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<b>let </b><font color="Maroon">A</font> be   <a href="roughs_1.html#NM2">Tolerance_Space</a>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>







<b>assume </b><a NAME="E1:49"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">X</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">Y</font></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:49_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">X</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">Y</font> )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_1"><b>suppose </b></a><a NAME="E1:49_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">X</font>
 ;<br/><div class="add"><a NAME="E2:49_1_1"/><b>then </b>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/><a NAME="E3:49_1_1"/><b>then </b>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><b>hence </b><a NAME="E4:49_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="49_1_2"><b>suppose </b></a><a NAME="E1:49_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <font color="Maroon">Y</font>
 ;<br/><div class="add"><a NAME="E2:49_1_2"/><b>then </b>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/><a NAME="E3:49_1_2"/><b>then </b>
 <a href="eqrel_1.html#K7">Class</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</font>,<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T10">XBOOLE_1:10</a></i>;<br/><b>hence </b><a NAME="E4:49_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="roughs_1.html#K3" target="_self">LAp</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">Y</font></span>)</span>
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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