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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="euclid.html#K1" title="EUCLID:func.1">REAL</a> <font color="Maroon" title="c1">n</font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">x2</font> <a href="euclidlp.html#R3" title="EUCLIDLP:pred.3">are_lindependent2</a> 
 ;<br/>

<b>assume </b><a NAME="E2:43"/><i><font color="Green" title="E41">A2</font></i>: 
<font color="Maroon" title="c2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x2</font>
 ;<br/>

<span class="p1">(<span class="default">1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c2">x1</font></span>)</span> <a href="euclid.html#K7" title="EUCLID:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <font color="Maroon" title="c3">x2</font></span>)</span> = 
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x1</font> <a href="euclid.html#K8" title="EUCLID:func.8">-</a> <font color="Maroon" title="c3">x2</font></span>)</span>
<b>by </b><i><a class="ref" href="euclidlp.html#T17" target="_self" title="EUCLIDLP:th.17">Th17</a></i>
<br/>.= 
1 <a href="euclid.html#K9" title="EUCLID:func.9">*</a> <span class="p1">(<span class="default"><a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font></span>)</span>
<b>by </b><i><a class="txt" href="euclidlp.html#E2:43"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="euclidlp.html#T7" target="_self" title="EUCLIDLP:th.7">Th7</a></i>
<br/>.= 
 <a href="euclid.html#K5" title="EUCLID:func.5">0*</a> <font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="euclid_4.html#T2" title="EUCLID_4:th.2">EUCLID_4:2</a></i>
;<br/>
<b>hence </b><a NAME="E4:43"/>
contradiction
 <b>by </b><i><a class="txt" href="euclidlp.html#E1:43"><i><font color="Green" title="E40">A1</font></i></a>, <a class="ref" href="euclidlp.html#D2" target="_self" title="EUCLIDLP:def.2">Def2</a></i>;<br/>


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