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<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#V5" title="ORDERS_2:attr.5">antisymmetric</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">L</font> is  <a href="waybel_0.html#V25" title="WAYBEL_0:attr.25">/\-complete</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:142_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="waybel_0.html#V25" title="WAYBEL_0:attr.25">/\-complete</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">L</font> is  <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> </span><br/>

<a NAME="E2:142_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T76" target="_self" onmouseover="rs('waybel_0/T76')" onmouseout="rh()">Th76</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:142_1_1"/>
<font color="Maroon" title="c1">L</font> is  <a href="lattice3.html#V2" title="LATTICE3:attr.2">with_infima</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T21" onmouseover="rs('yellow_0/T21')" onmouseout="rh()">YELLOW_0:21</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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