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<b>reconsider </b><font color="Maroon" title="c1">T1</font> = <font color="Maroon">F<sub>1</sub></font>() as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c2">S1</font> = <font color="Maroon">F<sub>2</sub></font>() as   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">T1</font> ;<br/>
<a NAME="E3:55_1"/><i><font color="Green" title="E43">A2</font></i>: 
 ex <font color="Olive" title="b1">n</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 <br/>for <font color="Olive" title="b2">m</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> <br/> for <font color="Olive" title="b3">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T1</font>  st <font color="Olive" title="b1">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b3">x</font>]
 
<b>by </b><i><a class="txt" href="frechet2.html#E1:55"><i><font color="Green" title="E42">A1</font></i></a></i>;<br/>
<a NAME="E4:55_1"/>
 ex <font color="Olive" title="b1">n</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 <br/>for <font color="Olive" title="b2">m</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">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<span class="p1">(<span class="default"><font color="Maroon" title="c2">S1</font> <a href="frechet2.html#K1" title="FRECHET2:func.1">*</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">m</font>]
 
<b>from </b><i><a class="ref" href="frechet2.html#S3" target="_self" title="FRECHET2:sch.3">FRECHET2:sch 3</a>(<a class="txt" href="frechet2.html#E3:55_1"><i><font color="Green" title="E43">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E5:55_1"/>
 ex <font color="Olive" title="b1">n</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 <br/>for <font color="Olive" title="b2">m</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">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">m</font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="frechet2.html#K1" title="FRECHET2:func.1">*</a> <font color="Maroon">F<sub>3</sub></font>()</span>)</span> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b2">m</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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