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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">p</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><a NAME="E1:86"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">p</font> <a href="waybel_1.html#NR10" target="_self">is_a_projection_operator</a> 
 ;<br/>

<b>let </b><font color="Maroon">Lc</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">Lk</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E2:86"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">Lc</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">c</font> where <font color="Olive">c</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font> </span>}</span> 
 ;<br/>

<b>set </b><font color="Maroon">Lk</font> = <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">k</font> </span>}</span> ;<br/>
<a NAME="E3:86"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Lc</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">k</font> </span>}</span> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E4:86"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">Lc</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">Lc</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Maroon">p</font> <a href="funct_2.html#K3">.</a> <font color="Olive">k</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">k</font> </span>}</span> 
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:86"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">Lc</font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Lc</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E6:86"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">Lc</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">Lc</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E7:86"/>
<font color="Maroon">p</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">Lc</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">Lc</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/>
<b>hence </b><a NAME="E8:86"/>
<font color="Maroon">p</font> <a href="partfun1.html#K2">|</a> <font color="Maroon">Lc</font> is   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">Lc</font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">Lc</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="funct_2.html#T8">FUNCT_2:8</a></i>;<br/>


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