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

<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>



<b>given </b><font color="Maroon">c<sub>3</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>, <font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:76"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="orders_3.html#V5">monotone</a>
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="orders_3.html#V5">monotone</a>
 <b>and </b><br/><a NAME="E3:76"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E4:76"/><i><font color="Green">E51</font></i>: 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<i><font color="Green">E52</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel_1.html#E4:76"><i><font color="Green">E51</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#D11">GRCAT_1:def 11</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<b>thus </b><a NAME="E6:76"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="quantal1.html#V11">idempotent</a>
 <b>by </b><i><a class="txt" href="waybel_1.html#E3:76"><i><font color="Green">E50</font></i></a>, <a class="txt" href="waybel_1.html#E5:76"><i><font color="Green">E52</font></i></a>, <a class="ref" href="waybel_1.html#T22" target="_self">Th22</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D13" target="_self">WAYBEL_1:def 13</a><br/>

<b>thus </b><a NAME="E7:76"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="orders_3.html#V5">monotone</a>
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:76"><i><font color="Green">E48</font></i></a>, <a class="txt" href="waybel_1.html#E2:76"><i><font color="Green">E49</font></i></a>, <a class="txt" href="waybel_1.html#E3:76"><i><font color="Green">E50</font></i></a>, <a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>


</div>
