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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">x</font>
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">y</font>
 ;<br/>

<a NAME="E3:22"/><i><font color="Green" title="E17">A3</font></i>: 
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c1">x</font> &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c2">y</font> )
 
<b>by </b><i><a class="txt" href="square_1.html#E1:22"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="square_1.html#E2:22"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="square_1.html#D4" target="_self" title="SQUARE_1:def.4">Def4</a></i>;<br/>
<a NAME="E4:22"/>
( <span class="p1">(<span class="default"><a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> &amp; <span class="p1">(<span class="default"><a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">y</font> )
 
<b>by </b><i><a class="txt" href="square_1.html#E1:22"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="square_1.html#E2:22"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="square_1.html#D4" target="_self" title="SQUARE_1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
 <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c1">x</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="square_1.html#K6" title="SQUARE_1:func.6">sqrt</a> <font color="Maroon" title="c2">y</font>
 <b>by </b><i><a class="txt" href="square_1.html#E2:22"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="square_1.html#E3:22"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="square_1.html#T77" target="_self" title="SQUARE_1:th.77">Th77</a></i>;<br/>


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