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<b>let </b><font color="Maroon" title="c4">D1</font>, <font color="Maroon" title="c5">D2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font></span><br/>

<b>thus </b><a NAME="E1:12_1_1"/>
<font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font> or <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font> )</span><br/>

<b>assume </b><a NAME="E1:12_1_1_1"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font></span><br/>

<b>then consider </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E3:12_1_1_1"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c8">y</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> )
 ;<br/>
<b>thus </b><a NAME="E4:12_1_1_1"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font>
 <b>by </b><i><a class="txt" href="#E3:12_1_1_1"><i><font color="Green" title="E5">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>let </b><font color="Maroon" title="c6">q</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font> or <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font> )</span><br/>

<b>assume </b><a NAME="E2:12_1_1"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c4">D1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font></span><br/>

<b>then consider </b><font color="Maroon" title="c7">x</font>, <font color="Maroon" title="c8">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E4:12_1_1"/><i><font color="Green" title="E5">A2</font></i>: 
( <font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c8">y</font> &amp; <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D2</font> &amp; <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> )
 ;<br/>
<b>thus </b><a NAME="E5:12_1_1"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D1</font> <a href="yellow_4.html#K1" title="YELLOW_4:func.1">"\/"</a> <font color="Maroon" title="c5">D2</font>
 <b>by </b><i><a class="txt" href="#E4:12_1_1"><i><font color="Green" title="E5">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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