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<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ;<br/><b>let </b><font color="Maroon" title="c3">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="E1:4"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">a</font> <a href="integra2.html#K1" title="INTEGRA2:func.1">**</a> <font color="Maroon" title="c2">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<b>consider </b><font color="Maroon" title="c5">y</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E4:4"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c4">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <font color="Maroon" title="c5">y</font> )
 <b>by </b><i><a class="txt" href="int_4.html#E1:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="integra2.html#D2" title="INTEGRA2:def.2">INTEGRA2:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">y'</font> = <font color="Maroon" title="c5">y</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> <b>by </b><i><a class="txt" href="int_4.html#E4:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<a NAME="E6:4"/>
<font color="Maroon" title="c4">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c6">y'</font>
 
<b>by </b><i><a class="txt" href="int_4.html#E4:4"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:4"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>


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