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<span class="kw">let </span><font color="Maroon" title="c2">e</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">e</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:13_1_1_1"/>
( <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  not <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:13_1_1_1_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">e</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_1_1_1_1"/>
<font color="Maroon" title="c2">e</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="subset_1.html#D1" onmouseover="rs('subset_1/D1')" onmouseout="rh()">SUBSET_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:13_1_1_1_2"/>
 not <font color="Maroon" title="c1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">e</font> is  <a href="rat_1.html#V1" title="RAT_1:attr.1">rational</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:13_1_1_1_2"/>
<font color="Maroon" title="c2">e</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="membered.html#D4" target="_self" onmouseover="rs('membered/D4')" onmouseout="rh()">Def4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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