<?xml version="1.0"?>
<div class="add">

<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">M</font> being <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>  <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b3">Y</font> is    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Olive" title="b1">M</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b3">Y</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Olive" title="b2">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Olive" title="b1">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Olive" title="b3">Y</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">M</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>  <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"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b2">Y</font> is    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Maroon" title="c2">M</font> holds <br/><span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Olive" title="b2">Y</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Olive" title="b2">Y</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">Y</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Maroon" title="c2">M</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">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font> is    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Maroon" title="c2">M</font> implies <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c4">Y</font></span>)</span> )</span><br/>





<b>set </b><font color="Maroon" title="c5">F</font> =  <a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font>;<br/>
<b>assume </b><a NAME="E1:18"/>
<font color="Maroon" title="c3">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font> is    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of <font color="Maroon" title="c2">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c4">Y</font></span>)</span></span><br/>

<b>hence </b><span class="p1">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font></span>)</span> = 
<font color="Maroon" title="c3">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font>
<b>by </b><i><a class="ref" href="closure1.html#T8" target="_self" title="CLOSURE1:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c4">Y</font>
<b>by </b><i><a class="ref" href="closure1.html#T8" target="_self" title="CLOSURE1:th.8">Th8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2" title="MSUALG_3:func.2">id</a> <font color="Maroon" title="c2">M</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c4">Y</font></span>)</span>
<b>by </b><i><a class="ref" href="closure1.html#T8" target="_self" title="CLOSURE1:th.8">Th8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
