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<b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E1:36"/><i><font color="Green">E20</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">b</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E21</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">a</font>
 
;<br/>
<a NAME="E3:36"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, </i>;<br/>
<b>hence </b>1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> </span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> </span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="square_1.html#E3"><i><font color="Green">Lemma22</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i>, <a class="txt" href="square_1.html#E3"><i><font color="Green">Lemma22</font></i></a></i>
;<br/><br/>


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