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<b>let </b><font color="Maroon" title="c1">X</font> be    <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"> ( not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a> implies  not <font color="Maroon" title="c1">X</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a> )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:62_1_1"/><i><font color="Green" title="E16">A1</font></i>: 
not <font color="Maroon" title="c1">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>and </b><br/><a NAME="E2:62_1_1"/><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c1">X</font> is <a href="setfam_1.html#V2" title="SETFAM_1:attr.2">empty-membered</a></span><br/>

<b>consider </b><font color="Maroon" title="c2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:62_1_1"/><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="setfam_1.html#E1:62_1_1"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="subset_1.html#T10" title="SUBSET_1:th.10">SUBSET_1:10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">x</font> as  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>  <b>by </b><i><a class="txt" href="setfam_1.html#E2:62_1_1"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="setfam_1.html#E4:62_1_1"><i><font color="Green" title="E18">A3</font></i></a>, <a class="ref" href="setfam_1.html#D9" target="_self" title="SETFAM_1:def.9">Def9</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">x</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="setfam_1.html#D11" target="_self" title="SETFAM_1:def.11">SETFAM_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<b>thus </b><a NAME="E6:62_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="txt" href="setfam_1.html#E4:62_1_1"><i><font color="Green" title="E18">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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