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<span class="kw">set </span><font color="Maroon" title="c5">W2</font> = <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>);<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="120_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_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="E1:120_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> ) 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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="120_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:120_1_1_1_1_1"/><span class="lab"><font color="Green" title="E99">A1</font></span>: 
(  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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> </span><br/><div class="add"><a NAME="E2:120_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A2</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><a NAME="E3:120_1_1_1_1_1"/>
<font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="txt" href="glib_001.html#E92"><span class="lab"><font color="Green" title="E84">Lm55</font></span></a></span>;<br/><a NAME="E4:120_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E101">A3</font></span>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E100">A2</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><a NAME="E5:120_1_1_1_1_1"/><span class="lab"><font color="Green" title="E102">A4</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">m</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="ref" href="abian.html#T12" title="ABIAN:th.12">ABIAN:12</a></span>;<br/><a NAME="E6:120_1_1_1_1_1"/>
<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#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="#E1:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="txt" href="glib_001.html#E52"><span class="lab"><font color="Green" title="E44">Lm15</font></span></a></span>;<br/><a NAME="E7:120_1_1_1_1_1"/><span class="kw">then </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"><font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</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> 1 <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="#E1:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E99">A1</font></span></a>, <a class="txt" href="#E5:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E102">A4</font></span></a>, <a class="txt" href="#E4:120_1_1_1_1_1"><span class="lab"><font color="Green" title="E101">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><span class="kw">hence </span><a NAME="E8:120_1_1_1_1_1"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="glib_001.html#E92"><span class="lab"><font color="Green" title="E84">Lm55</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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="120_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:120_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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:120_1_1_1_1_2"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_001.html#D11" target="_self" title="GLIB_001:def.11">Def11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:120_1_1"/>
<font color="Maroon" title="c2">W</font> <a href="glib_001.html#K8" title="GLIB_001:func.8">.cut</a> (<font color="Maroon" title="c3">m</font>,<font color="Maroon" title="c4">n</font>) is  <a href="glib_001.html#V3" title="GLIB_001:attr.3">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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