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<b>set </b><font color="Maroon" title="c5">W2</font> = <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>;<br/>
<a NAME="E1:128_1_1"/><i><font color="Green" title="E104">A1</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <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">W</font>
 
<b>by </b><i><a class="txt" href="glib_001.html#E67"><i><font color="Green" title="E59">Lm30</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_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="E1:128_1_1_1_1"/>
( ( not <font color="Maroon" title="c3">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c4">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c4">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">W</font> &amp; <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> ) or <font color="Maroon" title="c3">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or <font color="Maroon" title="c4">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> or  not <font color="Maroon" title="c4">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">W</font> or  not <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1"/><i><font color="Green" title="E105">A2</font></i>: 
( not <font color="Maroon" title="c3">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; not <font color="Maroon" title="c4">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> &amp; <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c4">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">W</font> &amp; <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> )
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon" title="c6">m'</font> = <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c7">n'</font> = <font color="Maroon" title="c4">n</font> as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <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>  <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <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> ;<br/><b>assume </b><a NAME="E1:128_1_1_1_1_1_1"/><i><font color="Green" title="E106">A3</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font> )
 ;<br/><a NAME="E2:128_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E107">A4</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">x</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c8">x</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E3:128_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E108">A5</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> &amp; <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="ref" href="finseq_3.html#T27" title="FINSEQ_3:th.27">FINSEQ_3:27</a></i>;<br/><a NAME="E4:128_1_1_1_1_1_1"/><i><font color="Green" title="E109">A6</font></i>: 
( <font color="Maroon" title="c8">x</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">W</font> &amp; <font color="Maroon" title="c9">y</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">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1"><i><font color="Green" title="E107">A4</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1"><i><font color="Green" title="E104">A1</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_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="E1:128_1_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font> or ( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c8">x</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E3:128_1_1_1_1_1_1"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="glib_001.html#E75"><i><font color="Green" title="E67">Lm38</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font>
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E110">A7</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E70"><i><font color="Green" title="E62">Lm33</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_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="E1:128_1_1_1_1_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font> or ( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E3:128_1_1_1_1_1_1"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="glib_001.html#E75"><i><font color="Green" title="E67">Lm38</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font>
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_1_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E70"><i><font color="Green" title="E62">Lm33</font></i></a></i>;<br/><a NAME="E3:128_1_1_1_1_1_1_1_1_1_1_1_1"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E4:128_1_1_1_1_1_1"><i><font color="Green" title="E109">A6</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_1"><i><font color="Green" title="E110">A7</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a></i>;<br/><b>hence </b><a NAME="E4:128_1_1_1_1_1_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1"><i><font color="Green" title="E104">A1</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_1_1_1_2"/><i><font color="Green" title="E111">A8</font></i>: 
( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E112">A9</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</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="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> is    <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>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">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">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">y2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">m'</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">n'</font> as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <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>  <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E111">A8</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><a NAME="E4:128_1_1_1_1_1_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E5:128_1_1_1_1_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E113">A10</font></i>: 
( <font color="Maroon" title="c8">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c10">y2</font> &amp; <font color="Maroon" title="c10">y2</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">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E111">A8</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E6:128_1_1_1_1_1_1_1_1_1_1_1_2"/><b>then </b>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c10">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_1"><i><font color="Green" title="E110">A7</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E112">A9</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a></i>;<br/><b>then </b><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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">m</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E65"><i><font color="Green" title="E57">Lm28</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">y</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font>

