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<b>let </b><font color="Maroon">L1</font> be   <a href="lattices.html#NM1">Lattice</a>, <font color="Maroon">L2</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">D1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L1</font>, <font color="Maroon">E1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">D2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L2</font>, <font color="Maroon">E2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L2</font>;<br/>





<b>assume </b><a NAME="E1:68"/><i><font color="Green">E14</font></i>: 
(  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L1</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L1</font> #) <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">L2</font>,the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">L2</font> #) &amp; <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D2</font> &amp; <font color="Maroon">E1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E2</font> )
 ;<br/>

<b>thus </b><a NAME="E2:68"/>
<font color="Maroon">D1</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E2</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<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="E1:68_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E1</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font><b> such that </b><br/><a NAME="E3:68_1"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E1</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font> <b>by </b><i/>;<br/>
<a NAME="E5:68_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b'</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:68_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E2</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>

<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="E3:68"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E2</font>
 ;<br/>

<b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font><b> such that </b><br/><a NAME="E5:68"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D2</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">E2</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font>, <font color="Maroon">b'</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/>
<a NAME="E7:68"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a'</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b'</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:68"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D1</font> <a href="filter_0.html#K5">"/\"</a> <font color="Maroon">E1</font>
 <b>by </b><i>, </i>;<br/>


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