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<b>let </b><font color="Maroon" title="c1">L</font>, <font color="Maroon" title="c2">S</font>, <font color="Maroon" title="c3">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c5">g</font> be    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">T</font>;<br/>





<a NAME="E1:4"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c4">f</font> is <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a> &amp; <font color="Maroon" title="c5">g</font> is <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a> &amp; <font color="Maroon" title="c4">f</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> &amp; <font color="Maroon" title="c5">g</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> )
 
<b>by </b><i><a class="ref" href="waybel16.html#D1" title="WAYBEL16:def.1">WAYBEL16:def 1</a></i>;<br/>
<a NAME="E2:4"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> is <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel20.html#T26" title="WAYBEL20:th.26">WAYBEL20:26</a></i>;<br/>
<a NAME="E3:4"/>
<font color="Maroon" title="c5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</font> is <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel22.html#E1:4"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="waybel20.html#T29" title="WAYBEL20:th.29">WAYBEL20:29</a></i>;<br/>
<b>hence </b><a NAME="E4:4"/>
<font color="Maroon" title="c5">g</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c4">f</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="c3">T</font>
 <b>by </b><i><a class="txt" href="waybel22.html#E2:4"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="waybel16.html#D1" title="WAYBEL16:def.1">WAYBEL16:def 1</a></i>;<br/>


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