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<span class="kw">let </span><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">G</font> being   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><br/>  for <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">c1</font> being   <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="Olive" title="b1">G</font>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> &amp; <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">c</font> &amp; <font color="Olive" title="b3">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Olive" title="b2">c</font> holds <br/> <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Olive" title="b3">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="b2">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">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">c</font>, <font color="Olive" title="b2">c1</font> being   <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="c3">G</font>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> &amp; <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">c</font> &amp; <font color="Olive" title="b2">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Olive" title="b1">c</font> holds <br/> <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Olive" title="b2">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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">c</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">c1</font> be   <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="c3">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> &amp; <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</font> implies  <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</font></span>)</span> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:20"/><span class="lab"><font color="Green" title="E11">A1</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font>
 <span class="kw">and </span><br/><a NAME="E2:20"/><span class="lab"><font color="Green" title="E12">A2</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font>
 <span class="kw">and </span><br/><a NAME="E3:20"/><span class="lab"><font color="Green" title="E13">A3</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">c</font>
 <span class="kw">and </span><br/><a NAME="E4:20"/><span class="lab"><font color="Green" title="E14">A4</font></span>: 
<font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<font color="Maroon" title="c2">n</font>) <a href="finseq_6.html#K4" title="FINSEQ_6:func.4">-cut</a> <font color="Maroon" title="c4">c</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">  <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</font></span>)</span></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">mn1c</font> = (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</font></span>)</span>;<br/>
<a NAME="E5:20"/><span class="lab"><font color="Green" title="E15">A5</font></span>: 
 not <font color="Maroon" title="c4">c</font> 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="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a></span>;<br/>
<a NAME="E6:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A6</font></span>: 
 <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c4">c</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/>
<a NAME="E7:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A7</font></span>: 
(<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</font></span>)</span> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c5">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="graph_2.html#T42" onmouseover="rs('graph_2/T42')" onmouseout="rh()">GRAPH_2:42</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">vsc</font> =  <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font>;<br/>
<a NAME="E8:20"/><span class="lab"><font color="Green" title="E18">A8</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="nat_1.html#T12" onmouseover="rs('nat_1/T12')" onmouseout="rh()">NAT_1:12</a></span>;<br/>
<a NAME="E9:20"/><span class="lab"><font color="Green" title="E19">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c4">c</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="c4">c</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:20"><span class="lab"><font color="Green" title="E16">A6</font></span></a></span>;<br/>
<a NAME="E10:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A10</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</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="c4">c</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/>
<a NAME="E11:20"/><span class="lab"><font color="Green" title="E21">A11</font></span>: 
 not <font color="Maroon" title="c5">c1</font> 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="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="ref" href="msscyc_1.html#T12" target="_self" onmouseover="rs('msscyc_1/T12')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E12:20"/><span class="kw">then </span>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">c1</font>
 
;<br/>
<a NAME="E13:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A12</font></span>: 
<font color="Maroon" title="c5">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="txt" href="#E4:20"><span class="lab"><font color="Green" title="E14">A4</font></span></a>, <a class="ref" href="finseq_6.html#D4" onmouseover="rs('finseq_6/D4')" onmouseout="rh()">FINSEQ_6:def 4</a></span>;<br/>
<a NAME="E14:20"/><span class="lab"><font color="Green" title="E23">A13</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="ref" href="nat_1.html#T12" onmouseover="rs('nat_1/T12')" onmouseout="rh()">NAT_1:12</a></span>;<br/>
<a NAME="E15:20"/>
 not  <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font> 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="#E9:20"><span class="lab"><font color="Green" title="E19">A9</font></span></a></span>;<br/>
<a NAME="E16:20"/><span class="kw">then </span>
 not (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</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="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E8:20"><span class="lab"><font color="Green" title="E18">A8</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="ref" href="msscyc_1.html#T12" target="_self" onmouseover="rs('msscyc_1/T12')" onmouseout="rh()">Th11</a></span>;<br/>
<a NAME="E17:20"/><span class="kw">then </span>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</a> <span class="p2">(<span class="default"><a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span>
 
;<br/>
<a NAME="E18:20"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A14</font></span>: 
<span class="p1">(<span class="default"><a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</a> <span class="p2">(<span class="default"><a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <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="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E10:20"><span class="lab"><font color="Green" title="E20">A10</font></span></a>, <a class="txt" href="#E14:20"><span class="lab"><font color="Green" title="E23">A13</font></span></a>, <a class="ref" href="finseq_6.html#D4" onmouseover="rs('finseq_6/D4')" onmouseout="rh()">FINSEQ_6:def 4</a></span>;<br/>
<a NAME="E19:20"/>
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20"><span class="lab"><font color="Green" title="E12">A2</font></span></a>, <a class="txt" href="#E3:20"><span class="lab"><font color="Green" title="E13">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E20:20"/><span class="kw">then </span>
<span class="p1">(<span class="default">(<font color="Maroon" title="c1">m</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</a> <span class="p2">(<span class="default"><a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c4">c</font></span>)</span></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>  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:20"><span class="lab"><font color="Green" title="E11">A1</font></span></a>, <a class="txt" href="#E5:20"><span class="lab"><font color="Green" title="E15">A5</font></span></a>, <a class="txt" href="#E13:20"><span class="lab"><font color="Green" title="E22">A12</font></span></a>, <a class="txt" href="#E18:20"><span class="lab"><font color="Green" title="E24">A14</font></span></a>, <a class="ref" href="msscyc_1.html#T11" target="_self" onmouseover="rs('msscyc_1/T11')" onmouseout="rh()">Th10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:20"/>
 <a href="graph_2.html#K3" title="GRAPH_2:func.3">vertex-seq</a> <font color="Maroon" title="c5">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> (<font color="Maroon" title="c1">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="finseq_6.html#K5" title="FINSEQ_6:func.5">-cut</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="c4">c</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:20"><span class="lab"><font color="Green" title="E17">A7</font></span></a>, <a class="txt" href="#E11:20"><span class="lab"><font color="Green" title="E21">A11</font></span></a>, <a class="ref" href="graph_2.html#D10" onmouseover="rs('graph_2/D10')" onmouseout="rh()">GRAPH_2:def 10</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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