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<b>let </b><font color="Maroon" title="c1">W</font> be  <a href="setfam_1.html#NV3" title="SETFAM_1:NV.3">with_non-empty_element</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">W</font> <a href="waybel34.html#K4" title="WAYBEL34:func.4">-INF_category</a> ,<font color="Maroon" title="c1">W</font> <a href="waybel34.html#K5" title="WAYBEL34:func.5">-SUP_category</a>  <a href="functor0.html#R2" title="FUNCTOR0:pred.2">are_anti-isomorphic</a> </span><br/>

<b>take </b>
<font color="Maroon" title="c1">W</font> <a href="waybel34.html#K6" title="WAYBEL34:func.6">LowerAdj</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D41" title="FUNCTOR0:def.41">FUNCTOR0:def 41</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">W</font> <a href="waybel34.html#K6" title="WAYBEL34:func.6">LowerAdj</a>  is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c1">W</font> <a href="waybel34.html#K6" title="WAYBEL34:func.6">LowerAdj</a>  is <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a> )</span><br/>

<b>thus </b><a NAME="E1:37"/>
( <font color="Maroon" title="c1">W</font> <a href="waybel34.html#K6" title="WAYBEL34:func.6">LowerAdj</a>  is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c1">W</font> <a href="waybel34.html#K6" title="WAYBEL34:func.6">LowerAdj</a>  is <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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