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<b>reconsider </b><font color="Maroon" title="c3">s1</font> =  <a href="funct_3.html#K6" title="FUNCT_3:func.6">incl</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  as  <a href="seqm_3.html#V1" title="SEQM_3:attr.1">increasing</a> <a href="seqm_3.html#NM1" title="SEQM_3:NM.1">Seq_of_Nat</a> <b>by </b><i><a class="ref" href="seqm_3.html#T80" title="SEQM_3:th.80">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" title="c1">X</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or  not <font color="Maroon" title="c1">X</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">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" title="c1">X</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ;<br/><div class="add"><a NAME="E2:32_1_1_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/><a NAME="E3:32_1_1_1_1"/><b>then </b><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><b>take </b>
<font color="Maroon" title="c2">s</font>
;<br/><b>take </b>
<font color="Maroon" title="c3">s1</font>
;<br/><b>thus </b><a NAME="E4:32_1_1_1_1"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">s1</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T62" title="RELAT_1:th.62">RELAT_1:62</a>, <a class="txt" href="bhsp_3.html#E3:32_1_1_1_1"><i><font color="Green" title="E12">A1</font></i></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" title="E12">A2</font></i>: 
not <font color="Maroon" title="c1">X</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ;<br/><div class="add"><b>take </b>
<font color="Maroon" title="c2">s</font>
;<br/><b>take </b>
<font color="Maroon" title="c3">s1</font>
;<br/><b>reconsider </b><font color="Maroon" title="c4">X</font> = <font color="Maroon" title="c1">X</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  <b>by </b><i><a class="txt" href="bhsp_3.html#E1:32_1_1_1_2"><i><font color="Green" title="E12">A2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c2">s</font> as   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c4">X</font> ;<br/><b>thus </b><a NAME="E4:32_1_1_1_2"/>
<font color="Maroon" title="c2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c3">s1</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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