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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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being  <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a><br/> for <font color="Olive" title="b2">vs</font>, <font color="Olive" title="b3">vs1</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="Olive" title="b1">G</font><br/> for <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">c1</font> being   <a href="graph_1.html#M2" title="GRAPH_1:mode.2">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="b4">c</font> &amp; <font color="Olive" title="b5">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Olive" title="b4">c</font> &amp; <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="b4">c</font> &amp; <font color="Olive" title="b3">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Olive" title="b2">vs</font> holds <br/><font color="Olive" title="b3">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b5">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">G</font> be   <a href="graph_1.html#NM3" title="GRAPH_1:NM.3">Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">vs</font>, <font color="Olive" title="b2">vs1</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="c3">G</font><br/> for <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">c1</font> being   <a href="graph_1.html#M2" title="GRAPH_1:mode.2">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="b3">c</font> &amp; <font color="Olive" title="b4">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Olive" title="b1">vs</font> holds <br/><font color="Olive" title="b2">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b4">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">vs</font>, <font color="Maroon" title="c5">vs1</font> be    <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="c3">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="graph_1.html#M2" title="GRAPH_1:mode.2">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Olive" title="b1">c</font> &amp; <font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b1">c</font> &amp; <font color="Maroon" title="c5">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font> holds <br/><font color="Maroon" title="c5">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Olive" title="b2">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">c</font>, <font color="Maroon" title="c7">c1</font> be    <a href="graph_1.html#M2" title="GRAPH_1:mode.2">Chain</a> of <font color="Maroon" title="c3">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c6">c</font> &amp; <font color="Maroon" title="c7">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c6">c</font> &amp; <font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c6">c</font> &amp; <font color="Maroon" title="c5">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font> implies <font color="Maroon" title="c5">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c7">c1</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:61"/><span class="lab"><font color="Green" title="E51">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="E2:61"/><span class="lab"><font color="Green" title="E52">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="E3:61"/><span class="lab"><font color="Green" title="E53">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="c6">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c6">c</font> or  not <font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c6">c</font> or  not <font color="Maroon" title="c5">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font> or <font color="Maroon" title="c5">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c7">c1</font> )</span><br/>

<a NAME="E4:61"/><span class="lab"><font color="Green" title="E54">A4</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#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E52">A2</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:61"/><span class="lab"><font color="Green" title="E55">A5</font></span>: 
<font color="Maroon" title="c7">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="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c6">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c6">c</font> or  not <font color="Maroon" title="c5">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font> or <font color="Maroon" title="c5">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c7">c1</font> )</span><br/>

<a NAME="E6:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A6</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="txt" href="graph_2.html#E8"><span class="lab"><font color="Green" title="E8">Lm2</font></span></a></span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E7:61"/><span class="lab"><font color="Green" title="E57">A7</font></span>: 
<font color="Maroon" title="c4">vs</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">and </span><br/><a NAME="E8:61"/><span class="lab"><font color="Green" title="E58">A8</font></span>: 
<font color="Maroon" title="c5">vs1</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#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="graph_2.html#K2" title="GRAPH_2:func.2">-cut</a> <font color="Maroon" title="c4">vs</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">vs1</font> <a href="graph_2.html#R1" title="GRAPH_2:pred.1">is_vertex_seq_of</a> <font color="Maroon" title="c7">c1</font></span><br/>

<a NAME="E9:61"/><span class="lab"><font color="Green" title="E59">A9</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">vs</font> <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="c6">c</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:61"><span class="lab"><font color="Green" title="E57">A7</font></span></a>, <a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">Def7</a></span>;<br/>
<a NAME="E10:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A10</font></span>: 
<font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</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> <font color="Maroon" title="c4">vs</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E11:61"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E58">A8</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:61"/><span class="lab"><font color="Green" title="E61">A11</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">vs1</font> <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="c7">c1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E56">A6</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">GRAPH_2:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b1">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="c7">c1</font> holds <br/><font color="Maroon" title="c7">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">n</font> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b1">n</font>,<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c8">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c8">k</font> &amp; <font color="Maroon" title="c8">k</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="c7">c1</font> implies <font color="Maroon" title="c7">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E13:61"/><span class="lab"><font color="Green" title="E62">A12</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 <span class="kw">and </span><br/><a NAME="E14:61"/><span class="lab"><font color="Green" title="E63">A13</font></span>: 
<font color="Maroon" title="c8">k</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="c7">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span><br/>

