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<span class="kw">set </span><font color="Maroon" title="c4">Rotated</font> = <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">IT</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span> ;<br/>
<a NAME="E1:71_1_1"/>
 not <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span>  is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:71"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="ref" href="graph_3.html#T52" target="_self" title="GRAPH_3:th.52">Th57</a></span>;<br/>
<a NAME="E2:71_1_1"/><span class="kw">then </span>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span> 
 
;<br/>
<a NAME="E3:71_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">c9</font> being    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  st <br/>(  <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b2">c9</font> where <font color="Olive" title="b2">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b2">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b3">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b3">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b2">c9</font> &amp; <font color="Olive" title="b3">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c9</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) )
 
;<br/>
<span class="kw">hence </span><a NAME="E4:71_1_1"/>
 <a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">c9</font> where <font color="Olive" title="b1">c9</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a>  : (  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c3">c</font> &amp;  ex <font color="Olive" title="b2">vs</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive" title="b2">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c9</font> &amp; <font color="Olive" title="b2">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> ) ) </span> } </span>  is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">G</font> <a href="graph_3.html#K9" title="GRAPH_3:func.9">-CycleSet</a> 
 ; <a class="txt" 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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