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<b>let </b><font color="Maroon">L</font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>set </b><font color="Maroon">S</font> =  <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #);<br/>
<a NAME="E1:75"/>
 <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) is    <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:75_1"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13" target="_self">YELLOW_0:def 13</a><br/>

<b>thus </b><a NAME="E2:75_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">S</font> =  <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) as    <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">L</font> ;<br/>
<a NAME="E3:75"/>
<font color="Maroon">S</font> is <a href="yellow_0.html#V4" target="_self">full</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="75_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:75_2"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D14" target="_self">YELLOW_0:def 14</a><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:75"/>
 <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) is  <a href="yellow_0.html#V4" target="_self">full</a>  <a href="yellow_0.html#M1" target="_self">SubRelStr</a> of <font color="Maroon">L</font>
 ;<br/>


</div>
