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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">M</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">P</font>, <font color="Olive" title="b3">R</font> being  <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Olive" title="b1">M</font>  st <font color="Olive" title="b2">P</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  &amp; <font color="Olive" title="b3">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  holds <br/><font color="Olive" title="b2">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Olive" title="b3">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M</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"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">R</font> being  <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Maroon" title="c2">M</font>  st <font color="Olive" title="b1">P</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  &amp; <font color="Olive" title="b2">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  holds <br/><font color="Olive" title="b1">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Olive" title="b2">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font>, <font color="Maroon" title="c4">R</font> be   <a href="closure1.html#NM1" title="CLOSURE1:NM.1">MSSetOp</a> of <font color="Maroon" title="c2">M</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">P</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c4">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  implies <font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Maroon" title="c4">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  )</span><br/>







<span class="kw">assume </span><a NAME="E1:31"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
( <font color="Maroon" title="c3">P</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c4">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a>  )
 ; <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">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Maroon" title="c4">R</font> is  <a href="closure1.html#V1" title="CLOSURE1:attr.1">reflexive</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c5">X</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">Element</a> of  <a href="mssubfam.html#K5" title="MSSUBFAM:func.5">bool</a> <font color="Maroon" title="c2">M</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="closure1.html#D2" target="_self" title="CLOSURE1:def.2">CLOSURE1:def 2</a> <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="c5">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Maroon" title="c4">R</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font></span><br/>

<a NAME="E2:31"/>
( <font color="Maroon" title="c5">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c4">R</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c4">R</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">P</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:31"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="closure1.html#D2" target="_self" title="CLOSURE1:def.2">Def2</a></span>;<br/>
<a NAME="E3:31"/><span class="kw">then </span>
(  <a href="funct_6.html#K2" title="FUNCT_6:func.2">doms</a> <font color="Maroon" title="c4">R</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a>  <a href="mssubfam.html#K5" title="MSSUBFAM:func.5">bool</a> <font color="Maroon" title="c2">M</font> &amp; <font color="Maroon" title="c5">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">P</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">R</font> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mssubfam.html#T17" title="MSSUBFAM:th.17">MSSUBFAM:17</a>, <a class="ref" href="pboole.html#T15" title="PBOOLE:th.15">PBOOLE:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:31"/>
<font color="Maroon" title="c5">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">**</a> <font color="Maroon" title="c4">R</font></span>)</span> <a href="closure1.html#K2" title="CLOSURE1:func.2">..</a> <font color="Maroon" title="c5">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="closure1.html#T4" target="_self" title="CLOSURE1:th.4">Th4</a>, <a class="ref" href="mssubfam.html#T12" title="MSSUBFAM:th.12">MSSUBFAM:12</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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