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<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c5">x</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><br/>









<b>assume </b><a NAME="E1:35"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="group_3.html#K3" title="GROUP_3:func.3">|^</a> <font color="Maroon" title="c4">C</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E3:35"/><i><font color="Green" title="E28">A1</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">C</font> )
 ;<br/>
<b>consider </b><font color="Maroon" title="c8">g</font>, <font color="Maroon" title="c9">h</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><b> such that </b><br/><a NAME="E5:35"/><i><font color="Green" title="E29">A2</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c9">h</font> &amp; <font color="Maroon" title="c8">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> )
 <b>by </b><i><a class="txt" href="group_3.html#E3:35"><i><font color="Green" title="E28">A1</font></i></a></i>;<br/>
<a NAME="E6:35"/>
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">g</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">h</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c7">b</font></span>)</span> &amp; <font color="Maroon" title="c8">g</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="group_3.html#K3" title="GROUP_3:func.3">|^</a> <font color="Maroon" title="c4">C</font> &amp; <font color="Maroon" title="c9">h</font> <a href="group_3.html#K2" title="GROUP_3:func.2">|^</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="group_3.html#K3" title="GROUP_3:func.3">|^</a> <font color="Maroon" title="c4">C</font> )
 
<b>by </b><i><a class="txt" href="group_3.html#E3:35"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="group_3.html#E5:35"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="group_3.html#T28" target="_self" title="GROUP_3:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="group_3.html#K3" title="GROUP_3:func.3">|^</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="group_3.html#K3" title="GROUP_3:func.3">|^</a> <font color="Maroon" title="c4">C</font></span>)</span>
 ;<br/>


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