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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</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="c1">S</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> <font color="Maroon" title="c1">S</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">thus </span><a NAME="E1:4_4_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">S</font> implies <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="ref" href="rat_1.html#D2" title="RAT_1:def.2">RAT_1:def 2</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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