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<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="msscyc_1.html#V2" title="MSSCYC_1:attr.2">empty</a> <a href="graph_1.html#NM1" title="GRAPH_1:NM.1">Graph</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">oc</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>  <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c1">G</font>  st <font color="Olive" title="b1">oc</font> is <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a> holds <br/><span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Olive" title="b1">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Olive" title="b1">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">oc</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">oc</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="msscyc_1.html#NV1" title="MSSCYC_1:NV.1">directed</a>  <a href="graph_1.html#M1" title="GRAPH_1:mode.1">Chain</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">oc</font> is <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a> implies <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/>



<b>assume </b><a NAME="E1:27"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c2">oc</font> is <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><br/>

<b>set </b><font color="Maroon" title="c3">vsoc</font> =  <a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font>;<br/>
<a NAME="E2:27"/><i><font color="Green" title="E18">A2</font></i>: 
 <a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c2">oc</font>
 
<b>by </b><i><a class="ref" href="graph_2.html#D11" title="GRAPH_2:def.11">GRAPH_2:def 11</a></i>;<br/>
<a NAME="E3:27"/><b>then </b>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="graph_2.html#D7" title="GRAPH_2:def.7">GRAPH_2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:27"/>
<span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="graph_2.html#K7" title="GRAPH_2:func.7">vertex-seq</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">oc</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="msscyc_1.html#E1:27"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="msscyc_1.html#E2:27"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="msscyc_1.html#T6" target="_self" title="MSSCYC_1:th.6">Th6</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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