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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<i><font color="Green">E33</font></i>:  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" target="_self">*</a> <font color="Maroon">N</font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" target="_self">*</a> <font color="Maroon">N</font></span>)</span> #) = 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #)
<b>by </b><i/>
<br/>.= 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span> #)
<b>by </b><i><a class="ref" href="waybel_2.html#D3">WAYBEL_2:def 3</a></i>
;<br/>
<b>set </b><font color="Maroon">n</font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font>;<br/>
<a NAME="E2:62"/><i><font color="Green">E34</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="waybel_2.html#D3">WAYBEL_2:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f2</font> = the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E4:62"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="yellow_6.html#K3">.</a> <font color="Olive">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/>

<b>consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:62_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c</font>
 <b>and </b><br/><a NAME="E3:62_2"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">f2</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K11">"/\"</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="waybel_2.html#D3">WAYBEL_2:def 3</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="yellow_6.html#K3">.</a> <font color="Maroon">y</font>
<b>by </b><i>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>
<br/>.= 
<font color="Maroon">f2</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="waybel_9.html#T1" target="_self">Th1</a>, <a class="ref" href="waybel_1.html#D18">WAYBEL_1:def 18</a></i>
;<br/>


</div><b>end;</b></div>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" target="_self">*</a> <font color="Maroon">N</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="partfun1.html#K1">*</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font>
<b>by </b><i/>
<br/>.= 
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>
;<br/>
<b>hence </b><a NAME="E6:62"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="waybel_1.html#K4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" target="_self">*</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="waybel_2.html#K3">"/\"</a> <font color="Maroon">N</font>
 <b>by </b><i/>;<br/>


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