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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">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">p</font>, <font color="Olive" title="b2">q</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st <font color="Maroon" title="c1">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">p</font> holds <br/>1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Olive" title="b2">q</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>; <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="c1">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="c2">p</font> implies 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span> )</span><br/>



<span class="kw">assume </span><a NAME="E1:3"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c1">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="c2">p</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:3_1"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 or 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1"><span class="kw">suppose </span></a><a NAME="E1:3_1_1"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span><br/><div class="add"><a NAME="E2:3_1_1"/><span class="kw">then </span>
1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:3_1_1"/>
1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_2"><span class="kw">suppose </span></a><a NAME="E1:3_1_2"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span><br/><div class="add"><span class="kw">set </span><font color="Maroon" title="c4">cp</font> = 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font>;<br/><span class="kw">set </span><font color="Maroon" title="c5">cpq</font> = 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="3_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:3_1_2_1"/><span class="lab"><font color="Green" title="E4">A4</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span></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">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="#E1:3"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E1:3_1_2"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></span>;<br/><a NAME="E2:3_1_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</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">p</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T35" title="FINSEQ_1:th.35">FINSEQ_1:35</a></span>;<br/><a NAME="E3:3_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A5</font></span>: 
<font color="Maroon" title="c1">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> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E2">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="E4:3_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A6</font></span>: 
<span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p2">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span></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">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="#E1:3_1_2"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E5:3_1_2_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_2_1"><span class="lab"><font color="Green" title="E4">A4</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"> for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">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> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> holds <br/><span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">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="c6">k</font> &amp; <font color="Maroon" title="c6">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> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> implies <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:3_1_2_1"/><span class="lab"><font color="Green" title="E7">A7</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">k</font>
 <span class="kw">and </span><br/><a NAME="E7:3_1_2_1"/><span class="lab"><font color="Green" title="E8">A8</font></span>: 
<font color="Maroon" title="c6">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> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font></span><br/><a NAME="E8:3_1_2_1"/>
<font color="Maroon" title="c6">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="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E1:3_1_2_1"><span class="lab"><font color="Green" title="E4">A4</font></span></a>, <a class="txt" href="#E7:3_1_2_1"><span class="lab"><font color="Green" title="E8">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E9:3_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A9</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c2">p</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:3_1_2_1"><span class="lab"><font color="Green" title="E7">A7</font></span></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></span>;<br/><a NAME="E10:3_1_2_1"/>
<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="E11:3_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A10</font></span>: 
 ex <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>(  <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="Olive" title="b1">i</font> &amp; <font color="Olive" title="b1">i</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> <span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> &amp; <font color="Maroon" title="c6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">i</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="#E6:3_1_2_1"><span class="lab"><font color="Green" title="E7">A7</font></span></a>, <a class="txt" href="#E7:3_1_2_1"><span class="lab"><font color="Green" title="E8">A8</font></span></a>, <a class="ref" href="graph_2.html#T1" title="GRAPH_2:th.1">GRAPH_2:1</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font> = 
<font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E1:3_1_2"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:3_1_2_1"><span class="lab"><font color="Green" title="E9">A9</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>
<br/>.= 
<span class="p1">(<span class="default">1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">k</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_2"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="txt" href="#E3:3_1_2_1"><span class="lab"><font color="Green" title="E5">A5</font></span></a>, <a class="txt" href="#E1:3_1_2_1"><span class="lab"><font color="Green" title="E4">A4</font></span></a>, <a class="txt" href="#E4:3_1_2_1"><span class="lab"><font color="Green" title="E6">A6</font></span></a>, <a class="txt" href="#E11:3_1_2_1"><span class="lab"><font color="Green" title="E10">A10</font></span></a>, <a class="ref" href="graph_2.html#D1" title="GRAPH_2:def.1">GRAPH_2:def 1</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:3_1_2"/>
1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1,<font color="Maroon" title="c1">n</font> <a href="graph_2.html#K1" title="GRAPH_2:func.1">-cut</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <font color="Maroon" title="c3">q</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T18" title="FINSEQ_1:th.18">FINSEQ_1:18</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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