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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="membered.html#V2">real-membered</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="membered.html#V2">real-membered</a>  <a href="hidden.html#M1">set</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:55"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E2:55"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="seq_4.html#V2" target="_self">bounded_below</a>
 ;<br/>

<a NAME="E3:55"/>
for <font color="Olive">b<sub>1</sub></font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="seq_4.html#K3" target="_self">lower_bound</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="seq_4.html#E1:55"><i><font color="Green">E41</font></i></a>, <a class="txt" href="seq_4.html#E2:55"><i><font color="Green">E42</font></i></a>, <a class="ref" href="seq_4.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E4:55"/>
 <a href="seq_4.html#K3" target="_self">lower_bound</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="seq_4.html#K3" target="_self">lower_bound</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="seq_4.html#T60" target="_self">Th60</a></i>;<br/>


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