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<b>let </b><font color="Maroon">H</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> ;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">P1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">H</font>;<br/><b>let </b><font color="Maroon">Q1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">H</font>;<br/>









<b>assume </b><a NAME="E1:7"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">P1</font> &amp; <font color="Maroon">Q</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q1</font> )
 ;<br/>

<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="E2:7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="group_2.html#K2">*</a> <font color="Maroon">Q</font>
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>, <font color="Maroon">t</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font><b> such that </b><br/><a NAME="E4:7"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="group_1.html#K1">*</a> <font color="Maroon">t</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Q</font> )
 <b>by </b><i><a class="ref" href="group_2.html#T12">GROUP_2:12</a></i>;<br/>
<b>thus </b><a NAME="E5:7"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P1</font> <a href="group_2.html#K2">*</a> <font color="Maroon">Q1</font>
 <b>by </b><i>, , <a class="ref" href="group_2.html#T12">GROUP_2:12</a></i>;<br/>


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