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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font>;<br/>



<b>assume </b><a NAME="E1:75"/>
<font color="Maroon" title="c2">f</font> <a href="waybel_1.html#NR10" title="WAYBEL_1:NR.10">is_a_projection_operator</a> 
 ;<br/>

<a NAME="E2:75"/><b>then </b><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c2">f</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> &amp; <font color="Maroon" title="c2">f</font> is <a href="quantal1.html#V11" title="QUANTAL1:attr.11">idempotent</a> )
 
<b>by </b><i><a class="ref" href="waybel_1.html#D13" target="_self" title="WAYBEL_1:def.13">Def13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">T</font> =  <a href="yellow_2.html#K1" title="YELLOW_2:func.1">Image</a> <font color="Maroon" title="c2">f</font> as  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c4">q</font> =  <a href="waybel_1.html#K2" title="WAYBEL_1:func.2">corestr</a> <font color="Maroon" title="c2">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c3">T</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">i</font> =  <a href="waybel_1.html#K3" title="WAYBEL_1:func.3">inclusion</a> <font color="Maroon" title="c2">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">T</font>,<font color="Maroon" title="c1">L</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">T</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c4">q</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c5">i</font>
;<br/>

<b>thus </b><a NAME="E6:75"/>
<font color="Maroon" title="c4">q</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a>
 <b>by </b><i><a class="txt" href="waybel_1.html#E2:75"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="waybel_1.html#T33" target="_self" title="WAYBEL_1:th.33">Th33</a></i>;<br/>

<b>thus </b><a NAME="E7:75"/>
<font color="Maroon" title="c4">q</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 ;<br/>

<b>thus </b><a NAME="E8:75"/>
( <font color="Maroon" title="c5">i</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> &amp; <font color="Maroon" title="c5">i</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 ;<br/>

<b>thus </b><a NAME="E9:75"/>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">i</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="ref" href="waybel_1.html#T35" target="_self" title="WAYBEL_1:th.35">Th35</a></i>;<br/>

<b>thus </b><a NAME="E10:75"/>
 <a href="grcat_1.html#K7" title="GRCAT_1:func.7">id</a> <font color="Maroon" title="c3">T</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">q</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">i</font>
 <b>by </b><i><a class="txt" href="waybel_1.html#E2:75"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="waybel_1.html#T36" target="_self" title="WAYBEL_1:th.36">Th36</a></i>;<br/>


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