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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></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="E1:32"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:32"/><b>then </b>
(  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>2</sub></font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>1</sub></font> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="square_1.html#D4" target="_self">Def4</a>, <a class="ref" href="square_1.html#T96" target="_self">Th96</a></i>;<br/>
<a NAME="E3:32"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K6" target="_self">sqrt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="square_1.html#K3" target="_self">^2</a> 
 
<b>by </b><i><a class="txt" href="square_1.html#E90"><i><font color="Green">Lemma21</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
<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">c<sub>1</sub></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">c<sub>2</sub></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
 ;<br/>


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