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<b>let </b><font color="Maroon">d</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>







<a NAME="E1:119"/><i><font color="Green">E37</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">a</font> <a href="square_1.html#K5">^2</a>  &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">b</font> <a href="square_1.html#K5">^2</a>  &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> <a href="square_1.html#K5">^2</a>  &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">d</font> <a href="square_1.html#K5">^2</a>  )
 
<b>by </b><i><a class="ref" href="square_1.html#T72">SQUARE_1:72</a></i>;<br/>
<a NAME="E2:119"/>
<font color="Maroon">d</font> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T33">XREAL_1:33</a></i>;<br/>
<a NAME="E3:119"/><b>then </b>
0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="square_1.html#K5">^2</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E4:119"/><b>then </b>
0 <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<b>hence </b><a NAME="E5:119"/>
<font color="Maroon">d</font> <a href="square_1.html#K5">^2</a>  <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="square_1.html#K5">^2</a> </span>)</span>
 ;<br/>


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