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<b>reconsider </b><font color="Maroon">T'</font> = <font color="Maroon">F<sub>1</sub></font>() as  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a>  ;<br/>
<b>reconsider </b><font color="Maroon">S'</font> = <font color="Maroon">F<sub>2</sub></font>() as   <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">T'</font> ;<br/>
<a NAME="E3:17_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   ex <font color="Olive">m</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ex <font color="Olive">x</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T'</font> st <br/>( <font color="Olive">n</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">m</font> &amp; <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S'</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">m</font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">x</font>] )
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">S1</font> being    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">S'</font><b> such that </b><br/><a NAME="E5:17_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">S1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font>]
 <b>from </b><i><a class="ref" href="frechet2.html#S1" target="_self">FRECHET2:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">S1</font> = <font color="Maroon">S1</font> as    <a href="bhsp_3.html#M1">subsequence</a> of <font color="Maroon">F<sub>2</sub></font>() ;<br/>
<b>take </b>
<font color="Maroon">S1</font>
;<br/>

<b>thus </b><a NAME="E7:17_1"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">S1</font> <a href="normsp_1.html#K2">.</a> <font color="Olive">n</font>]
 <b>by </b><i/>;<br/>


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