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<span class="kw">assume </span><a NAME="E1:41_1_1"/>
 not  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <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"> contradiction</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:41_1_1"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font>
 ;<br/>
<a NAME="E4:41_1_1"/>
 ex <font color="Olive" title="b1">g</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> &amp; <font color="Olive" title="b1">g</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:41_1_1"><span class="lab"><font color="Green" title="E30">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:41_1_1"/>
contradiction
 ; <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/>


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