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<b>let </b><font color="Maroon" title="c2">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:61_1_2_1"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#NK6" title="SEQ_4:NK.6">min</a> <font color="Maroon" title="c1">A</font>
 ;<br/><b>hence </b><a NAME="E2:61_1_2_1"/>
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="seq_4.html#E72"><i><font color="Green" title="E39">Lm2</font></i></a></i>;<br/><b>thus </b><a NAME="E3:61_1_2_1"/>
for <font color="Olive" title="b1">k</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 <b>by </b><i><a class="txt" href="seq_4.html#E1:61_1_2_1"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="seq_4.html#D5" target="_self" title="SEQ_4:def.5">Def5</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:61_1_2"/><i><font color="Green" title="E40">A2</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font>
 ;<br/>

<b>assume </b><a NAME="E3:61_1_2"/>
for <font color="Olive" title="b1">k</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 ;<br/>

<a NAME="E4:61_1_2"/><b>then </b>
for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">A</font> holds <br/><font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font>
 
;<br/>
<b>hence </b><a NAME="E5:61_1_2"/>
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="seq_4.html#K3" title="SEQ_4:func.3">lower_bound</a> <font color="Maroon" title="c1">A</font>
 <b>by </b><i><a class="txt" href="seq_4.html#E2:61_1_2"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="seq_4.html#E71"><i><font color="Green" title="E38">Lm1</font></i></a></i>;<br/>


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