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<b>let </b><font color="Maroon" title="c1">D</font>, <font color="Maroon" title="c2">D'</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">UN</font> being  <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a><br/> for <font color="Olive" title="b2">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">D'</font>  st <font color="Maroon" title="c1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">UN</font> &amp; <font color="Maroon" title="c2">D'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">UN</font> holds <br/><font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">UN</font></span><br/><b>let </b><font color="Maroon" title="c3">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</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="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">D'</font>  st <font color="Maroon" title="c1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> &amp; <font color="Maroon" title="c2">D'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> holds <br/><font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">D'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> &amp; <font color="Maroon" title="c2">D'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> implies <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> )</span><br/>







<b>assume </b><a NAME="E1:59"/>
( <font color="Maroon" title="c1">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> &amp; <font color="Maroon" title="c2">D'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font></span><br/>

<a NAME="E2:59"/><b>then </b><i><font color="Green" title="E45">A1</font></i>: 
 <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">D'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font>
 
<b>by </b><i><a class="ref" href="classes2.html#T67" title="CLASSES2:th.67">CLASSES2:67</a></i>;<br/>
<a NAME="E3:59"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon" title="c1">D</font>,<font color="Maroon" title="c2">D'</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T11" title="FUNCT_2:th.11">FUNCT_2:11</a></i>;<br/>
<b>hence </b><a NAME="E4:59"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">UN</font>
 <b>by </b><i><a class="txt" href="mod_2.html#E2:59"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="grcat_1.html#T4" title="GRCAT_1:th.4">GRCAT_1:4</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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