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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>, <font color="Olive" title="b2">Y</font> being   <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st <font color="Olive" title="b1">X</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> &amp; <font color="Olive" title="b1">X</font> <a href="pboole.html#R7" title="PBOOLE:pred.7">[=</a> <font color="Olive" title="b2">Y</font> holds <br/><font color="Olive" title="b2">Y</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</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#V2" title="RELAT_1:attr.2">non-empty</a> &amp; <font color="Maroon" title="c2">X</font> <a href="pboole.html#R7" title="PBOOLE:pred.7">[=</a> <font color="Maroon" title="c3">Y</font> implies <font color="Maroon" title="c3">Y</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )</span><br/>





<b>assume </b><a NAME="E1:139"/><i><font color="Green" title="E75">A1</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"> (  not <font color="Maroon" title="c2">X</font> <a href="pboole.html#R7" title="PBOOLE:pred.7">[=</a> <font color="Maroon" title="c3">Y</font> or <font color="Maroon" title="c3">Y</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )</span><br/>

<b>assume </b><a NAME="E2:139"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R7" title="PBOOLE:pred.7">[=</a> <font color="Maroon" title="c3">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">Y</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a></span><br/>

<a NAME="E3:139"/><b>then </b>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Y</font>
 
<b>by </b><i><a class="txt" href="pboole.html#E1:139"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="pboole.html#T144" target="_self" title="PBOOLE:th.144">Th144</a></i>;<br/>
<b>hence </b><a NAME="E4:139"/>
<font color="Maroon" title="c3">Y</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 <b>by </b><i><a class="txt" href="pboole.html#E1:139"><i><font color="Green" title="E75">A1</font></i></a>, <a class="ref" href="pboole.html#T143" target="_self" title="PBOOLE:th.143">Th143</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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