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<b>let </b><font color="Maroon" title="c1">I</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">I</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies for <font color="Olive" title="b1">X</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  holds <br/>(  not <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a> or  not <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> ) )</span><br/>

<b>assume </b><a NAME="E1:2"/><i><font color="Green" title="E2">A1</font></i>: 
not <font color="Maroon" title="c1">I</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">X</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  holds <br/>(  not <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a> or  not <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )</span><br/>

<b>given </b><font color="Maroon" title="c2">X</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><b> such that </b><a NAME="E3:2"/><i><font color="Green" title="E3">A2</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green" title="E4">A3</font></i>: 
<font color="Maroon" title="c2">X</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>consider </b><font color="Maroon" title="c3">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:2"/><i><font color="Green" title="E5">A4</font></i>: 
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="txt" href="pzfmisc1.html#E1:2"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E7:2"/>
( <font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="pzfmisc1.html#E3:2"><i><font color="Green" title="E3">A2</font></i></a>, <a class="txt" href="pzfmisc1.html#E4:2"><i><font color="Green" title="E4">A3</font></i></a>, <a class="txt" href="pzfmisc1.html#E6:2"><i><font color="Green" title="E5">A4</font></i></a>, <a class="ref" href="pboole.html#D15" title="PBOOLE:def.15">PBOOLE:def 15</a>, <a class="ref" href="pboole.html#D16" title="PBOOLE:def.16">PBOOLE:def 16</a></i>;<br/>
<b>hence </b><a NAME="E8:2"/>
contradiction
 ; <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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