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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">x1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="euclid.html#K1">REAL</a> <font color="Maroon">n</font>;<br/>





<a NAME="E1:14"/><i><font color="Green">E41</font></i>: 
( 1 <a href="real_1.html#K5">-</a> 0 <a href="hidden.html#R1">=</a> 1 &amp; 1 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; 0 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> &amp; <font color="Maroon">x1</font> <a href="euclid.html#K7">+</a> <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E2:14"/>
( 1 <a href="real_1.html#K5">-</a> 1 <a href="hidden.html#R1">=</a> 0 &amp; 0 <a href="euclid.html#K9">*</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="euclid.html#K5">0*</a> <font color="Maroon">n</font> &amp; 1 <a href="euclid.html#K9">*</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <span class="p1">(<span class="default"><a href="euclid.html#K5">0*</a> <font color="Maroon">n</font></span>)</span> <a href="euclid.html#K7">+</a> <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:14"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="euclid_4.html#K2" target="_self">Line</a> <font color="Maroon">x1</font>,<font color="Maroon">x2</font> )
 <b>by </b><i/>;<br/>


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