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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:80"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">f</font> is <a href="quantal1.html#V11">idempotent</a> &amp; <font color="Maroon">f</font> is <a href="orders_3.html#V5">monotone</a> )
 <b>and </b><br/><a NAME="E2:80"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">f</font> <a href="yellow_2.html#R1">&lt;=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">L</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D13" target="_self">WAYBEL_1:def 13</a>,<a class="ref" href="waybel_1.html#D15" target="_self">WAYBEL_1:def 15</a><br/>

<b>set </b><font color="Maroon">g</font> =  <a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">d</font> =  <a href="waybel_1.html#K3" target="_self">inclusion</a> <font color="Maroon">f</font>;<br/>
<a NAME="E3:80"/><i><font color="Green">E45</font></i>: 
 <a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i>, <a class="ref" href="waybel_1.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:80"/>
<span class="p1">(<span class="default"><a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K3" target="_self">inclusion</a> <font color="Maroon">f</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:80"/><b>then </b><i><font color="Green">E48</font></i>: 
 <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">f</font></span>)</span> <a href="yellow_2.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K3" target="_self">inclusion</a> <font color="Maroon">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T5" target="_self">Th5</a></i>;<br/>
<a NAME="E6:80"/>
<span class="p1">(<span class="default"><a href="waybel_1.html#K3" target="_self">inclusion</a> <font color="Maroon">f</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font></span>)</span> <a href="yellow_2.html#R1">&lt;=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">L</font>
 
<b>by </b><i>, <a class="ref" href="waybel_1.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E7:80"/>
<span class="p1"><a href="waybel_1.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K2" target="_self">corestr</a> <font color="Maroon">f</font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel_1.html#K3" target="_self">inclusion</a> <font color="Maroon">f</font></span>)</span></span><a href="waybel_1.html#K1" target="_self">]</a></span> is <a href="waybel_1.html#V3" target="_self">Galois</a>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D2" target="_self">Def2</a></i>;<br/>


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