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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:137_1_1_1"/>
( <font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_1_1_1"><b>suppose </b></a><a NAME="E1:137_1_1_1_1"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive">b<sub>1</sub></font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c2">s</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T25" title="RELSET_1:th.25">RELSET_1:25</a></i>;<br/><b>take </b>
<font color="Maroon" title="c2">s</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">s</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><b>thus </b><a NAME="E3:137_1_1_1_1"/>
<font color="Maroon" title="c2">s</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="137_1_1_1_2"><b>suppose </b></a><a NAME="E1:137_1_1_1_2"/>
<font color="Maroon" title="c1">X</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font> st <font color="Olive">b<sub>1</sub></font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:137_1_1_1_2"/><i><font color="Green" title="E30">W1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c3">s</font> = <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <font color="Maroon" title="c2">x</font> as   <a href="nat_1.html#NM2" title="NAT_1:NM.2">sequence</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="#E3:137_1_1_1_2"><i><font color="Green" title="E30">W1</font></i></a>, <a class="ref" href="funcop_1.html#T57" title="FUNCOP_1:th.57">FUNCOP_1:57</a></i>;<br/><b>take </b>
<font color="Maroon" title="c3">s</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">s</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a></span><br/><b>thus </b><a NAME="E5:137_1_1_1_2"/>
<font color="Maroon" title="c3">s</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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