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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="orders_2.html#NM1">Poset</a>, <font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="orders_2.html#NM1">Poset</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="lattice3.html#V3">complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">L</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>





<a NAME="E1:4"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">f</font> is <a href="waybel_0.html#V17">infs-preserving</a> &amp; <font color="Maroon">g</font> is <a href="waybel_0.html#V17">infs-preserving</a> &amp; <font color="Maroon">f</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> &amp; <font color="Maroon">g</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> )
 
<b>by </b><i><a class="ref" href="waybel16.html#D1">WAYBEL16:def 1</a></i>;<br/>
<a NAME="E2:4"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is <a href="waybel_0.html#V17">infs-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel20.html#T26">WAYBEL20:26</a></i>;<br/>
<a NAME="E3:4"/>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i>, <a class="ref" href="waybel20.html#T29">WAYBEL20:29</a></i>;<br/>
<b>hence </b><a NAME="E4:4"/>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> is    <a href="waybel16.html#M1">CLHomomorphism</a> of <font color="Maroon">L</font>,<font color="Maroon">T</font>
 <b>by </b><i>, <a class="ref" href="waybel16.html#D1">WAYBEL16:def 1</a></i>;<br/>


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