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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">X</font> is  <a href="membered.html#V4" title="MEMBERED:attr.4">rational-membered</a>  ) implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">F</font> is  <a href="membered.html#V4" title="MEMBERED:attr.4">rational-membered</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:106"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
 for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">X</font> is  <a href="membered.html#V4" title="MEMBERED:attr.4">rational-membered</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">F</font> is  <a href="membered.html#V4" title="MEMBERED:attr.4">rational-membered</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="membered.html#D4" target="_self" title="MEMBERED:def.4">MEMBERED:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">F</font> implies <font color="Maroon" title="c2">x</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:106"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">X</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:106"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">and </span><br/><a NAME="E5:106"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<font color="Maroon" title="c3">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/>
<a NAME="E6:106"/>
<font color="Maroon" title="c3">X</font> is  <a href="membered.html#V4" title="MEMBERED:attr.4">rational-membered</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:106"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E5:106"><span class="lab"><font color="Green" title="E27">A3</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:106"/>
<font color="Maroon" title="c2">x</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:106"><span class="lab"><font color="Green" title="E26">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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