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<b>let </b><font color="Maroon" title="c1">L1</font>, <font color="Maroon" title="c2">L2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="waybel_0.html#V24" title="WAYBEL_0:attr.24">up-complete</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">L1</font>,<font color="Maroon" title="c2">L2</font>;<br/>



<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L1</font>;<br/>

<b>thus </b><a NAME="E2:35"/>
( <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> implies <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_1"/>
<font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 ;<br/>

<a NAME="E2:35_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/>
<a NAME="E3:35_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="waybel13.html#T27" target="_self" title="WAYBEL13:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E4:35_1"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 <b>by </b><i><a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:35"/>
( <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> implies <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:35_2"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 ;<br/>

<a NAME="E2:35_2"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/>
<a NAME="E3:35_2"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c4">x</font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:35"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="waybel13.html#T27" target="_self" title="WAYBEL13:th.27">Th27</a></i>;<br/>
<b>hence </b><a NAME="E4:35_2"/>
<font color="Maroon" title="c4">x</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a>
 <b>by </b><i><a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/>


</div><b>end;</b></div>


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