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<b>let </b><font color="Maroon" title="c3">P</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">P</font> is <a href="closure1.html#V4" title="CLOSURE1:attr.4">topological</a> implies <font color="Maroon" title="c3">P</font> is <a href="closure1.html#V2" title="CLOSURE1:attr.2">monotonic</a> )</span><br/>

<b>assume </b><a NAME="E1:28_1_1"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c3">P</font> is <a href="closure1.html#V4" title="CLOSURE1:attr.4">topological</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">P</font> is <a href="closure1.html#V2" title="CLOSURE1:attr.2">monotonic</a></span><br/>

<b>let </b><font color="Maroon" title="c4">X</font>, <font color="Maroon" title="c5">Y</font> be    <a href="pboole.html#M2" title="PBOOLE:mode.2">Element</a> of  <a href="mssubfam.html#K7" title="MSSUBFAM:func.7">bool</a> <font color="Maroon" title="c2">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="closure1.html#D3" target="_self" title="CLOSURE1:def.3">CLOSURE1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">Y</font> implies <font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c5">Y</font> )</span><br/>

<b>assume </b><a NAME="E2:28_1_1"/><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c4">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c5">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">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c5">Y</font></span><br/>

<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">X</font></span>)</span> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</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="c5">Y</font></span>)</span> = 
<font color="Maroon" title="c3">P</font> <a href="closure1.html#K1" title="CLOSURE1:func.1">..</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="pboole.html#K2" title="PBOOLE:func.2">\/</a> <font color="Maroon" title="c5">Y</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:28_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="closure1.html#D5" target="_self" title="CLOSURE1:def.5">Def5</a></i>
<br/>.= 
<font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c5">Y</font>
<b>by </b><i><a class="txt" href="#E2:28_1_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="pboole.html#T24" title="PBOOLE:th.24">PBOOLE:24</a></i>
;<br/>
<b>hence </b><a NAME="E4:28_1_1"/>
<font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">P</font> <a href="closure1.html#K3" title="CLOSURE1:func.3">..</a> <font color="Maroon" title="c5">Y</font>
 <b>by </b><i><a class="ref" href="pboole.html#T28" title="PBOOLE:th.28">PBOOLE:28</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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