<?xml version="1.0"?>
<div class="add">

<b>reconsider </b><font color="Maroon">s1</font> =  <a href="funct_3.html#K6">incl</a> <a href="numbers.html#K5">NAT</a>  as  <a href="seqm_3.html#V1">increasing</a> <a href="seqm_3.html#NM1">Seq_of_Nat</a> <b>by </b><i><a class="ref" href="seqm_3.html#T80">SEQM_3:80</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_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"/>
( <font color="Maroon">X</font> is <a href="struct_0.html#V3">empty</a> or  not <font color="Maroon">X</font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1_1"><b>suppose </b></a><a NAME="E1:32_1_1_1_1"/>
<font color="Maroon">X</font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><a NAME="E2:32_1_1_1_1"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/><a NAME="E3:32_1_1_1_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>take </b>
<font color="Maroon">s</font>
;<br/><b>take </b>
<font color="Maroon">s1</font>
;<br/><b>thus </b><a NAME="E4:32_1_1_1_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">s1</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T62">RELAT_1:62</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_1_1_1_2"><b>suppose </b></a><a NAME="E1:32_1_1_1_2"/><i><font color="Green">E51</font></i>: 
not <font color="Maroon">X</font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>take </b>
<font color="Maroon">s</font>
;<br/><b>take </b>
<font color="Maroon">s1</font>
;<br/><b>reconsider </b><font color="Maroon">X</font> = <font color="Maroon">X</font> as  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a>  <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">s</font> as   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">X</font> ;<br/><a NAME="E4:32_1_1_1_2"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">s1</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>;<br/><b>hence </b><a NAME="E5:32_1_1_1_2"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">s1</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
