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<b>let </b><font color="Maroon" title="c2">it1</font>, <font color="Maroon" title="c3">it2</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="arrow.html#K2" title="ARROW:func.2">LinPreorders</a> <font color="Maroon" title="c1">A</font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:6_1_2"/><i><font color="Green" title="E4">A2</font></i>: 
( <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c2">it1</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c3">it2</font>] )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">R</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arrow.html#K2" title="ARROW:func.2">LinPreorders</a> <font color="Maroon" title="c1">A</font>;<br/><a NAME="E1:6_1_2_1"/>
( ( <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">it1</font> implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">R</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">R</font>] implies <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">it1</font> ) &amp; ( <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">it2</font> implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">R</font>] ) &amp; ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">R</font>] implies <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">it2</font> ) )
 <b>by </b><i><a class="txt" href="arrow.html#E1:6_1_2"><i><font color="Green" title="E4">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E2:6_1_2_1"/>
( <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">it1</font> iff <font color="Maroon" title="c4">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">it2</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:6_1_2"/>
<font color="Maroon" title="c2">it1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">it2</font>
 <b>by </b><i><a class="ref" href="subset_1.html#T8" title="SUBSET_1:th.8">SUBSET_1:8</a></i>;<br/>


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