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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"> 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/> ( <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a> iff <font color="Olive" title="b1">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> )</span><br/><b>let </b><font color="Maroon" title="c2">X</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a> iff <font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> )</span><br/>



<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font> implies <font color="Maroon" title="c2">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:134_1"/>
<font color="Maroon" title="c2">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font></span><br/><a NAME="E2:134_1"/><b>then </b>
for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> holds <br/><font color="Maroon" title="c2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="pboole.html#D15" target="_self" title="PBOOLE:def.15">Def15</a></i>;<br/><b>hence </b><a NAME="E3:134_1"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</font>
 <b>by </b><i><a class="ref" href="pboole.html#T6" target="_self" title="PBOOLE:th.6">Th6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:134"/><i><font color="Green" title="E73">A1</font></i>: 
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="pboole.html#K1" title="PBOOLE:func.1">[0]</a> <font color="Maroon" title="c1">I</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">X</font> is <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a></span><br/>

<b>let </b><font color="Maroon" title="c3">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D15" target="_self" title="PBOOLE:def.15">PBOOLE:def 15</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">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> implies <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> )</span><br/>

<b>assume </b><a NAME="E3:134"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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></span><br/>

<b>thus </b><a NAME="E4:134"/>
<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="#E2:134"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="pboole.html#T5" target="_self" title="PBOOLE:th.5">Th5</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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