;<br/><b>hence </b><a NAME="E8:128_1_1_1_1_1_1_1_1_1_1_1_2"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_1"><i><font color="Green" title="E110">A7</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E112">A9</font></i></a>, <a class="txt" href="glib_001.html#E5:128_1_1_1_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E113">A10</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:128_1_1_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_2"/><i><font color="Green" title="E110">A11</font></i>: 
( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c8">x</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_2"/><b>then </b><i><font color="Green" title="E111">A12</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</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="c8">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> is    <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>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">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">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">x2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">m'</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">n'</font> as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <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>  <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E110">A11</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:128_1_1_1_1_1_1_1_1_2_1_1"/>
( <font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font> or ( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> ) )
 </span><b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E3:128_1_1_1_1_1_1"><i><font color="Green" title="E108">A5</font></i></a>, <a class="txt" href="glib_001.html#E75"><i><font color="Green" title="E67">Lm38</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c9">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">m</font>
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/><b>hence </b><a NAME="E3:128_1_1_1_1_1_1_1_1_2_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E110">A11</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_1_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E112">A13</font></i>: 
( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">y</font> &amp; <font color="Maroon" title="c9">y</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">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/><div class="add"><a NAME="E2:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E113">A14</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</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="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> is    <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>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">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">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">y2</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c6">m'</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c7">n'</font> as  <a href="abian.html#NV3" title="ABIAN:NV.3">odd</a>  <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>  <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E112">A13</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E71"><i><font color="Green" title="E63">Lm34</font></i></a></i>;<br/><a NAME="E4:128_1_1_1_1_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="ref" href="xreal_1.html#T10" title="XREAL_1:th.10">XREAL_1:10</a></i>;<br/><a NAME="E5:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E114">A15</font></i>: 
<font color="Maroon" title="c10">x2</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c11">y2</font>
 ;<br/><a NAME="E6:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E115">A16</font></i>: 
( <font color="Maroon" title="c10">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c11">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">W</font> )
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E111">A12</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E113">A14</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a></i>;<br/><b>then </b><i><font color="Green" title="E116">A17</font></i>: <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">m</font>
<b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E65"><i><font color="Green" title="E57">Lm28</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">y</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c4">n</font>

;<br/><b>reconsider </b><font color="Maroon" title="c12">xm4</font> = <font color="Maroon" title="c8">x</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font> as    <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>  <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E110">A11</font></i></a>, <a class="ref" href="int_1.html#T18" title="INT_1:th.18">INT_1:18</a></i>;<br/><a NAME="E9:128_1_1_1_1_1_1_1_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n'</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a></i>;<br/><a NAME="E10:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b>
<font color="Maroon" title="c10">x2</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c7">n'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E6:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E115">A16</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E11:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E117">A18</font></i>: 
<font color="Maroon" title="c12">xm4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E12:128_1_1_1_1_1_1_1_1_2_1_1_2"/><b>then </b><i><font color="Green" title="E118">A19</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">m</font>
 ;<br/><a NAME="E13:128_1_1_1_1_1_1_1_1_2_1_1_2"/><i><font color="Green" title="E119">A20</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="glib_001.html#E1:128_1_1_1_1_1"><i><font color="Green" title="E105">A2</font></i></a>, <a class="txt" href="glib_001.html#E5:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E114">A15</font></i></a>, <a class="txt" href="glib_001.html#E1:128_1_1_1_1_1_1"><i><font color="Green" title="E106">A3</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_2"><i><font color="Green" title="E111">A12</font></i></a>, <a class="txt" href="glib_001.html#E2:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E113">A14</font></i></a>, <a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a>, <a class="txt" href="glib_001.html#E11:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E117">A18</font></i></a></i>;<br/><a NAME="E14:128_1_1_1_1_1_1_1_1_2_1_1_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c6">m'</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1" title="HEYTING3:th.1">HEYTING3:1</a></i>;<br/><b>hence </b><a NAME="E15:128_1_1_1_1_1_1_1_1_2_1_1_2"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_001.html#E7:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E116">A17</font></i></a>, <a class="txt" href="glib_001.html#E12:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E118">A19</font></i></a>, <a class="txt" href="glib_001.html#E13:128_1_1_1_1_1_1_1_1_2_1_1_2"><i><font color="Green" title="E119">A20</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:128_1_1_1_1_1_1_1_1_2"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:128_1_1_1_1_1_1"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c9">y</font> <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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font></span>)</span> )
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:128_1_1_1_1_1"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D28" target="_self" title="GLIB_001:def.28">Def28</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:128_1_1_1_1_2"/>
( <font color="Maroon" title="c3">m</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or <font color="Maroon" title="c4">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a> or  not <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> or  not <font color="Maroon" title="c4">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">W</font> or  not <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:128_1_1_1_1_2"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 <b>by </b><i><a class="ref" href="glib_001.html#D12" target="_self" title="GLIB_001:def.12">Def12</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:128_1_1"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K9" title="GLIB_001:func.9">.remove</a> <font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font> is <a href="glib_001.html#V5" title="GLIB_001:attr.5">Path-like</a>
 ;<br/>


</div>
