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<b>set </b><font color="Maroon">W2</font> = <font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_1_1_1_1"/>
( ( not <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> &amp; not <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> ) or <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> or <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> or  not <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> or  not <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:32_1_1_1_1_1"/><i><font color="Green">E37</font></i>: 
( not <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> &amp; not <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> &amp; <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> )
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">m'</font> = <font color="Maroon">m</font> as  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:32_1_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span>
 ;<br/><a NAME="E2:32_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E51</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> )
 <b>by </b><i><a class="ref" href="glib_001.html#T13">GLIB_001:13</a></i>;<br/><b>set </b><font color="Maroon">v1b</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>;<br/><b>set </b><font color="Maroon">eb</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">v2b</font> = <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/><a NAME="E3:32_1_1_1_1_1_1"/><i><font color="Green">E82</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">W</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">W</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">W</font> )
 <b>by </b><i>, , <a class="ref" href="glib_001.html#T48">GLIB_001:48</a></i>;<br/><b>then reconsider </b><font color="Maroon">a</font> = <span class="p1">(<span class="default"><font color="Maroon">m'</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">x</font></span>)</span> <a href="real_1.html#K5">-</a> 1, <font color="Maroon">a1</font> = <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1, <font color="Maroon">a2</font> = <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 as    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">a</font> as  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/><b>set </b><font color="Maroon">v1a</font> = <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>;<br/><b>set </b><font color="Maroon">ea</font> = <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon">v2a</font> = <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>;<br/><a NAME="E6:32_1_1_1_1_1_1"/>
<font color="Maroon">a2</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font>
 <b>by </b><i>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E7:32_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1</span>)</span> <a href="real_1.html#K5">-</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 0
 <b>by </b><i><a class="ref" href="real_1.html#T92">REAL_1:92</a></i>;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:32_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">G</font>
 ;<br/><a NAME="E2:32_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">G</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:32_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K6">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K5">the_Weight_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E9:32_1_1_1_1_1_1"/>
not <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">G</font>
 ;<br/><a NAME="E10:32_1_1_1_1_1_1"/><b>then </b>
not <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="glib_000.html#R2">DJoins</a> <font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">W</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="nat_1.html#K1">+</a> 2</span>)</span>,<font color="Maroon">G</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E11:32_1_1_1_1_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6">the_ELabel_of</a> <font color="Maroon">G</font></span>)</span> <a href="seq_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:32_1_1_1_1_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> is <a href="glib_005.html#V7" target="_self">augmenting</a>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:32_1_1_1_1_2"/>
( <font color="Maroon">m</font> is <a href="abian.html#V1">even</a> or <font color="Maroon">n</font> is <a href="abian.html#V1">even</a> or  not <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> or  not <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">W</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:32_1_1_1_1_2"/>
<font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> is <a href="glib_005.html#V7" target="_self">augmenting</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D11">GLIB_001:def 11</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:32_1_1"/>
<font color="Maroon">W</font> <a href="glib_001.html#K8">.cut</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> is <a href="glib_005.html#V7" target="_self">augmenting</a>
 ;<br/>


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