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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/><b>let </b><font color="Maroon" title="c2">k</font> be  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> <a href="waybel_1.html#V8" title="WAYBEL_1:attr.8">kernel</a> <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>set </b><font color="Maroon" title="c3">R</font> =  <a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font>;<br/>
<b>thus </b><a NAME="E1:45"/><i><font color="Green" title="E31">A1</font></i>: 
 <a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font> is   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="ref" href="waybel20.html#T2" target="_self" title="WAYBEL20:th.2">Th2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel20.html#D2" target="_self" title="WAYBEL20:def.2">WAYBEL20:def 2</a><br/>

<b>consider </b><font color="Maroon" title="c4">LR</font> being  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><b> such that </b><br/><a NAME="E3:45"/><i><font color="Green" title="E32">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">LR</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" title="WAYBEL20:func.2">EqRel</a> <span class="p2">(<span class="default"><a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:45"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">LR</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p4">(<span class="default"><a href="waybel20.html#K2" title="WAYBEL20:func.2">EqRel</a> <span class="p5">(<span class="default"><a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Olive" title="b1">x</font></span>)</span>,<span class="p3">(<span class="default"><a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p4">(<span class="default"><a href="waybel20.html#K2" title="WAYBEL20:func.2">EqRel</a> <span class="p5">(<span class="default"><a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Olive" title="b2">y</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> : <font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c2">k</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> </span>}</span> 
 <b>and </b><br/><a NAME="E5:45"/><i><font color="Green" title="E33">A3</font></i>: 
for <font color="Olive" title="b1">g</font> being  <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="c4">LR</font>  st ( for <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> <span class="p1">(<span class="default"><a href="waybel20.html#K2" title="WAYBEL20:func.2">EqRel</a> <span class="p2">(<span class="default"><a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font></span>)</span></span>)</span>,<font color="Olive" title="b2">x</font> ) holds <br/><font color="Olive" title="b1">g</font> is    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c4">LR</font>
 <b>by </b><i><a class="ref" href="waybel20.html#T38" target="_self" title="WAYBEL20:th.38">Th38</a></i>;<br/>
<b>thus </b><a NAME="E6:45"/>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <span class="p1">(<span class="default"><a href="waybel20.html#K4" title="WAYBEL20:func.4">kernel_congruence</a> <font color="Maroon" title="c2">k</font></span>)</span> is   <a href="waybel_5.html#NM3" title="WAYBEL_5:NM.3">CLSubFrame</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>
 <b>by </b><i><a class="txt" href="waybel20.html#E1:45"><i><font color="Green" title="E31">A1</font></i></a>, <a class="txt" href="waybel20.html#E3:45"><i><font color="Green" title="E32">A2</font></i></a>, <a class="txt" href="waybel20.html#E5:45"><i><font color="Green" title="E33">A3</font></i></a>, <a class="ref" href="waybel20.html#T39" target="_self" title="WAYBEL20:th.39">Th39</a></i>;<br/>


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