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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">R</font> be  <a href="waybel_4.html#V4">auxiliary(iv)</a> <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel35.html#D3" target="_self">WAYBEL35:def 3</a><br/>







<b>assume </b><a NAME="E1:24"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span>,<font color="Maroon">x</font></span><a href="domain_1.html#K7">}</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font></span>)</span>,<font color="Maroon">x</font></span><a href="domain_1.html#K7">}</a></span> )
 ;<br/>

<a NAME="E2:24"/><b>then </b>
( ( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) &amp; ( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">L</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:24"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">a</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> )
 <b>by </b><i><a class="ref" href="waybel_4.html#D7">WAYBEL_4:def 7</a></i>;<br/>


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