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<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:22_1_2"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> iff ( <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">c</font> &amp; <font color="Olive">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> ) )
 <b>and </b><br/><a NAME="E2:22_1_2"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> iff ( <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">c</font> &amp; <font color="Olive">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> ) )
 ;<br/>

<div><i><font color="Green">E42</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 ;<br/><b>then reconsider </b><font color="Maroon">c</font> = <font color="Maroon">c1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/><a NAME="E3:22_1_2_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> iff ( <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:22_1_2_1"/>
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:22_1_2_2"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 ;<br/><b>then reconsider </b><font color="Maroon">c</font> = <font color="Maroon">c1</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/><a NAME="E3:22_1_2_2"/>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> iff ( <font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font> ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:22_1_2_2"/>
<font color="Maroon">c1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<a NAME="E5:22_1_2"/><b>then </b>
( <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:22_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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