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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" 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">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>  st <font color="Olive" title="b1">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="Olive" title="b2">W2</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  holds <br/><span class="p1">(<span class="default"><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></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">W1</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">W2</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font>, <font color="Maroon" title="c3">H</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" 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="c2">P</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="c3">H</font> <a href="glib_001.html#K3" title="GLIB_001:func.3">.first()</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:29"/>
<font color="Maroon" title="c3">H</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="c2">P</font> <a href="glib_001.html#K4" title="GLIB_001:func.4">.last()</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span></span><br/>

<span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K7" title="GLIB_001:func.7">.append</a> <font color="Maroon" title="c3">H</font></span>)</span> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a>  = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#T85" onmouseover="rs('glib_001/T85')" onmouseout="rh()">GLIB_001:85</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">P</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H</font> <a href="glib_001.html#K15" title="GLIB_001:func.15">.length()</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T22" onmouseover="rs('finseq_1/T22')" onmouseout="rh()">FINSEQ_1:22</a></span>
;<br/> <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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