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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">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">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#K3" title="GRAPH_2:func.3">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#K3" title="GRAPH_2:func.3">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span><br/><span class="kw">let </span><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" 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">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#K3" title="GRAPH_2:func.3">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#K3" title="GRAPH_2:func.3">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:24"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">oc</font> is  <a href="msscyc_1.html#V1" title="MSSCYC_1:attr.1">cyclic</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"><a href="graph_2.html#K3" title="GRAPH_2:func.3">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#K3" title="GRAPH_2:func.3">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">vsoc</font> =  <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c2">oc</font>;<br/>
<a NAME="E2:24"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <a href="graph_2.html#K3" title="GRAPH_2:func.3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="graph_2.html#D10" onmouseover="rs('graph_2/D10')" onmouseout="rh()">GRAPH_2:def 10</a></span>;<br/>
<span class="kw">thus </span><a NAME="E3:24"/>
<span class="p1">(<span class="default"><a href="graph_2.html#K3" title="GRAPH_2:func.3">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#K3" title="GRAPH_2:func.3">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="msscyc_1.html#T6" target="_self" onmouseover="rs('msscyc_1/T6')" onmouseout="rh()">Th5</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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