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<b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a> ;<br/><b>let </b><font color="Maroon">g</font> be    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a> ;<br/><b>let </b><font color="Maroon">h</font> be    <a href="finseq_2.html#M2">Element</a> of <a href="numbers.html#K1">REAL</a>  <a href="finseq_2.html#K3">*</a> ;<br/>









<b>assume </b><a NAME="E1:78"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">f</font>,<font color="Maroon">g</font> <a href="graphsp.html#R2" target="_self">equal_at</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> &amp; <font color="Maroon">g</font>,<font color="Maroon">h</font> <a href="graphsp.html#R2" target="_self">equal_at</a> <font color="Maroon">m</font>,<font color="Maroon">n</font> )
 ;<br/>

<a NAME="E2:78"/><b>then </b><i><font color="Green">E52</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> holds <br/><font color="Maroon">f</font> <a href="goboard1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="goboard1.html#K1">.</a> <font color="Olive">k</font> ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:78"/><i><font color="Green">E53</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">h</font> &amp; ( for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">g</font> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">k</font> &amp; <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> holds <br/><font color="Maroon">g</font> <a href="goboard1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="goboard1.html#K1">.</a> <font color="Olive">k</font> ) )
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:78_1"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> &amp; <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> )
 ;<br/><b>hence </b><font color="Maroon">f</font> <a href="goboard1.html#K1">.</a> <font color="Maroon">k</font> = 
<font color="Maroon">g</font> <a href="goboard1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">h</font> <a href="goboard1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, , , </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:78"/>
<font color="Maroon">f</font>,<font color="Maroon">h</font> <a href="graphsp.html#R2" target="_self">equal_at</a> <font color="Maroon">m</font>,<font color="Maroon">n</font>
 <b>by </b><i>, , </i>;<br/>


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