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

<a NAME="E1:7"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">r</font>,0 &amp; <font color="Maroon">s</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">r</font>,0 &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0 )
 
<b>by </b><i><a class="ref" href="square_1.html#T46">SQUARE_1:46</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:7_1_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font> or <font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_1"><b>case </b></a><a NAME="E1:7_1_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font>
 ;<br/><div class="add"><a NAME="E2:7_1_1_1"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/><a NAME="E3:7_1_1_1"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">r</font>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0</span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E4:7_1_1_1"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">r</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0</span>)</span>
 ;<br/><b>hence </b><a NAME="E5:7_1_1_1"/>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">s</font></span>)</span>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="7_1_1_2"><b>case </b></a><a NAME="E1:7_1_1_2"/>
<font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:7_1_1_2"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="nat_1.html#K1">+</a> 0
 <b>by </b><i><a class="ref" href="xxreal_0.html#D9">XXREAL_0:def 9</a></i>;<br/><a NAME="E3:7_1_1_2"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">r</font>,0</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0</span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/><a NAME="E4:7_1_1_2"/><b>then </b>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">r</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K4">max</a> <font color="Maroon">s</font>,0</span>)</span>
 ;<br/><b>hence </b><a NAME="E5:7_1_1_2"/>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">s</font></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:7"/>
 <a href="rfunct_3.html#K2" target="_self">max+</a> <span class="p1">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">s</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">r</font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K2" target="_self">max+</a> <font color="Maroon">s</font></span>)</span>
 ;<br/>


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