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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">s1</font> be   <a href="normsp_1.html#NM2" title="NORMSP_1:NM.2">sequence</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">j</font> be    <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="E1:72"/><i><font color="Green" title="E45">A1</font></i>: 
<font color="Maroon" title="c2">s1</font> is <a href="wellfnd1.html#V3" title="WELLFND1:attr.3">descending</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">s2</font> =  <a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font>;<br/>
<b>set </b><font color="Maroon" title="c5">IR</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="72_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">n</font> be    <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>set </b><font color="Maroon" title="c7">nj</font> = <font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">j</font>;<br/><a NAME="E1:72_1"/><i><font color="Green" title="E46">A2</font></i>: 
<span class="p1">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">s1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="bagorder.html#D20" target="_self" title="BAGORDER:def.20">Def20</a></i>;<br/><i><font color="Green" title="E47">A3</font></i>: <span class="p1">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<font color="Maroon" title="c2">s1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">j</font></span>)</span>
<b>by </b><i><a class="ref" href="bagorder.html#D20" target="_self" title="BAGORDER:def.20">Def20</a></i>
<br/>.= 
<font color="Maroon" title="c2">s1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Maroon" title="c3">j</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>

;<br/><b>hence </b><a NAME="E3:72_1"/>
<span class="p1">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">n</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E1:72"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="bagorder.html#E1:72_1"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="wellfnd1.html#D7" title="WELLFND1:def.7">WELLFND1:def 7</a></i>;<br/><b>thus </b><a NAME="E4:72_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">n</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="bagorder.html#E1:72"><i><font color="Green" title="E45">A1</font></i></a>, <a class="txt" href="bagorder.html#E1:72_1"><i><font color="Green" title="E46">A2</font></i></a>, <a class="txt" href="bagorder.html#E2:72_1"><i><font color="Green" title="E47">A3</font></i></a>, <a class="ref" href="wellfnd1.html#D7" title="WELLFND1:def.7">WELLFND1:def 7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:72"/>
 <a href="bagorder.html#K16" title="BAGORDER:func.16">SeqShift</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">j</font> is <a href="wellfnd1.html#V3" title="WELLFND1:attr.3">descending</a>
 <b>by </b><i><a class="ref" href="wellfnd1.html#D7" title="WELLFND1:def.7">WELLFND1:def 7</a></i>;<br/>


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