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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:142_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V25" target="_self">/\-complete</a>
 ;<br/>

<a NAME="E2:142_1_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T76" target="_self">Th76</a></i>;<br/>
<b>hence </b><a NAME="E3:142_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="lattice3.html#V2">with_infima</a>
 <b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>


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