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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">f</font> is <a href="bspace.html#V1" title="BSPACE:attr.1">Singleton</a></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c2">f</font> is <a href="bspace.html#V1" title="BSPACE:attr.1">Singleton</a> )</span><br/>



<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c2">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="bspace.html#K9" title="BSPACE:func.9">singletons</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> is <a href="bspace.html#V1" title="BSPACE:attr.1">Singleton</a></span><br/>

<a NAME="E2:37"/>
<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>
 
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E26">A1</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c3">g</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c3">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font>
 <b>and </b><br/><a NAME="E5:37"/><i><font color="Green" title="E28">A3</font></i>: 
<font color="Maroon" title="c3">g</font> is <a href="bspace.html#V1" title="BSPACE:attr.1">Singleton</a>
 ;<br/>
<b>thus </b><a NAME="E6:37"/>
<font color="Maroon" title="c2">f</font> is <a href="bspace.html#V1" title="BSPACE:attr.1">Singleton</a>
 <b>by </b><i><a class="txt" href="#E4:37"><i><font color="Green" title="E27">A2</font></i></a>, <a class="txt" href="#E5:37"><i><font color="Green" title="E28">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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