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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.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/><span class="kw">let </span><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>





<span class="kw">assume </span><a NAME="E1:151"/><span class="lab"><font color="Green" title="E75">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E2:151"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:151"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="pboole.html#T144" target="_self" title="PBOOLE:th.144">Th144</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:151"/>
<font color="Maroon" title="c3">Y</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:151"><span class="lab"><font color="Green" title="E75">A1</font></span></a>, <a class="ref" href="pboole.html#T143" target="_self" title="PBOOLE:th.143">Th143</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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