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



<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green">E20</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E3:22"/><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">y</font>
 
<b>by </b><i><a class="txt" href="square_1.html#E7"><i><font color="Green">Lemma26</font></i></a>, <a class="txt" href="square_1.html#E31"><i><font color="Green">Lemma27</font></i></a></i>;<br/>
<a NAME="E4:22"/><b>then </b><i><font color="Green">E35</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">x</font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="txt" href="square_1.html#E7"><i><font color="Green">Lemma26</font></i></a>, <a class="txt" href="square_1.html#E3"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<a NAME="E5:22"/>
( <span class="p1">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">x</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">y</font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="txt" href="square_1.html#E7"><i><font color="Green">Lemma26</font></i></a>, <a class="txt" href="square_1.html#E32"><i><font color="Green">Lemma28</font></i></a>, <a class="txt" href="square_1.html#E3"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
 <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="square_1.html#E31"><i><font color="Green">Lemma27</font></i></a>, , </i>;<br/>


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