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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:45"/><i><font color="Green">E33</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 4
 <b>and </b><br/><a NAME="E2:45"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">m</font> <a href="wsierp_1.html#K3">.</a> 1 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <font color="Maroon">m</font> <a href="wsierp_1.html#K3">.</a> 2 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <font color="Maroon">m</font> <a href="wsierp_1.html#K3">.</a> 3 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <font color="Maroon">m</font> <a href="wsierp_1.html#K3">.</a> 4 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> )
 ;<br/>

<a NAME="E3:45"/>
1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E5:45"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E4:45"/><b>then </b>
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E5:45"/><b>then </b><i><font color="Green">E36</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E6:45"/>
2 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E5:45"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:45"/><b>then </b>
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E8:45"/><b>then </b><i><font color="Green">E39</font></i>: 
2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E9:45"/>
3 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="txt" href="idea_1.html#E5:45"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E10:45"/><b>then </b>
3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E11:45"/><b>then </b><i><font color="Green">E40</font></i>: 
3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E12:45"/>
4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">m</font></span>)</span>
 
<b>by </b><i><a class="txt" href="idea_1.html#E5:45"><i><font color="Green">E36</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E13:45"/><b>then </b>
4 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E14:45"/>
( <span class="p1">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">m</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 1 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">m</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 2 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">m</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 3 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> &amp; <span class="p1">(<span class="default"><a href="idea_1.html#K13" target="_self">IDEAoperationC</a> <font color="Maroon">m</font></span>)</span> <a href="wsierp_1.html#K3">.</a> 4 <a href="idea_1.html#R1" target="_self">is_expressible_by</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="txt" href="idea_1.html#E2"><i><font color="Green">Lemma37</font></i></a>, , <a class="txt" href="idea_1.html#E8:45"><i><font color="Green">E39</font></i></a>, <a class="txt" href="idea_1.html#E11:45"><i><font color="Green">E40</font></i></a>, <a class="txt" href="idea_1.html#E1:45"><i><font color="Green">E33</font></i></a>, , <a class="txt" href="idea_1.html#E2:45"><i><font color="Green">E35</font></i></a></i>;<br/>


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