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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">B</font> be  <a href="waybel23.html#V6" target="_self">with_bottom</a>  <a href="waybel23.html#M1" target="_self">CLbasis</a> of <font color="Maroon">L</font>;<br/>



<b>set </b><font color="Maroon">f</font> =  <a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="96_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>assume </b><a NAME="E1:96_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 ;<br/><a NAME="E2:96_1"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/><a NAME="E3:96_1"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/><a NAME="E4:96_1"/>
 <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#T12">WAYBEL_3:12</a></i>;<br/><a NAME="E5:96_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/><b>hence </b><a NAME="E6:96_1"/>
<span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:96"/>
 <a href="waybel23.html#K5" target="_self">baseMap</a> <font color="Maroon">B</font> is <a href="orders_3.html#V5">monotone</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#D2">WAYBEL_1:def 2</a></i>;<br/>


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