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<b>let </b><font color="Maroon">R</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">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>;<br/>



<a NAME="E1:38"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T6">YELLOW_9:6</a>, <a class="ref" href="yellow_9.html#T7">YELLOW_9:7</a></i>;<br/>
<a NAME="E2:38"/><b>then </b><i><font color="Green">E30</font></i>: 
(  <a href="relset_1.html#K4">dom</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp;  <a href="relset_1.html#K4">dom</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:38_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon">i</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_9.html#T6">YELLOW_9:6</a></i>;<br/><b>thus </b>the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">i</font>

<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="yellow_9.html#T6">YELLOW_9:6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:38"/>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K2">+id</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="waybel19.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="38_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:38_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/><b>then reconsider </b><font color="Maroon">i</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <b>by </b><i><a class="ref" href="yellow_9.html#T7">YELLOW_9:7</a></i>;<br/><b>thus </b>the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">i</font>

<br/>.= 
<font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="yellow_9.html#T7">YELLOW_9:7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:38"/>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="yellow_9.html#K3">opp+id</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K6">id</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="waybel19.html#D1" target="_self">Def1</a>, <a class="ref" href="funct_1.html#T34">FUNCT_1:34</a></i>;<br/>


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