<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="waybel_3.html#V2" title="WAYBEL_3:attr.2">satisfying_axiom_of_approximation</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="waybel_3.html#V2" title="WAYBEL_3:attr.2">satisfying_axiom_of_approximation</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:37_1_1"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Olive" title="b1">x</font></span>)</span>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel_3.html#D5" target="_self" title="WAYBEL_3:def.5">WAYBEL_3:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
