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<b>let </b><font color="Maroon">L</font> be  <a href="waybel_1.html#V2">distributive</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">l1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:47_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">l1</font> <a href="hidden.html#R2">in</a>  <a href="waybel_6.html#K4" target="_self">PRIME</a> <font color="Maroon">L</font>
 ;<br/><b>then reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l1</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="waybel_6.html#K4" target="_self">PRIME</a> <font color="Maroon">L</font> ;<br/><b>reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/><a NAME="E4:47_1"/>
<font color="Maroon">l</font> is <a href="waybel_6.html#V5" target="_self">prime</a>
 <b>by </b><i>, </i>;<br/><a NAME="E5:47_1"/><b>then </b>
<font color="Maroon">l</font> is <a href="waybel_6.html#V2" target="_self">meet-irreducible</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:47_1"/>
<font color="Maroon">l1</font> <a href="hidden.html#R2">in</a>  <a href="waybel_6.html#K3" target="_self">IRR</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:47"/>
 <a href="waybel_6.html#K4" target="_self">PRIME</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_6.html#K3" target="_self">IRR</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">l1</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:47_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">l1</font> <a href="hidden.html#R2">in</a>  <a href="waybel_6.html#K3" target="_self">IRR</a> <font color="Maroon">L</font>
 ;<br/><b>then reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l1</font> as    <a href="subset_1.html#M1">Element</a> of  <a href="waybel_6.html#K3" target="_self">IRR</a> <font color="Maroon">L</font> ;<br/><b>reconsider </b><font color="Maroon">l</font> = <font color="Maroon">l</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> <b>by </b><i/>;<br/><a NAME="E4:47_2"/>
<font color="Maroon">l</font> is <a href="waybel_6.html#V2" target="_self">meet-irreducible</a>
 <b>by </b><i>, </i>;<br/><a NAME="E5:47_2"/><b>then </b>
<font color="Maroon">l</font> is <a href="waybel_6.html#V5" target="_self">prime</a>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:47_2"/>
<font color="Maroon">l1</font> <a href="hidden.html#R2">in</a>  <a href="waybel_6.html#K4" target="_self">PRIME</a> <font color="Maroon">L</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:47"/>
 <a href="waybel_6.html#K3" target="_self">IRR</a> <font color="Maroon">L</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_6.html#K4" target="_self">PRIME</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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