<a NAME="E15:61"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:61"><span class="lab"><font color="Green" title="E62">A12</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c9">j</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E17:61"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">j</font>
 <span class="kw">and </span><br/><a NAME="E18:61"/><span class="lab"><font color="Green" title="E64">A14</font></span>: 
<font color="Maroon" title="c9">j</font> <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="c7">c1</font>
 <span class="kw">and </span><br/><a NAME="E19:61"/><span class="lab"><font color="Green" title="E65">A15</font></span>: 
<font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E63">A13</font></span></a>, <a class="ref" href="graph_2.html#T1" target="_self" title="GRAPH_2:th.1">Th1</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">i</font> = <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font>;<br/>
<a NAME="E20:61"/>
<font color="Maroon" title="c9">j</font> <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">vs1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="txt" href="#E18:61"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E21:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A16</font></span>: 
<font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">vs</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#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E58">A8</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="txt" href="#E10:61"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></span>;<br/>
<a NAME="E22:61"/>
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c8">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c7">c1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:61"><span class="lab"><font color="Green" title="E63">A13</font></span></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E23:61"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</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="c7">c1</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c1">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></span>;<br/>
<a NAME="E24:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A17</font></span>: 
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</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="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="txt" href="#E6:61"><span class="lab"><font color="Green" title="E56">A6</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E25:61"/><span class="kw">then </span>
<font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</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">vs</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E59">A9</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E26:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A18</font></span>: 
<font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">vs</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#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E27:61"/><span class="lab"><font color="Green" title="E69">A19</font></span>: 
<font color="Maroon" title="c8">k</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="c7">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:61"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E28:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A20</font></span>: 
<font color="Maroon" title="c8">k</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="c5">vs1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E29:61"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E30:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A21</font></span>: 
<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="txt" href="#E27:61"><span class="lab"><font color="Green" title="E69">A19</font></span></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E31:61"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
;<br/>
<a NAME="E32:61"/><span class="kw">then </span>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E33:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A22</font></span>: 
<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:61"><span class="lab"><font color="Green" title="E70">A20</font></span></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">v2</font> = <font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">v1</font> = <font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span>;<br/>
<a NAME="E34:61"/><span class="lab"><font color="Green" title="E73">A23</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E35:61"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E36:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A24</font></span>: 
<font color="Maroon" title="c6">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#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span>,<font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:61"><span class="lab"><font color="Green" title="E57">A7</font></span></a>, <a class="txt" href="#E24:61"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="ref" href="graph_2.html#D7" target="_self" title="GRAPH_2:def.7">Def7</a></span>;<br/>
<a NAME="E37:61"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T12" title="NAT_1:th.12">NAT_1:12</a></span>;<br/>
<a NAME="E38:61"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A25</font></span>: 
<font color="Maroon" title="c4">vs</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:61"><span class="lab"><font color="Green" title="E59">A9</font></span></a>, <a class="txt" href="#E24:61"><span class="lab"><font color="Green" title="E67">A17</font></span></a>, <a class="ref" href="finseq_4.html#T24" title="FINSEQ_4:th.24">FINSEQ_4:24</a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></span>;<br/>
<a NAME="E39:61"/>
<font color="Maroon" title="c9">j</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <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">vs1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:61"><span class="lab"><font color="Green" title="E61">A11</font></span></a>, <a class="txt" href="#E18:61"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></span>;<br/>
<a NAME="E40:61"/><span class="kw">then </span>
<font color="Maroon" title="c5">vs1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">vs</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">m</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c9">j</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E8:61"><span class="lab"><font color="Green" title="E58">A8</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="txt" href="#E10:61"><span class="lab"><font color="Green" title="E60">A10</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="txt" href="#E34:61"><span class="lab"><font color="Green" title="E73">A23</font></span></a>, <a class="ref" href="graph_2.html#D1" target="_self" title="GRAPH_2:def.1">Def1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E41:61"/>
<font color="Maroon" title="c7">c1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">k</font> <a href="graph_1.html#R2" title="GRAPH_1:pred.2">joins</a> <font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c8">k</font>,<font color="Maroon" title="c5">vs1</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E51">A1</font></span></a>, <a class="txt" href="#E3:61"><span class="lab"><font color="Green" title="E53">A3</font></span></a>, <a class="txt" href="#E5:61"><span class="lab"><font color="Green" title="E55">A5</font></span></a>, <a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E54">A4</font></span></a>, <a class="txt" href="#E18:61"><span class="lab"><font color="Green" title="E64">A14</font></span></a>, <a class="txt" href="#E19:61"><span class="lab"><font color="Green" title="E65">A15</font></span></a>, <a class="txt" href="#E36:61"><span class="lab"><font color="Green" title="E74">A24</font></span></a>, <a class="txt" href="#E21:61"><span class="lab"><font color="Green" title="E66">A16</font></span></a>, <a class="txt" href="#E26:61"><span class="lab"><font color="Green" title="E68">A18</font></span></a>, <a class="txt" href="#E38:61"><span class="lab"><font color="Green" title="E75">A25</font></span></a>, <a class="txt" href="#E33:61"><span class="lab"><font color="Green" title="E72">A22</font></span></a>, <a class="txt" href="#E30:61"><span class="lab"><font color="Green" title="E71">A21</font></span></a>, <a class="txt" href="graph_2.html#E8"><span class="lab"><font color="Green" title="E8">Lm2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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