5">z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> &amp; <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> holds <br/><font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b3">z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c6">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font> &amp; <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">z</font> implies <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">z</font> )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:166"/><span class="lab"><font color="Green" title="E114">A1</font></span>: 
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font>
 <span class="kw">and </span><br/><a NAME="E2:166"/><span class="lab"><font color="Green" title="E115">A2</font></span>: 
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">z</font></span><br/>

<a NAME="E3:166"/><span class="lab"><font color="Green" title="E116">A3</font></span>: 
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:166"><span class="lab"><font color="Green" title="E114">A1</font></span></a>, <a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></span>;<br/>
<a NAME="E4:166"/><span class="lab"><font color="Green" title="E117">A4</font></span>: 
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:166"><span class="lab"><font color="Green" title="E115">A2</font></span></a>, <a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></span>;<br/>
<a NAME="E5:166"/><span class="lab"><font color="Green" title="E118">A5</font></span>: 
<font color="Maroon" title="c3">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:166"><span class="lab"><font color="Green" title="E115">A2</font></span></a>, <a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></span>;<br/>
<a NAME="E6:166"/>
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:166"><span class="lab"><font color="Green" title="E114">A1</font></span></a>, <a class="ref" href="glib_001.html#D23" target="_self" title="GLIB_001:def.23">Def23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:166"/>
<font color="Maroon" title="c2">W1</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">W2</font> <a href="glib_001.html#R1" title="GLIB_001:pred.1">is_Walk_from</a> <font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c6">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:166"><span class="lab"><font color="Green" title="E116">A3</font></span></a>, <a class="txt" href="#E5:166"><span class="lab"><font color="Green" title="E118">A5</font></span></a>, <a class="txt" href="#E4:166"><span class="lab"><font color="Green" title="E117">A4</font></span></a>, <a class="txt" href="glib_001.html#E48"><span class="lab"><font color="Green" title="E40">Lm11</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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