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<b>let </b><font color="Maroon">L1</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">L2</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">L3</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">g1</font> be  <a href="waybel_0.html#V17">infs-preserving</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L1</font>,<font color="Maroon">L2</font>;<br/><b>let </b><font color="Maroon">g2</font> be  <a href="waybel_0.html#V17">infs-preserving</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L2</font>,<font color="Maroon">L3</font>;<br/>





<a NAME="E1:18"/>
( <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">g1</font>,<span class="p2">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g1</font></span>)</span></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a> &amp; <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">g2</font>,<span class="p2">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g2</font></span>)</span></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:18"/><b>then </b>
( <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g1</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g2</font></span>)</span></span>)</span></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a> &amp; <font color="Maroon">g2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g1</font> is <a href="waybel_0.html#V17">infs-preserving</a> )
 
<b>by </b><i><a class="ref" href="waybel15.html#T7">WAYBEL15:7</a>, <a class="ref" href="waybel20.html#T26">WAYBEL20:26</a></i>;<br/>
<b>hence </b><a NAME="E3:18"/>
 <a href="waybel34.html#K1" target="_self">LowerAdj</a> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g1</font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" target="_self">LowerAdj</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i/>;<br/>


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